IBPS PO Prelims Memory Based Paper (Held On: 23 September 2023 Shift 2) (Previous Year Paper)

The correct answer is option 2.

Key Points

• To answer this question, refer to the following lines from the third paragraph of the passage discussing the evolution of major occupations in Kolkata's slums:
• "The major occupations in slums in Kolkata have remained the same over the decade, with a fourth of the working population taking on unskilled labour. It is the most stable and significant occupation in slums."
• This part of the passage clearly indicates that unskilled labour remains the most stable and predominant occupation in Kolkata's slums over the past decade. Despite mentioning other occupations such as skilled or semi-skilled labour, employment in private organizations, and owning petty businesses or small shops, the passage emphasizes that unskilled labour continues to be the most stable and significant occupation in slums.
• Therefore, the correct answer is "Unskilled labour remains the most stable and predominant occupation in slums."

The correct answer is option 5.

Key Points

• To answer this question, refer to the following lines from the second paragraph of the passage discussing migration patterns in India based on the IER 2024:
• "As in the IER 2024, although overall migration has increased, the migration of males has declined by 1.2% during 2000-08 and further marginally in 2021. This implies that migration for economic mobility is losing its sheen."
• This part of the passage indicates that male migration for economic reasons is decreasing, leading to increased migration to urban slums. It suggests that although overall migration has increased, there's a decline in male migration for economic mobility.
• Therefore, the correct answer is "Male migration for economic reasons is decreasing, leading to increased migration to urban slums."

The correct answer is option 4.

Key Points

• To answer this question, let's break down the sentences given in the question:
• Sentence A: Over the decade, the proportion of individuals engaged in skilled and semi-skilled labour decreased by 6%.
• This sentence can be inferred from the passage. The passage mentions that the share of employment in skilled and semi-skilled labour decreased by 6% between 2012-19 in slums, reflecting a similar trend found in the IER 2024 for the overall Indian workforce.
• Sentence B: Higher unemployment rates in urban areas are juxtaposed with significantly higher average monthly earnings.
• This sentence can also be inferred from the passage. The passage discusses how there is a higher unemployment rate in urban areas compared to rural areas, yet the average monthly earnings are significantly higher for various categories of workers in urban areas, as highlighted in the IER 2024.
• Sentence C: Migration for economic mobility among males declined by 1.2% during 2000-08 and marginally in 2021.
• This sentence can be inferred from the passage as well. The passage mentions the decline in male migration for economic mobility during the stated periods, aligning with the findings of the IER 2024.
• So, out of the three sentences given in the question, all sentences A, B, and C can be inferred from the passage.
• Therefore, the correct answer is "All A, B, and C."

The correct answer is option 2.

Key Points

• To answer this question, refer to the following lines from the first paragraph of the passage discussing the trend of unemployment rates between rural and urban areas:
• "It also shows a divergent trend between rural and urban areas in terms of employment and income. It demonstrates a relatively higher unemployment rate in urban areas, at 4.8% in 2000 over the 1.5% in rural areas."
• This comparison clearly indicates that urban areas consistently experience higher unemployment rates compared to their rural counterparts.
• Therefore, the correct answer is "Urban areas experience higher unemployment rates compared to rural areas."

The correct answer is option 2.

Key Points

• To answer this question, let's first understand the meanings of the words given in bold:
• Coexistence - the state or fact of existing together at the same time or in the same place, often in a peaceful manner (सहजीवन)
• For Example -
• The coexistence of various ethnic groups in the neighbourhood contributed to its cultural richness.
• Underrated - not given enough credit or recognition for one's value or importance; underestimated (कम महत्व दिया गया)
• For Example -
• Although she was an underrated actress at the beginning of her career, her talent soon became widely acknowledged in the industry.
• Petty - of little importance; trivial (तुच्छ)
• For Example -
• Arguing over petty issues only serves to distract from the real problems at hand.
• Momentum - the impetus gained by a moving object; the force or speed of movement; figuratively, the strength or force that allows something to continue or to grow stronger or faster as time passes (गति)
• For Example -
• The team's successful product launch gained momentum as positive reviews spread, leading to increased sales.
• Now, let's evaluate the sentences with the highlighted words from the passage:
• The coexistence of higher unemployment and wages requires further investigation to understand its implications for the urban poor.
• The highlighted word "coexistence" is used correctly in this sentence. It refers to the simultaneous existence of higher unemployment and wages, requiring further investigation.
• The higher income in urban areas and a better life have underrated rural-urban migration in the past.
• The highlighted word "underrated" implies undervaluation, which doesn't align with the context of this sentence. Instead, something like "prompted" would better fit here to convey that higher urban income and lifestyle encouraged rural-urban migration.
• Other major occupations in slums were skilled or semi-skilled labour work, and people as employees in private organisations, and owning petty businesses or small shops.
• The highlighted word "petty" is used correctly in this sentence. It describes businesses or shops of little importance, aligning with the context of small-scale enterprises.
• Among occupations that were less popular earlier but which gained momentum in the last 10 years are truck driving and cleaning, by 5%, and construction and related work, by 4%.
• The highlighted word "momentum" is used correctly in this sentence. It indicates the increase in popularity or activity of certain occupations over time, fitting well within the context of growth in specific job sectors.
• Therefore, the correct answer is "underrated."

The correct answer is option 1.

Key Points

• To answer this question, let's first understand the underlined sentence from the passage:
• "An analysis of income and employment trends among slum dwellers in urban India reveals prospects for economic mobility and decent work, as poor rural households often migrate to slums rather than formal settlements."
• This sentence suggests that there are prospects for economic mobility and decent work for slum dwellers in urban India, particularly for poor rural households who often choose to migrate to slums rather than formal settlements.
• Now, let's break down the options:
• Option 1: Migration to urban slums in India offers potential economic advancement and job opportunities for poor rural households.
• This inference aligns with the underlined sentence because it highlights the potential for economic mobility and decent work for slum dwellers, indicating that migrating to urban slums can provide opportunities for improving their economic conditions. The passage implies that despite the challenges of urban poverty and informal employment, slums offer a better alternative for economic advancement compared to rural areas.
• Option 2: Stagnation in urban slums' economy persists, with a significant portion engaged in unskilled labour for over a decade.
• While the underlined sentence acknowledges migration to slums, it doesn't imply stagnation; rather, it suggests prospects for economic mobility and decent work. Thus, this inference cannot be drawn from the underlined sentence.
• Option 3: Choosing formal settlements over urban slums limits economic mobility and work prospects for poor rural households in India.
• This sentence implies that choosing urban slums over formal settlements may offer better economic prospects, indicating that opting for formal settlements might limit economic mobility and work opportunities. Thus, this inference cannot be drawn from the underlined sentence.
• Option 4: Investigating simultaneous high unemployment and wages is crucial for understanding urban poverty dynamics.
• Although the underlined sentence mentions income and employment trends among slum dwellers, it doesn't specifically address simultaneous high unemployment and wages, so it doesn't provide a basis for understanding these dynamics. Thus, this inference cannot be drawn from the underlined sentence.
• Option 5: Income and employment conditions in urban slums tend to perpetuate rather than alleviate systemic poverty and inequality.
• While the sentence acknowledges income and employment conditions in urban slums, it doesn't provide enough information to conclude whether these conditions perpetuate or alleviate systemic poverty and inequality. Thus, this inference cannot be drawn from the underlined sentence.
• Therefore, the correct answer is "Migration to urban slums in India offers potential economic advancement and job opportunities for poor rural households."

The correct answer is option 3.

Key Points

• To answer this question, let's examine each sentence given in the question:
• Sentence A: Skilled and semi-skilled labour saw a 6% increase, unlike unskilled labour.
• This sentence is false. The passage states that the share of employment in skilled and semi-skilled labour decreased by 6% between 2012-19, unlike unskilled labour.
• Sentence B: Employment in skilled and semi-skilled labour decreased over the decade.
• This sentence is true. According to the passage, the share of employment in skilled and semi-skilled labour decreased by 6% between 2012-19.
• Sentence C: The urban unemployment rate decreased consistently from 2015-16 to 2022-23.
• This sentence is false. The passage mentions a relatively higher unemployment rate in urban areas, at 4.8% in 2000 over the 1.5% in rural areas, indicating fluctuations rather than a consistent decrease.
• Sentence D: The number of surveyed slum households decreased from 513 to 396.
• This sentence is true. The passage states that the number of surveyed slum households decreased from 513 in 2012 to 396 in 2021-22.
• Sentence E: Urban areas exhibit higher unemployment rates compared to rural areas.
• This sentence is true. The passage mentions a higher unemployment rate in urban areas (4.8% in 2000) compared to rural areas (1.5% in 2000).
• So, out of the given sentences, sentences B, D, and E are true, while sentences A and C are false.
• Therefore, the correct answer is "All B, D, and E are true."

The correct answer is option 4.

Key Points

• To answer this question, let's break down the sentences given in the question:
• Sentence A: The higher wages in urban areas have resulted in a decrease in migration for economic mobility.
• This sentence cannot be inferred from the passage. While the passage discusses higher average monthly earnings in urban areas, it does not explicitly mention any decrease in migration due to lower wages.
• Sentence B: The survey revealed that all 396 households in 2021-22 had improved economically since 2012.
• This sentence cannot be inferred from the passage. While the passage discusses surveys conducted among slum households in Kolkata in 2012 and 2021-22, it does not provide explicit information about the economic improvement of all households surveyed in 2021-22.
• Sentence C: Truck driving and cleaning have decreased in popularity as occupations in slums in the last decade.
• This sentence cannot be inferred from the passage. The passage mentions an increase in the popularity of occupations such as truck driving and cleaning in slums over the last decade, indicating the opposite trend.
• So, out of the three sentences given in the question, none can be inferred from the passage.
• Therefore, the correct answer is "All A, B, and C."

The correct answer is option 3.

Key Points

To answer this question, first, read the third paragraph of the passage carefully and understand the key points mentioned:

The passage's third paragraph discusses the predominant occupations in Kolkata's slums, emphasizing unskilled labour's stability. It also highlights shifts in employment trends over a decade, with a rise in petty businesses and emerging occupations like truck driving and construction work.

• Now, let's analyze the options:
• Option 1: The divergence in employment and income trends between rural and urban areas is highlighted in the report, emphasizing the dynamics of slum economies.
• This option discusses the divergence in employment and income trends between rural and urban areas, which is not directly related to the content of the third paragraph of the passage. Thus, this cannot be the correct answer.
• Option 2: The data collected from Kolkata's slums shows a shift towards formal employment and away from self-employment, contradicting the findings of the IER 2024.
• This option suggests a shift towards formal employment in Kolkata's slums, contradicting the findings of the IER 2024. However, the third paragraph doesn't mention such a shift. Thus, this also cannot be the correct answer.
• Option 3: While unskilled labour remains dominant in Kolkata's slums, skilled labour and formal employment have decreased, replaced by petty businesses.
• This option accurately summarizes the content of the third paragraph. It highlights that while unskilled labour remains dominant in Kolkata's slums, there has been a decrease in skilled labour and formal employment, with an increase in petty businesses. Thus, this is the correct answer.
• Option 4: The survey conducted in 2022-23 covered all 37 slums in Kolkata that were surveyed in 2012, although some slums had either been redeveloped or evicted.
• This option talks about the survey coverage in Kolkata's slums, which is not relevant to the content of the third paragraph. Thus, this cannot be the correct answer.
• Option 5: The income and employment trends in slums were found to be unaffected by the COVID-19 pandemic during the pre-COVID-19 year of 2019.
• The option discusses the unaffected nature of income and employment trends in slums by the COVID-19 pandemic, which is not mentioned in the third paragraph. Thus, this cannot be the correct answer.
• Therefore, the correct answer is "While unskilled labour remains dominant in Kolkata's slums, skilled labour and formal employment have decreased, replaced by petty businesses."

The correct answer is 'Neither Sameera nor Vinod knows anything about the accident' i.e. this sentence is grammatically and contextually correct.

Key Points

• Let us explore the grammatical errors in the sentences:
• In Option 1, the use of the plural form of the verb 'were' is incorrect.
• We know that if two subjects are joined by expressions like ''either…or, or neither … nor, or, nor, not only...but also'', the verb agrees with the subject nearest to it.
• For Example - Neither John nor his friends are coming today. (Here, the verb agrees with the second subject i.e. his friends)
• Therefore, the singular form of the verb 'was' (since 'principal' is singular) should be used in place of the plural form of the verb 'were'.
• Correct Sentence: Neither the contestants nor the principal was aware of the fire.
• In Option 2, the use of the plural form of the adverb 'instead' is incorrect.
• In the sentence, 'instead' must be replaced with the prepositional phrase ''instead of'' which means ''in place of.''
• Correct Sentence: Instead of criticizing why don't you help with the presentation?
• In Option 3, the use of the adjective 'urgent' is incorrect.
• In the sentence, 'urgent' is an adjective and fails to modify the verb 'send'.
• We know that if a verb is to be modified, we should use an adverb.
• Therefore, the adverb 'urgently' should be used in place of the adjective 'urgent'.
• Correct Sentence: It is requested that a detailed report be sent urgently on the representations and ongoing strike by the employees.
• In Option 4, the verb agrees correctly with the subject nearest to it i.e. Vinod. It is a singular subject. Therefore, 'knows' will be used.
  

Hence, the correct answer is option 4.

The correct answer is 'The girl, with several others, was late for school.' i.e. this sentence is grammatically and contextually correct.

Key Points

• Let us explore the grammatical errors in the sentences:
• In Option 1, the use of the definite article 'the' is erroneous.
• 'Approval' is an uncountable noun and uncountable nouns take 'the' when used in a particular sense.
• In the given sentence, 'approval' is not specified, nor is it qualified by any adjective.
• Therefore, we will omit the article 'the' before 'approval'.
• Correct Sentence: The developers submitted building plans to the council for approval.
• In Option 3, the use of the adverb 'lately' is incorrect.
• 'Lately' is an adverb that denotes 'recently'.
• 'Late' denotes 'after the fixed, right, or usual time.'
• Therefore, the adverb 'late' should be used in place of the adverb 'lately'.
• Correct Sentence: She was heavily fined last month for coming late.
• In Option 4, the use of the plural form of the verb 'have' is incorrect.
• We know that expressions such as each of, one of, anybody, each, every, and nobody must be followed by a singular verb.
• Therefore, the singular form of the verb 'has' should be used in place of the plural form of the verb 'have'.
• Correct Sentence: Each of the ladies has a designer handbag.
  

Hence, the correct answer is option 2.

The correct answer is 'No sooner had he arrived in Delhi than he was kidnapped' i.e. this sentence is grammatically and contextually correct.

Key Points

• Let us explore the grammatical errors in the sentences:
• In Option 1, the use of the determiner 'fewer' is incorrect.
• The determiner 'fewer' is used to refer to numbers among things that are counted.
• The determiner 'less' is used to refer to quantity or amount among things that are measured.
• Therefore, the determiner 'less' should be used in place of the determiner 'fewer'.
• Correct Sentence: I see you have eaten less than ten percent of your mashed potatoes.
• In Option 2, the use of the preposition 'with' is incorrect.
• The verb 'assign' is followed by the preposition 'to'.
• If someone is assigned to a particular place, case, group, or person, they are sent there, usually in order to work at that place or for that case.
• Therefore, the preposition 'to' should be used in place of the preposition 'with'.
• Correct Sentence: A different policeman has been assigned to the case.
• In Option 4, the use of the plural form of the verb 'are' is incorrect.
• We know that amounts, even if plural, have a singular verb.
• Therefore, the singular form of the verb 'is' should be used in place of the plural form of the verb 'are'.
• Correct Sentence: Five kilograms of flour is all that I need for my baking.
  

Hence, the correct answer is option 3.

The correct answer is 'Several members of the party have resurrected the idea of constitutional change' i.e. this sentence is grammatically and contextually correct.

Key Points

• Let us explore the grammatical errors in the sentences:
• In Option 2, the use of the singular form of the verb 'lives' is incorrect.
• We know that the words (People, Children, Men, Women, Mice, Feet, etc.) are irregular plural nouns (nouns that are not formed by adding -s) and they take the plural form of the verb.
• Therefore, the plural form of the verb 'live' should be used in place of the singular form of the verb 'lives'.
• Correct Sentence: I clearly empathize with the people who live in those neighborhoods.
• In Option 3, the use of the singular form of the verb 'was' is incorrect.
• We know that the words (Both Of, A Few Of, Many, Several) always take the plural form of the verb.
• Therefore, the plural form of the verb 'were' should be used in place of the singular form of the verb 'was'.
• Correct Sentence: When the ship finally reached land, only a few of the crew were left to witness the event.
• In Option 4, the use of the plural form of the verb 'have' is incorrect.
• We know that 'Everyone' is a collective noun and it refers to multiple people but they are grouped into a single entity.
• The word (Everybody, Anybody, Somebody, Nobody, Everyone, Anyone, Someone, No One) subjects are all singular.
• Therefore, the singular form of the verb 'has' should be used in place of the plural form of the verb 'have'.
• Correct Sentence: Everyone has their own ideas about the best way to bring up children.
  

Hence, the correct answer is option 1.

The correct answer is 'BDCAE'.

Key Points

• Part B will be the first sentence of the sequence because it introduces the topic of an outbreak that was mistaken for Japanese encephalitis.
• Part D will come after B as it gives information about physicians in the area who noted something.
• Part C will come after D as it gives information that physicians noted the persons who had been vaccinated against Japanese encephalitis.
• Part A will come after C as it further gives information that the persons who had been vaccinated against Japanese encephalitis were not protected in the epidemic.
• Part 'E' is the concluding or last part as it concludes that the number of cases among adults was unusual.
  

Hence, the correct answer is option 5.

Correct Sentence: The outbreak was originally mistaken for Japanese encephalitis, but physicians in the area noted that persons who had been vaccinated against Japanese encephalitis were not protected in the epidemic, and the number of cases among adults was unusual.

Important Points

• Important Rules to Solve the Sentence Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentences.
• Try to identify the opening and closing sentences.
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is 'CEABD'.

Key Points

• Part C will be the first sentence of the sequence because it introduces the topic of SAF which is made from renewable biomass and waste resources.
• Part E will come after C as it gives information about the potential of SAF that it can deliver the performance.
• Part A will come after E as it further gives information about the performance i.e. of petroleum-based jet fuel.
• Part B will come after A as it explains that the SAF delivers performance however with a fraction of its carbon footprint, giving airlines solid footing.
• Part 'D' is the concluding or last part as it concludes why carbon footprint, giving airlines solid footing i.e. for decoupling greenhouse gas (GHG) emissions from flight.
  

Hence, the correct answer is option 2.

Correct Sentence: SAF made from renewable biomass and waste resources has the potential to deliver the performance of petroleum-based jet fuel but with a fraction of its carbon footprint, giving airlines solid footing for decoupling greenhouse gas (GHG) emissions from flight.

Important Points

• Important Rules to Solve the Sentence Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentences.
• Try to identify the opening and closing sentences.
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is 'DBCEA'.

Key Points

• Part D will be the first sentence of the sequence because it introduces the topic of banana ketchup.
• Part B will come after D as it gives information about the first commercial mass production of banana ketchup.
• Part C will come after B as it gives information about who first mass-produced banana ketchup commercially i.e. Magdalo V. Francisco Sr.
• Part E will come after C as it further gives information about Magdalo V. Francisco Sr., he is the founder of the brand name Mafran.
• Part 'A' is the concluding or last part as it concludes that Magdalo V. Francisco Sr. registered the brand name Mafran with the Bureau of Patents.
  

Hence, the correct answer is option 4.

Correct Sentence: In 1942, banana ketchup was first mass-produced commercially by Magdalo V. Francisco Sr. who founded the brand name Mafran which he registered with the Bureau of Patents.

Important Points

• Important Rules to Solve the Sentence Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentences.
• Try to identify the opening and closing sentences.
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is 'assistive, support.'

Key Points

• The given sentence is talking about hiring some personnel for Rekha.
• ​Let us explore the words in the given options:
• 'Assistive' means denoting a person who is employed to provide basic help.
• 'Support' means to help somebody by saying that you agree with them.

Conclusion: Rekha's family hired a person to provide basic help to Rekha in her daily tasks.

Hence, the correct answer is option 1.

Complete Sentence: Rekha's family hired assistive personnel to support her in daily tasks like bathing and preparing meals.

Additional Information

• The meaning of other options:
• 'Sabotage' means to deliberately destroy, damage, or obstruct something.
• 'Antagonistic' means showing or feeling active opposition or hostility towards someone or something.
• 'Undercut' means to undermine or destroy the force, value, or effectiveness of something.
• 'Hostile' means having very strong feelings against somebody or something.
• 'Weaken' means to become less strong; to make somebody/something less strong.
• 'Fierce' means very strong; violent.
• 'Controvert' means to deny the truth of something.
• 'Scrape' means to manage to get or win something with difficulty.

The correct answer is 'aid, recovery.'

Key Points

• The given sentence is talking about the Red Cross workers and how they work.
• ​Let us explore the words in the given options:
• 'Aid' means to help somebody or something.
• 'Recovery' means getting back something that was lost, stolen, or missing.

Conclusion: During natural disasters, the Red Cross workers help the victims in getting back from injuries.

Hence, the correct answer is option 3.

Complete Sentence: Red Cross workers usually aid in the recovery of victims of natural disasters by providing medical care to those who are injured.

Additional Information

• The meaning of other options:
• 'Relapse' means to become worse again after an improvement.
• 'Obstacle' means something that makes it difficult for you to do something or go somewhere.
• 'Regression' means a return to a former or less developed state.
• 'Constraint' means a limitation or restriction.
• 'Loss' means the fact or process of losing something or someone.
• 'Hindrance' means a thing that provides resistance, delay, or obstruction to something or someone.
• 'Misplace' means to put an object in the wrong place and so lose it temporarily.
• 'Drawback' means a disadvantage or problem.

The correct answer is 'approve, cover.'

Key Points

• The given sentence is talking about taking a day off and the shift of work.
• ​Let us explore the words in the given options:
• 'Approve' means to agree formally to something.
• 'Cover' means to do somebody’s job while he or she is away from work.

Conclusion: The supervisor does not agree to a day off due to the shortage or absence of other employees.

Hence, the correct answer is option 2.

Complete Sentence: My supervisor won’t approve my day off because there is no one to cover my shift.

Additional Information

• The meaning of other options:
• 'Bare' means basic and simple.
• 'Proscribe' means to order not to do or use or to be done or used.
• 'Expose' means to cause someone to be vulnerable or at risk.
• 'Prohibit' means to say that something is not allowed by law.
• 'Omit' means to not include something; to leave something out.
• 'Interdict' means to prohibit someone from doing something.
• 'Slur' means an unfair comment or an insult that could damage people’s opinion of somebody or something.
• 'Neglect' means to give too little or no attention or care to somebody or something.

The correct answer is 'maintain, frequently.'

Key Points

• The given sentence is talking about how to keep the lawn nice and fresh.
• ​Let us explore the words in the given options:
• 'Maintain' means to keep something in good condition by checking and repairing it regularly.
• 'Frequently' means regularly or habitually; often.

Conclusion: To keep the lawn nice and fresh, you have to water it regularly.

Hence, the correct answer is option 4.

Complete Sentence: If you want to maintain your lawn, you will need to water it frequently so it stays nice and fresh.

Additional Information

• The meaning of other options:
• 'Rare' means not occurring very often.
• 'Ignore' means to refuse to take notice of or acknowledge; disregard intentionally.
• 'Seldom' means not often; rarely.
• 'Withdraw' means to remove or take away something from a particular place or position.
• 'Perpetually' means in a way that never ends or changes; constantly.
• 'Retract' means to say that something you have said is not true.
• 'Constant' means happening or existing all the time or again and again.
• 'Negotiate' means to decide or agree on something by talking about it.

The correct answer is 'D.'

Key Points

• The correct sequence of the segments after rearrangement is DACEB.
• The sentence 'D' is independent of any other sentence as it is giving general information about "Elon Musk". Hence, 'D' is the first part.
• Sentence A will come after D as it further gives information about the education of Elon Musk.
• Sentence C will come after A as it is giving information about Elon Musk's contribution to making PayPal.
• Sentence E will come after C as it is giving information about Elon Musk's shocking or impressive success.
• The sentence 'B' is the concluding part because it is telling, he is the richest person in the world now.
• From the above sequence, we can say that sentence 'D' is the first sentence after rearrangement.
  

Hence, the correct answer is option 4.

Paragraph after rearranging the sentences: Elon Musk is the charismatic co-founder and CEO of electric car maker Tesla and rocket manufacturer SpaceX. Educated at the University of Pennsylvania in physics, Musk started getting his feet wet as a serial tech entrepreneur. He was instrumental in creating the company that became PayPal. His astounding success has given rise to comparisons to other visionary businessmen. He is surpassed only by Jeff Bezos as the richest person in the world.

Hint

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentence and eliminate the irrelevant options.
• Try to identify the opening (independent sentence) and closing sentences (concluding sentence).
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is 'A.'

Key Points

• The correct sequence of the segments after rearrangement is DACEB.
• The sentence 'D' is independent of any other sentence as it is giving general information about "Elon Musk". Hence, 'D' is the first part.
• Sentence A will come after D as it further gives information about the education of Elon Musk.
• Sentence C will come after A as it is giving information about Elon Musk's contribution to making PayPal.
• Sentence E will come after C as it is giving information about Elon Musk's impressive success.
• The sentence 'B' is the concluding part because it is telling, he is the richest person in the world now.
• From the above sequence, we can say that sentence 'A' is the second sentence after rearrangement.
  

Hence, the correct answer is option 1.

The correct answer is 'C.'

Key Points

• The correct sequence of the segments after rearrangement is DACEB.
• The sentence 'D' is independent of any other sentence as it is giving general information about "Elon Musk". Hence, 'D' is the first part.
• Sentence A will come after D as it further gives information about the education of Elon Musk.
• Sentence C will come after A as it is giving information about Elon Musk's contribution to making PayPal.
• Sentence E will come after C as it is giving information about Elon Musk's impressive success.
• The sentence 'B' is the concluding part because it is telling, he is the richest person in the world now.
• From the above sequence, we can say that sentence 'C' is the third sentence after rearrangement.
  

Hence, the correct answer is option 3.

The correct answer is 'E.'

Key Points

• The correct sequence of the segments after rearrangement is DACEB.
• The sentence 'D' is independent of any other sentence as it is giving general information about "Elon Musk". Hence, 'D' is the first part.
• Sentence A will come after D as it further gives information about the education of Elon Musk.
• Sentence C will come after A as it is giving information about Elon Musk's contribution to making PayPal.
• Sentence E will come after C as it is giving information about Elon Musk's impressive success.
• The sentence 'B' is the concluding part because it is telling, he is the richest person in the world now.
• From the above sequence, we can say that sentence 'E' is the fourth sentence after rearrangement.
  

Hence, the correct answer is option 5.

The correct answer is 'B.'

Key Points

• The correct sequence of the segments after rearrangement is DACEB.
• The sentence 'D' is independent of any other sentence as it is giving general information about "Elon Musk". Hence, 'D' is the first part.
• Sentence A will come after D as it further gives information about the education of Elon Musk.
• Sentence C will come after A as it is giving information about Elon Musk's contribution to making PayPal.
• Sentence E will come after C as it is giving information about Elon Musk's impressive success.
• The sentence 'B' is the concluding part because it is telling, he is the richest person in the world now.
• From the above sequence, we can say that sentence 'B' is the fifth sentence after rearrangement.
  

Hence, the correct answer is option 2.

The correct answer is 'Are rare among them'.

Key Points

• In the underlined segment, the use of the singular verb 'is' and the preposition 'between' is incorrect.
• The plural subject ''deformity and hereditary diseases'' will take a plural verb.
• Therefore, the plural verb 'are' should be used in place of the singular verb 'is'.
• Also, we use the preposition 'between' when referring to one-to-one relationships.
• 'Between' is used when naming distinct, individual items (can be 2, 3, or more).
• We use 'among' to talk about things that are not separated because they are part of a group, crowd or mass of objects.
• The preposition 'among' is used when referring to indistinct or nonspecific relationships.
• 'Among' is used when the items are part of a group or are not specifically named (must be 3 or more).
  

Hence, the correct answer is option 4.

Correct Sentence: As a whole, the Malays are, however, remarkably healthy people, and deformity and hereditary diseases are rare among them.

The correct answer is 'No correction required.'

Key Points

• In the underlined segment of the given sentence, no correction is required.
• The phrase ''one of the'' in the given sentence is a singular term and is generally used to talk about a noun or a pronoun.
• The noun or a pronoun used after the phrase ''one of the'' is always in the plural form (as we are talking of one person/place/thing out of many).
• Also, the singular verb 'is' is correctly used after the singular subject ''The location''.
• Thus no change is required in the given sentence.
  

Hence, the correct answer is option 5.

Correct sentence: The location is one of the most important things to consider when buying a house.

Additional Information

• The phrase ''One of the'' specifies a person, place, or thing in a sentence and shows that it is different from other people, places, or things or it also falls in the category of the best.
• Example: One of the students could not attempt all the questions.
• In the example, the phrase ''One of the'' shows that only one student attempted differently from other students. This phrase specifies a student who failed to attempt all questions.

The correct answer is 'Her room within reach.'

Key Points

• In the underlined segment, the use of the preposition 'for' is incorrect.
• The preposition 'for' is used to talk about a purpose or a reason for something.
• The given sentence is talking about checking to see if each resident has a pitcher of water in their room within their reach.
• The preposition 'within' means not outside the limits of somebody or something.
• The prepositional phrase 'within reach' means inside the distance to which someone can stretch out their hand.
• Therefore, the preposition 'within' should be used in place of the preposition 'for'.
  

Hence, the correct answer is option 2.

Correct Sentence: It is also important to check to see if each resident has a pitcher of water in his or her room within reach of the bed.

The correct answer is 'B-D.'

Key Points

• The given sentence says that if someone wants to maintain his or her lawn, they have to cut the grass using a machine and water it regularly so it stays nice and fresh.
• Let us explore the meaning of the highlighted words:
• Maintain - To keep something in good condition by checking and repairing it regularly. (किसी वस्‍तु की नियमित जाँच और मरम्‍मत करते हुए उसे सही हालत में रखना, किसी वस्‍तु का रख-रखाव करना)
• Fresh - Pleasantly clean or bright. (एकदम साफ़, चमकदार या रोशनीदार)
• Frequently - Regularly or habitually; often. (बार-बार)
• Mow - To cut grass using a machine. (विशेष मशीन से घास काटना)
• Thus, (B) and (D) must be interchanged.
  

Hence, the correct answer is option 2.

Correct Sentence: If you want to maintain your lawn, you will need to mow the grass and water it frequently so it stays nice and fresh.

The correct answer is **'**A-C.'

Key Points

• The given sentence talks about a defendant who was found innocent of all charges even though he could not provide any proof or evidence of his statement that says he was in a different place at the time of the murder.
• Let us explore the meaning of the highlighted words:
• Alibi - A statement by somebody that says you were in a different place at the time of a crime and so cannot be guilty of the crime. (अपराध के समय अन्‍यत्र उपस्थित होने का कथन यह सिद्ध करने के लिए की वह दोषी नहीं है)
• Substantiate - To give evidence or provide information to prove that something is true. (पुष्टि के लिए सूचना या प्रमाण देना, सही साबित करना, पुष्टि करना)
• Defendant - A person who is accused of a crime in a court of law. (वह व्यक्ति जिसपर न्यायालय में आरोप लगाया गया हो, प्रतिवादी, अभियुक्त)
• Innocent - Not having done wrong. (जिसने ग़लत काम नहीं किया; निर्दोष, बेगुनाह, बेक़सूर)
• Thus, (A) and (C) must be interchanged.
  

Hence, the correct answer is option 4.

Correct Sentence: Even though the defendant could not substantiate his alibi for the night of the murder, he was still found innocent of all charges.

General solution:

AMU college

Number females in AMU college in section A  = 6a

Number of males in AMU college in section A = 3b

Number of females in AMU college in section B = 5a

Number of males in AMU college in section B = 4b

Total males in in AMU college = (3b + 4b) = 7b

Total females in AMU college = (6a + 5a) = 11a

7b - 11a = 50 ............. (1)

Total number of students in section B = (5a + 4b) 

Total number of students in section A = (6a + 3b)

(5a + 4b) - (6a + 3b) = 10

-a + b = 10

(b - a) = 10 ................ (2)

 Solving 1 and 2 we get 

7b - 11a = 50

7b - 7a = 70

-4a = - 20

a = 5

b = 15

Number females in AMU college in section A  = 6a = 6 ×  5 = 30

Number of males in AMU college in section A = 3b = 3 ×  15 = 45

Number of females in AMU college in section B = 5a = 5 ×  5 = 25

Number of males in AMU college in section B = 4b = 4 ×  15 = 60

MMH college

Number females in MMH college in section A  = 5c

Number of males in MMH college in section A = d

Number of females in MMH college in section B = 4c

Number of males in MMH college in section B = 3d

Total males in in MMH college = (d + 3d) = 4d

Total females in MMH college = (5c + 4c) = 9c

9c - 4d = 30 ............. (3)

Total number of students in section B = (4c + 3d) 

Total number of students in section A = (5c + d)

(4c + 3d) - (5c + d) = 20

-c + 2d = 20

(2d - c) = 20 ............. (4)

Solving 3 and 4 we get 

9c - 4d = 30

9 × [(2d - c) = 20]

9c - 4d = 30

18d - 9c = 180

14d = 210

d = 15

c = 10

Number females in MMH college in section A  = 5c = 5 ×  10 = 50

Number of males in MMH college in section A = d = 15

Number of females in MMH college in section B = 4c = 4 ×  10 = 40

Number of males in MMH college in section B = 3d = 3 ×  15 = 45

LPU college

Number females in LPU college in section A  = 2e

Number of males in LPU college in section A = 4f

Number of females in LPU college in section B = 3e

Number of males in LPU college in section B = 3f

Total males in in LPU college = (4f + 3f) = 7f

Total females in LPU college = (3e + 2e) = 5e

5e - 7f = 55 ............. (5)

Total number of students in section B = (3e + 3f) 

Total number of students in section A = (2e + 4f)

(3e + 3f) - (2e + 4f) = 15

e - f = 15 ............. (6)

Solving 5 and 6 we get 

Multiply equation (6) by 5 and subtract from equation (5) we get

-2f = - 20

f = 10

e = 25 

Number females in LPU college in section A  = 2e = 2 ×  25 = 50

Number of males in LPU college in section A = 4f = 4 ×  10 = 40

Number of females in LPU college in section B = 3e = 3 ×  25 = 75

Number of males in LPU college in section B = 3f = 3 ×  10 = 30

Solution:

Number of males in section B from college AMU = 60

Total number of males in section B from all the colleges = (60 + 45 + 30) 

Required percentage = 60/135 × 100 = 44.44%

General solution:

AMU college

Number females in AMU college in section A  = 6a

Number of males in AMU college in section A = 3b

Number of females in AMU college in section B = 5a

Number of males in AMU college in section B = 4b

Total males in in AMU college = (3b + 4b) = 7b

Total females in AMU college = (6a + 5a) = 11a

7b - 11a = 50 ............. (1)

Total number of students in section B = (5a + 4b) 

Total number of students in section A = (6a + 3b)

(5a + 4b) - (6a + 3b) = 10

-a + b = 10

(b - a) = 10 ................ (2)

 Solving 1 and 2 we get 

7b - 11a = 50

7b - 7a = 70

-4a = - 20

a = 5

b = 15

Number females in AMU college in section A  = 6a = 6 ×  5 = 30

Number of males in AMU college in section A = 3b = 3 ×  15 = 45

Number of females in AMU college in section B = 5a = 5 ×  5 = 25

Number of males in AMU college in section B = 4b = 4 ×  15 = 60

MMH college

Number females in MMH college in section A  = 5c

Number of males in MMH college in section A = d

Number of females in MMH college in section B = 4c

Number of males in MMH college in section B = 3d

Total males in in MMH college = (d + 3d) = 4d

Total females in MMH college = (5c + 4c) = 9c

9c - 4d = 30 ............. (3)

Total number of students in section B = (4c + 3d) 

Total number of students in section A = (5c + d)

(4c + 3d) - (5c + d) = 20

-c + 2d = 20

(2d - c) = 20 ............. (4)

Solving 3 and 4 we get 

9c - 4d = 30

9 × [(2d - c) = 20]

9c - 4d = 30

18d - 9c = 180

14d = 210

d = 15

c = 10

Number females in MMH college in section A  = 5c = 5 ×  10 = 50

Number of males in MMH college in section A = d = 15

Number of females in MMH college in section B = 4c = 4 ×  10 = 40

Number of males in MMH college in section B = 3d = 3 ×  15 = 45

LPU college

Number females in LPU college in section A  = 2e

Number of males in LPU college in section A = 4f

Number of females in LPU college in section B = 3e

Number of males in LPU college in section B = 3f

Total males in in LPU college = (4f + 3f) = 7f

Total females in LPU college = (3e + 2e) = 5e

5e - 7f = 55 ............. (5)

Total number of students in section B = (3e + 3f) 

Total number of students in section A = (2e + 4f)

(3e + 3f) - (2e + 4f) = 15

e - f = 15 ............. (6)

Solving 5 and 6 we get 

Multiply equation (6) by 5 and subtract from equation (5) we get

-2f = - 20

f = 10

e = 25 

Number females in LPU college in section A  = 2e = 2 ×  25 = 50

Number of males in LPU college in section A = 4f = 4 ×  10 = 40

Number of females in LPU college in section B = 3e = 3 ×  25 = 75

Number of males in LPU college in section B = 3f = 3 ×  10 = 30

Solution:

Total number of male students in colleges AMU, MMH, LPU and PQR in section A = 45 × 4 = 180 

Number of male students in college PQR in section A = 180 - (45 + 15 + 40) = 80

Total number of female students in colleges AMU, MMH, LPU and PQR in section A = 40 × 4 = 160 

Number of female students in college PQR in section A = 160 - (30 + 50 +50) = 30

Required total= (80 + 30) = 110

General solution:

AMU college

Number females in AMU college in section A  = 6a

Number of males in AMU college in section A = 3b

Number of females in AMU college in section B = 5a

Number of males in AMU college in section B = 4b

Total males in in AMU college = (3b + 4b) = 7b

Total females in AMU college = (6a + 5a) = 11a

7b - 11a = 50 ............. (1)

Total number of students in section B = (5a + 4b) 

Total number of students in section A = (6a + 3b)

(5a + 4b) - (6a + 3b) = 10

-a + b = 10

(b - a) = 10 ................ (2)

 Solving 1 and 2 we get 

7b - 11a = 50

7b - 7a = 70

-4a = - 20

a = 5

b = 15

Number females in AMU college in section A  = 6a = 6 ×  5 = 30

Number of males in AMU college in section A = 3b = 3 ×  15 = 45

Number of females in AMU college in section B = 5a = 5 ×  5 = 25

Number of males in AMU college in section B = 4b = 4 ×  15 = 60

MMH college

Number females in MMH college in section A  = 5c

Number of males in MMH college in section A = d

Number of females in MMH college in section B = 4c

Number of males in MMH college in section B = 3d

Total males in in MMH college = (d + 3d) = 4d

Total females in MMH college = (5c + 4c) = 9c

9c - 4d = 30 ............. (3)

Total number of students in section B = (4c + 3d) 

Total number of students in section A = (5c + d)

(4c + 3d) - (5c + d) = 20

-c + 2d = 20

(2d - c) = 20 ............. (4)

Solving 3 and 4 we get 

9c - 4d = 30

9 × [(2d - c) = 20]

9c - 4d = 30

18d - 9c = 180

14d = 210

d = 15

c = 10

Number females in MMH college in section A  = 5c = 5 ×  10 = 50

Number of males in MMH college in section A = d = 15

Number of females in MMH college in section B = 4c = 4 ×  10 = 40

Number of males in MMH college in section B = 3d = 3 ×  15 = 45

LPU college

Number females in LPU college in section A  = 2e

Number of males in LPU college in section A = 4f

Number of females in LPU college in section B = 3e

Number of males in LPU college in section B = 3f

Total males in in LPU college = (4f + 3f) = 7f

Total females in LPU college = (3e + 2e) = 5e

5e - 7f = 55 ............. (5)

Total number of students in section B = (3e + 3f) 

Total number of students in section A = (2e + 4f)

(3e + 3f) - (2e + 4f) = 15

e - f = 15 ............. (6)

Solving 5 and 6 we get 

Multiply equation (6) by 5 and subtract from equation (5) we get

-2f = - 20

f = 10

e = 25 

Number females in LPU college in section A  = 2e = 2 ×  25 = 50

Number of males in LPU college in section A = 4f = 4 ×  10 = 40

Number of females in LPU college in section B = 3e = 3 ×  25 = 75

Number of males in LPU college in section B = 3f = 3 ×  10 = 30

Solution:

Total number of students in section A to colleges AMH and MMH = (45 + 15 + 30 + 50) = 140

Total number of female students in all the colleges to the section B = (25 + 40 + 75) = 140

Required ratio = 1: 1

General solution:

AMU college

Number females in AMU college in section A  = 6a

Number of males in AMU college in section A = 3b

Number of females in AMU college in section B = 5a

Number of males in AMU college in section B = 4b

Total males in in AMU college = (3b + 4b) = 7b

Total females in AMU college = (6a + 5a) = 11a

7b - 11a = 50 ............. (1)

Total number of students in section B = (5a + 4b) 

Total number of students in section A = (6a + 3b)

(5a + 4b) - (6a + 3b) = 10

-a + b = 10

(b - a) = 10 ................ (2)

 Solving 1 and 2 we get 

7b - 11a = 50

7b - 7a = 70

-4a = - 20

a = 5

b = 15

Number females in AMU college in section A  = 6a = 6 ×  5 = 30

Number of males in AMU college in section A = 3b = 3 ×  15 = 45

Number of females in AMU college in section B = 5a = 5 ×  5 = 25

Number of males in AMU college in section B = 4b = 4 ×  15 = 60

MMH college

Number females in MMH college in section A  = 5c

Number of males in MMH college in section A = d

Number of females in MMH college in section B = 4c

Number of males in MMH college in section B = 3d

Total males in in MMH college = (d + 3d) = 4d

Total females in MMH college = (5c + 4c) = 9c

9c - 4d = 30 ............. (3)

Total number of students in section B = (4c + 3d) 

Total number of students in section A = (5c + d)

(4c + 3d) - (5c + d) = 20

-c + 2d = 20

(2d - c) = 20 ............. (4)

Solving 3 and 4 we get 

9c - 4d = 30

9 × [(2d - c) = 20]

9c - 4d = 30

18d - 9c = 180

14d = 210

d = 15

c = 10

Number females in MMH college in section A  = 5c = 5 ×  10 = 50

Number of males in MMH college in section A = d = 15

Number of females in MMH college in section B = 4c = 4 ×  10 = 40

Number of males in MMH college in section B = 3d = 3 ×  15 = 45

LPU college

Number females in LPU college in section A  = 2e

Number of males in LPU college in section A = 4f

Number of females in LPU college in section B = 3e

Number of males in LPU college in section B = 3f

Total males in in LPU college = (4f + 3f) = 7f

Total females in LPU college = (3e + 2e) = 5e

5e - 7f = 55 ............. (5)

Total number of students in section B = (3e + 3f) 

Total number of students in section A = (2e + 4f)

(3e + 3f) - (2e + 4f) = 15

e - f = 15 ............. (6)

Solving 5 and 6 we get 

Multiply equation (6) by 5 and subtract from equation (5) we get

-2f = - 20

f = 10

e = 25 

Number females in LPU college in section A  = 2e = 2 ×  25 = 50

Number of males in LPU college in section A = 4f = 4 ×  10 = 40

Number of females in LPU college in section B = 3e = 3 ×  25 = 75

Number of males in LPU college in section B = 3f = 3 ×  10 = 30

Solution:

Total number of students in section B in MMH college = (40 + 45) = 85

Number of male students in section C in LPU = 85/17 × 10 = 50

Total male students in all the 3 three sections of LPU college = (50 + 40 + 30) = 120

General solution:

AMU college

Number females in AMU college in section A  = 6a

Number of males in AMU college in section A = 3b

Number of females in AMU college in section B = 5a

Number of males in AMU college in section B = 4b

Total males in in AMU college = (3b + 4b) = 7b

Total females in AMU college = (6a + 5a) = 11a

7b - 11a = 50 ............. (1)

Total number of students in section B = (5a + 4b) 

Total number of students in section A = (6a + 3b)

(5a + 4b) - (6a + 3b) = 10

-a + b = 10

(b - a) = 10 ................ (2)

 Solving 1 and 2 we get 

7b - 11a = 50

7b - 7a = 70

-4a = - 20

a = 5

b = 15

Number females in AMU college in section A  = 6a = 6 ×  5 = 30

Number of males in AMU college in section A = 3b = 3 ×  15 = 45

Number of females in AMU college in section B = 5a = 5 ×  5 = 25

Number of males in AMU college in section B = 4b = 4 ×  15 = 60

MMH college

Number females in MMH college in section A  = 5c

Number of males in MMH college in section A = d

Number of females in MMH college in section B = 4c

Number of males in MMH college in section B = 3d

Total males in in MMH college = (d + 3d) = 4d

Total females in MMH college = (5c + 4c) = 9c

9c - 4d = 30 ............. (3)

Total number of students in section B = (4c + 3d) 

Total number of students in section A = (5c + d)

(4c + 3d) - (5c + d) = 20

-c + 2d = 20

(2d - c) = 20 ............. (4)

Solving 3 and 4 we get 

9c - 4d = 30

9 × [(2d - c) = 20]

9c - 4d = 30

18d - 9c = 180

14d = 210

d = 15

c = 10

Number females in MMH college in section A  = 5c = 5 ×  10 = 50

Number of males in MMH college in section A = d = 15

Number of females in MMH college in section B = 4c = 4 ×  10 = 40

Number of males in MMH college in section B = 3d = 3 ×  15 = 45

LPU college

Number females in LPU college in section A  = 2e

Number of males in LPU college in section A = 4f

Number of females in LPU college in section B = 3e

Number of males in LPU college in section B = 3f

Total males in in LPU college = (4f + 3f) = 7f

Total females in LPU college = (3e + 2e) = 5e

5e - 7f = 55 ............. (5)

Total number of students in section B = (3e + 3f) 

Total number of students in section A = (2e + 4f)

(3e + 3f) - (2e + 4f) = 15

e - f = 15 ............. (6)

Solving 5 and 6 we get 

Multiply equation (6) by 5 and subtract from equation (5) we get

-2f = - 20

f = 10

e = 25 

Number females in LPU college in section A  = 2e = 2 ×  25 = 50

Number of males in LPU college in section A = 4f = 4 ×  10 = 40

Number of females in LPU college in section B = 3e = 3 ×  25 = 75

Number of males in LPU college in section B = 3f = 3 ×  10 = 30

Solution:

Total number of male students in college AMU and MMH = (45 + 60 + 15 + 45) = 165

Total number of female students in college MMH and LPU = (50 + 40 + 50 + 75) = 215

Required difference = (215 - 165) = 50

General solution:

AMU college

Number females in AMU college in section A  = 6a

Number of males in AMU college in section A = 3b

Number of females in AMU college in section B = 5a

Number of males in AMU college in section B = 4b

Total males in in AMU college = (3b + 4b) = 7b

Total females in AMU college = (6a + 5a) = 11a

7b - 11a = 50 ............. (1)

Total number of students in section B = (5a + 4b) 

Total number of students in section A = (6a + 3b)

(5a + 4b) - (6a + 3b) = 10

-a + b = 10

(b - a) = 10 ................ (2)

 Solving 1 and 2 we get 

7b - 11a = 50

7b - 7a = 70

-4a = - 20

a = 5

b = 15

Number females in AMU college in section A  = 6a = 6 ×  5 = 30

Number of males in AMU college in section A = 3b = 3 ×  15 = 45

Number of females in AMU college in section B = 5a = 5 ×  5 = 25

Number of males in AMU college in section B = 4b = 4 ×  15 = 60

MMH college

Number females in MMH college in section A  = 5c

Number of males in MMH college in section A = d

Number of females in MMH college in section B = 4c

Number of males in MMH college in section B = 3d

Total males in in MMH college = (d + 3d) = 4d

Total females in MMH college = (5c + 4c) = 9c

9c - 4d = 30 ............. (3)

Total number of students in section B = (4c + 3d) 

Total number of students in section A = (5c + d)

(4c + 3d) - (5c + d) = 20

-c + 2d = 20

(2d - c) = 20 ............. (4)

Solving 3 and 4 we get 

9c - 4d = 30

9 × [(2d - c) = 20]

9c - 4d = 30

18d - 9c = 180

14d = 210

d = 15

c = 10

Number females in MMH college in section A  = 5c = 5 ×  10 = 50

Number of males in MMH college in section A = d = 15

Number of females in MMH college in section B = 4c = 4 ×  10 = 40

Number of males in MMH college in section B = 3d = 3 ×  15 = 45

LPU college

Number females in LPU college in section A  = 2e

Number of males in LPU college in section A = 4f

Number of females in LPU college in section B = 3e

Number of males in LPU college in section B = 3f

Total males in in LPU college = (4f + 3f) = 7f

Total females in LPU college = (3e + 2e) = 5e

5e - 7f = 55 ............. (5)

Total number of students in section B = (3e + 3f) 

Total number of students in section A = (2e + 4f)

(3e + 3f) - (2e + 4f) = 15

e - f = 15 ............. (6)

Solving 5 and 6 we get 

Multiply equation (6) by 5 and subtract from equation (5) we get

-2f = - 20

f = 10

e = 25 

Number females in LPU college in section A  = 2e = 2 ×  25 = 50

Number of males in LPU college in section A = 4f = 4 ×  10 = 40

Number of females in LPU college in section B = 3e = 3 ×  25 = 75

Number of males in LPU college in section B = 3f = 3 ×  10 = 30

Solution:

Total males in MMH college = 60

Total females in MMH college = 90

150 - (x + x + 10) = 40

150 - 2x + 10 = 40

-2x = -100

x = 50

Shortcut Trick

Ratio of Speed of Boat (u) to Stream (v) = 5 : 1.

Ratio of Downstream Speed (u+v) to Upstream Speed (u-v) = (5+1) : (5-1) = 6 : 4 = 3 : 2.

Since distance is constant, Time Ratio is inverse of Speed Ratio = 2 : 3.

Difference in time ratio parts = 3 − 2 = 1 unit → 2 hours. Therefore, Upstream Time = 3 units = 6 hours.

Upstream Speed = 120 km ÷ 6 hours = 20 km/hr. Since (u − v) is 4 parts → 1 part = 5. Still water speed (5 parts) = 25 km/hr.

∴ The correct answer is 25 km/hr.

Alternate Method

Given: Ratio of boat speed (u) to stream speed (v) = 5 : 1. Distance (D) = 120 km. Time difference = 2 hours.

Formula Used: Time = Distance ÷ Speed; Upstream Speed = u − v; Downstream Speed = u + v.

⇒ Let Speed of Boat = 5x and Speed of Stream = x.

⇒ Downstream Speed = 6x and Upstream Speed = 4x.

⇒ [120 ÷ 4x] − [120 ÷ 6x] = 2

⇒ 30/x − 20/x = 2

⇒ 10/x = 2

⇒ x = 5 km/hr

⇒ Speed of boat in still water = 5x = 5 × 5 = 25 km/hr.

∴ The correct answer is 25 km/hr.

Additional Information

Still Water Speed formula

Speed of Boat in Still Water (u) = (Downstream Speed + Upstream Speed) ÷ 2.

Stream Speed formula

Speed of Current/Stream (v) = (Downstream Speed − Upstream Speed) ÷ 2.

Distance in T hours difference

Distance = [ (u² − v²) × Time Difference ] ÷ 2v.

Shortcut Trick

For Compound Interest, 44% in 2 years means the effective rate is 20% (since 20 + 20 + (20×20)/100 = 44%).

Given 2R = 20% ⇒ R = 10%.

For Simple Interest, Total interest = 40% of Sum.

R × Time = 40% ⇒ 10 × 2t = 40 ⇒ 2t = 4 ⇒ t = 2.

∴ The correct answer is 2 years.

Alternate Method

Given: Simple Interest (SI) = 40% of P for 2t years at R%; Compound Interest (CI) = 44% of P for 2 years at 2R%.

Formula Used: SI = (P×R×T)/100; Effective CI rate for 2 years = x + y + (xy/100).

⇒ Let Sum (P) = 100.

⇒ CI Rate (2R) effective for 2 years: 2R + 2R + (2R × 2R)/100 = 44.

⇒ 4R + 4R²/100 = 44 ⇒ R² + 100R − 1100 = 0.

⇒ (R + 110)(R − 10) = 0 ⇒ R = 10% (as Rate cannot be negative).

⇒ Now for SI: Interest = (P × R × Time)/100.

⇒ 40 = (100 × 10 × 2t)/100.

⇒ 40 = 20t.

⇒ t = 2 years.

∴ The correct answer is 2 years.

Additional Information

Effective Rate of Interest

For compound interest of 2 years, the net percentage change formula (x + y + xy/100) quickly gives the interest percentage of the principal.

Simple Interest vs Compound Interest

Simple interest is calculated only on the principal, whereas compound interest is calculated on the principal plus the accumulated interest of previous periods.

Rule of 72

A quick way to estimate the time required to double an investment: Time ≈ 72 ÷ Interest Rate.

Shortcut Trick

Profit ratio is calculated as Investment × Time.

Arun profit : Nisha profit = 9 : 10.

Arun total investment units = 3000 × 12 = 36000.

Nisha total investment units = (2000 × 4) + (2000 + P) × 8 = 8000 + 16000 + 8P.

Equating ratios: 36000 ÷ (24000 + 8P) = 9 ÷ 10 ⇒ 40000 = 24000 + 8P.

8P = 16000 ⇒ P = 2000.

∴ The correct answer is Rs. 2000.

Alternate Method

Given → Initial Investments: Nisha = Rs. 2000, Arun = Rs. 3000. Time = 12 months. Formulas: Profit Share = Investment × Time period | Ratio of Profits = (I₁ × T₁) : (I₂ × T₂)

⇒ Total investment-months for Arun = 3000 × 12 = 36000. ⇒ Total investment-months for Nisha = (2000 × 4) + (2000 + P) × 8 = 8000 + 16000 + 8P = 24000 + 8P. ⇒ According to question, Arun Profit = (9/10) × Nisha Profit. ⇒ Arun Profit / Nisha Profit = 9 / 10. ⇒ 36000 / (24000 + 8P) = 9 / 10. ⇒ 4000 / (24000 + 8P) = 1 / 10. ⇒ 40000 = 24000 + 8P ⇒ 8P = 16000. ⇒ P = 2000.

∴ The correct answer is Rs. 2000.

Additional Information

Partnership Basics

In a simple partnership, profits are shared in the ratio of investments if the time period is same. In a compound partnership, profits are shared in the ratio of the product of capital and time.

Ratio Proportionality

If A and B invest C₁ and C₂ for T₁ and T₂ respectively, then Profit A : Profit B = (C₁ × T₁) : (C₂ × T₂).

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

(71.98 + 143.9 × 3.99) ÷ 17.95 + 27.98 = ?

⇒ (72 + 144 × 4) ÷ 18 + 28 = ?

⇒ (72 + 576) ÷ 18 + 28 = ?

⇒ 648 ÷ 18 + 28 = ?

⇒ 36 + 28 = ?

∴ ? = 64

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

39.99% of (124.95 ÷ 25.05 × 3.94 + 15.05) = ?

⇒ 40% of (125 ÷ 25 × 4 + 15) = ?

⇒ 40% of (125 ÷ 25 × 4 + 15) = ?

⇒ 40% of  (5 × 4 + 15) = ?

⇒ 40% of (20 + 15) = ?

⇒ 40% of 35 = ?

⇒ ? = 14

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

6.97² + 161.92 ÷ 2.99² – 6.99 × 8.99 = ?

⇒ 72 + 162 ÷ 32 – 7 × 9 = ?

⇒ 49 + 162 ÷ 9 – 7 × 9 = ? 

⇒ 49 + 18 – 63 = ?

⇒ 67 – 63 = ?

⇒ ? = 4

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

79.98% of 599.98 + 192.02 ÷ 31.92 = √35.96 × ?

⇒ 80% of 600 + 192 ÷ 32 = √36 × ?

⇒ 480 + 192 ÷ 32 = 6 × ?

⇒ 480 + 6 = 6 × ?

⇒ 486 = 6 × ?

⇒ 81 = ?

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and following BODMAS rule in the bracket -

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 4: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since we need to find out the approximate value, we can write these values to their nearest integers.

Given expression is

11.98 – [25.96 – {1.98 + 4.95 × (6.06 – 2.93)}] = ?

⇒ 12 – [26 – {2 + 5 × (6 – 3)}] = ?

⇒ 12 – [26 – {2 + 5 × 3}] = ?

⇒ 12 – [26 – 17] = ?

⇒ 12 – 9 = ?

∴ ? = 3

Shortcut Trick

Let the Cost Price (CP) of the bulb be B and the fan be F.

Ratio of Selling Prices: B × 135% = F × 60%.

Ratio of Cost Prices: B / F = 60 / 135 = 4 / 9.

Difference in ratio parts = 9 − 4 = 5 units.

According to the question, 5 units = Rs. 250 ⇒ 1 unit = Rs. 50.

Cost of bulb = 4 units = 4 × 50 = Rs. 200.

∴ The correct answer is Rs. 200.

Alternate Method

Given: CP_fan = CP_bulb + 250, Profit%_bulb = 35%, Loss%_fan = 40%, SP_bulb = SP_fan.

Formulas: SP = CP × (100 + P%) ÷ 100 | SP = CP × (100 − L%) ÷ 100.

Let CP of bulb = x. Then CP of fan = x + 250.

⇒ SP of bulb = x × (135/100) = 1.35x.

⇒ SP of fan = (x + 250) × (60/100) = 0.6(x + 250).

⇒ 1.35x = 0.6x + 150.

⇒ 1.35x − 0.6x = 150 ⇒ 0.75x = 150.

⇒ x = 150 ÷ 0.75 = 200.

∴ The correct answer is Rs. 200.

Additional Information

Cost Price and Selling Price Relationship

When the selling prices are equal, the ratio of their cost prices is inversely proportional to their profit/loss multipliers: CP₁/CP₂ = (100 ± R₂)/(100 ± R₁).

Profit and Loss Percentage

Profit or Loss is always calculated on the Cost Price (CP) unless specifically stated otherwise in the problem.

Shortcut Trick Let the side of the square (and length of rectangle) be s. New square area − Rectangle area = 3 (s − 4)2 − (6 × s) = 3 Testing option 3: Area of rectangle = 78 ⇒ 6 × s = 78 ⇒ s = 13. Check: (13 − 4)2 − 78 = 92 − 78 = 81 − 78 = 3. (Satisfied) ∴ The correct answer is 78 cm2. Alternate Method

Given: Width of rectangle (w) = 6 cm Length of rectangle (l) = Side of square (s) New side of square = s − 4 Formula Used: Area of Rectangle = length × width Area of Square = (side)2 Calculations: ⇒ Area of Rectangle = 6 × s ⇒ Area of New Square = (s − 4)2 ⇒ (s − 4)2 = 6s + 3 ⇒ s2 − 8s + 16 = 6s + 3 ⇒ s2 − 14s + 13 = 0 ⇒ (s − 13)(s − 1) = 0 ⇒ s = 13 (Since s − 4 must be positive, s > 4) ⇒ Area of rectangle = 6 × 13 = 78 cm2 ∴ The correct answer is 78 cm2. Additional Information Area and Perimeter of Rectangle Area = length × width; Perimeter = 2 × (length + width). Area and Perimeter of Square Area = side2; Perimeter = 4 × side; Diagonal = side × √2. Quadratic Roots For ax2 + bx + c = 0, roots are found by factorisation or x = [−b ± √(b2 − 4ac)] / 2a.

Shortcut Trick

Speed of Train A = 36 × (5/18) = 10 m/s. Length A = 10 × 20 = 200 m.

Length B = 200 + 100 = 300 m. Platform = 500 m.

Total Distance for B = 300 + 500 = 800 m. Speed B = 18 × (5/18) = 5 m/s.

Time taken by B = 800 ÷ 5 = 160 sec.

∴ The correct answer is 160 sec.

Alternate Method

Given: Speed of Train A = 36 km/hr, Time to cross pole = 20 sec, Length of Train B = Length A + 100 m, Speed of Train B = 18 km/hr, Platform length = 500 m.

Formula Used: Distance = Speed × Time; Time = Distance ÷ Speed; 1 km/hr = 5/18 m/s.

⇒ Speed of Train A in m/s = 36 × (5/18) = 10 m/s.

⇒ Length of Train A = Speed × Time = 10 × 20 = 200 m.

⇒ Length of Train B = 200 + 100 = 300 m.

⇒ Speed of Train B in m/s = 18 × (5/18) = 5 m/s.

⇒ Total Distance to be covered by B = Length of B + Length of Platform = 300 + 500 = 800 m.

⇒ Time taken by B = 800 ÷ 5 = 160 sec.

∴ The correct answer is 160 sec.

Additional Information

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Train Crossing Concepts

When a train crosses a pole or stationary person, distance = length of train. When it crosses a platform or bridge, distance = length of train + length of platform.

Relative Speed

If two trains move in the same direction, relative speed = S₁ − S₂. If they move in opposite directions, relative speed = S₁ + S₂.

General solution:

Agent A

Number of health insurance sold to males and females = 150

Number of health insurance sold to males = 50

Number of health insurance sold to females = (150 - 50) = 100

Number of vehicle insurance sold to females = 85

Number of vehicle insurance sold to males = 85/5 ×  4 = 68

Agent B

Number of health insurance sold to males and females = 120

Number of health insurance sold to males = 50

Number of health insurance sold to females = (120 - 50) = 70

Number of vehicle insurance sold to females = 70

Number of vehicle insurance sold to males = 70/5 ×  4 = 56 

Agent C

Number of health insurance sold to males and females = 140

Number of health insurance sold to males = 50

Number of health insurance sold to females = (140 - 50) = 90

Number of vehicle insurance sold to females = 55

Number of vehicle insurance sold to males = 55/5 ×  4 = 44

Solution:

Number of health insurance sold by A = 150

Number of vehicle insurance sold by A = 153

If agent A sold '2y' more health and 'y' more vehicle insurance then

(150 + 2y) - (153 + y) = 27

-3 + y =  27

y = 30

General solution:

Agent A

Number of health insurance sold to males and females = 150

Number of health insurance sold to males = 50

Number of health insurance sold to females = (150 - 50) = 100

Number of vehicle insurance sold to females = 85

Number of vehicle insurance sold to males = 85/5 ×  4 = 68

Agent B

Number of health insurance sold to males and females = 120

Number of health insurance sold to males = 50

Number of health insurance sold to females = (120 - 50) = 70

Number of vehicle insurance sold to females = 70

Number of vehicle insurance sold to males = 70/5 ×  4 = 56 

Agent C

Number of health insurance sold to males and females = 140

Number of health insurance sold to males = 50

Number of health insurance sold to females = (140 - 50) = 90

Number of vehicle insurance sold to females = 55

Number of vehicle insurance sold to males = 55/5 ×  4 = 44

Solution:

Number of health and vehicle insurance sold by A = (100 + 50 + 68 + 85) = 303

Number of health and vehicle insurance sold by C = (50 + 90 + 44 + 55) = 239

Required ratio = (303: 239)

General solution:

Agent A

Number of health insurance sold to males and females = 150

Number of health insurance sold to males = 50

Number of health insurance sold to females = (150 - 50) = 100

Number of vehicle insurance sold to females = 85

Number of vehicle insurance sold to males = 85/5 ×  4 = 68

Agent B

Number of health insurance sold to males and females = 120

Number of health insurance sold to males = 50

Number of health insurance sold to females = (120 - 50) = 70

Number of vehicle insurance sold to females = 70

Number of vehicle insurance sold to males = 70/5 ×  4 = 56 

Agent C

Number of health insurance sold to males and females = 140

Number of health insurance sold to males = 50

Number of health insurance sold to females = (140 - 50) = 90

Number of vehicle insurance sold to females = 55

Number of vehicle insurance sold to males = 55/5 ×  4 = 44

Solution: 

Number of health insurance done by B = (50 + 70) = 120

Number of vehicle insurance done by C = (55 + 44) = 99

Difference between the total cost = 99 ×  2000 - 120 ×  1500 = (198000 - 180000) = 18000

General solution:

Agent A

Number of health insurance sold to males and females = 150

Number of health insurance sold to males = 50

Number of health insurance sold to females = (150 - 50) = 100

Number of vehicle insurance sold to females = 85

Number of vehicle insurance sold to males = 85/5 ×  4 = 68

Agent B

Number of health insurance sold to males and females = 120

Number of health insurance sold to males = 50

Number of health insurance sold to females = (120 - 50) = 70

Number of vehicle insurance sold to females = 70

Number of vehicle insurance sold to males = 70/5 ×  4 = 56 

Agent C

Number of health insurance sold to males and females = 140

Number of health insurance sold to males = 50

Number of health insurance sold to females = (140 - 50) = 90

Number of vehicle insurance sold to females = 55

Number of vehicle insurance sold to males = 55/5 ×  4 = 44

Solution:

Number of persons sold health insurance = 100

Total number of health insurance sold to females by all the agents = (100 + 70 + 90) = 260

Required percentage = 100/260 ×  100 = 38.46%

General solution:

Agent A

Number of health insurance sold to males and females = 150

Number of health insurance sold to males = 50

Number of health insurance sold to females = (150 - 50) = 100

Number of vehicle insurance sold to females = 85

Number of vehicle insurance sold to males = 85/5 ×  4 = 68

Agent B

Number of health insurance sold to males and females = 120

Number of health insurance sold to males = 50

Number of health insurance sold to females = (120 - 50) = 70

Number of vehicle insurance sold to females = 70

Number of vehicle insurance sold to males = 70/5 ×  4 = 56 

Agent C

Number of health insurance sold to males and females = 140

Number of health insurance sold to males = 50

Number of health insurance sold to females = (140 - 50) = 90

Number of vehicle insurance sold to females = 55

Number of vehicle insurance sold to males = 55/5 ×  4 = 44

Solution:

Vehicle insurance sold by B to all the people is = (56 + 70) = 126

21% = 126

100% = 600

Then the health insurance sold by all the people = (50 + 70) = 120

Required percentage = 120/600 × 100 = 20%

Shortcut Trick Combined efficiency of A + B + C = 1/40, A = 1/20, B = 1/24. Efficiency of Emptying Pipe C = (1/20 + 1/24) − 1/40 = (6 + 5 − 3)/120 = 8/120 = 1/15. Time taken by C to empty the cistern = 15 hours. Total Capacity = Emptying Rate × Time = 160 × 15 = 2400 liters. ∴ The correct answer is 2400 liters. Alternate Method Pipe Time (Hours) Total Work (LCM) Efficiency A (Inlet) 20 120 units +6 B (Inlet) 24 +5 A + B + C 40 +3 ⇒ Total efficiency of A + B = 6 + 5 = 11 units/hr. ⇒ Efficiency of Pipe C = (A + B + C) − (A + B) = 3 − 11 = −8 units/hr. ⇒ Time taken by Pipe C alone to empty = 120 ÷ 8 = 15 hours. ⇒ Given: Pipe C empties 160 liters in 1 hour. ⇒ Total Capacity = 160 liters/hr × 15 hours = 2400 liters. ∴ The correct answer is 2400 liters. Additional Information Inlet and Outlet Pipes Inlet pipes carry a positive efficiency (filling), while outlet/leakage pipes carry a negative efficiency (emptying). Capacity Formula Total Capacity = Rate of flow × Total time taken to fill or empty the tank. Pipes & Cisterns Logic If a tank is filled in 'x' hours and emptied in 'y' hours (y > x), the net part filled in 1 hour is (1/x − 1/y).

Shortcut Trick

Initial Ratio Alcohol : Water = 7 : 5 (Total 12 units)

Add 6L Alcohol and 5L Water → New Ratio = 34 : 25

Using Cross-Multiplication Method: (7 × 25) − (34 × 5) units = (34 × 5) − (25 × 6)

⇒ |175 − 170| units = |170 − 150| ⇒ 5 units = 20 litres ⇒ 1 unit = 4 litres

⇒ Initial Total Mixture = 12 units = 12 × 4 = 48 litres

∴ The correct answer is 48 litres.

Alternate Method

Given: Initial ratio = 7 : 5. Added Alcohol = 6L, Added Water = 5L. Final ratio = 34 : 25.

Let initial quantity of Alcohol be 7x and Water be 5x.

⇒ (7x + 6) / (5x + 5) = 34 / 25

⇒ 25 × (7x + 6) = 34 × (5x + 5)

⇒ 175x + 150 = 170x + 170

⇒ 175x − 170x = 170 − 150

⇒ 5x = 20 ⇒ x = 4

⇒ Initial Mixture = 7x + 5x = 12x = 12 × 4 = 48 litres.

∴ The correct answer is 48 litres.

Additional Information

Cross-Multiplication Technique

Useful for ratio problems where different constants are added/subtracted to parts: (a × d − b × c) units = (c × k₂ − d × k₁).

Mixture Replacement Formula

Final Quantity = Initial Quantity × (1 − Replacement/Total)ⁿ, where n is the number of times the process is repeated.

Alligation Rule

Used to find the ratio in which two mixtures of different concentrations are mixed to get a desired mean concentration.

The series follows the following pattern:

82 – 1 = 63

92 – 1 = 80

102 – 1 = 99

112 – 1 = 120

122 – 1 = 143

132 – 1 = 168

The series follows the following pattern:

7 × 1 + 1 = 8 

8 × 2 + 1 = 17 

17 × 3 + 1 = 52

52 × 4 + 1 = 209 

209 × 5 + 1 = 1046

The series follows the following pattern:

16 + 144 = 160

160 + 121 = 281

281 + 100 = 381

381 + 81 = 462

462 + 64 = 526

103 + 8³ = 615

615 + 7³ = 958

958 + 6³ = 1174

1174 + 5³ = 1299

1299 + 4³ = 1363

1363 + 3³ = 1390

Calculation:

The series follows the following pattern:

⇒ 7 × 1 = 7

⇒ 7 × 2 = 14

⇒ 14 × 3 = 42

⇒ 42 × 4 = 168

⇒ 168 × 5 = 840

∴ The missing term in the series is 42

Shortcut Trick

Total outcomes = 50 (numbers 1 to 50).

Multiples of 8 up to 50 = 50 ÷ 8 ≈ 6 (Specifically: 8, 16, 24, 32, 40, 48).

Probability = Favorable outcomes ÷ Total outcomes = 6 ÷ 50 = 3/25.

∴ The correct answer is 3/25.

Alternate Method

Given:

Total number of tickets = 50.

Condition: Drawn ticket must be a multiple of 8.

Formula Used:

Probability P(E) = n(E) ÷ n(S)

Calculations:

⇒ Sample space n(S) = {1, 2, 3, ..., 50} = 50.

⇒ Favorable outcomes E = {8, 16, 24, 32, 40, 48}.

⇒ Number of favorable outcomes n(E) = 6.

⇒ P(E) = 6 ÷ 50

⇒ P(E) = 3 ÷ 25

∴ The correct answer is 3/25.

Additional Information

Definition of Probability

Probability is the measure of likelihood of an event occurring, calculated as favorable outcomes divided by total possible outcomes. 0 ≤ P(E) ≤ 1.

Complementary Event

The probability of an event not occurring is P(E') = 1 − P(E). For this problem, probability of not picking a multiple of 8 is 1 − 3/25 = 22/25.

Multiples in a Range

The count of multiples of 'k' in the range 1 to 'n' is given by the greatest integer function [n/k]. Here, [50/8] = 6.

Shortcut Trick

Let the largest prime number in Set A be P and the largest odd number in Set B be Q.

Given: P + Q = 64 and P = 3Q − 4.

Substitute P: (3Q − 4) + Q = 64 ⇒ 4Q = 68 ⇒ Q = 17.

Then P = 64 − 17 = 47.

Set A consists of 3 consecutive prime numbers ending in 47: 41, 43, 47.

∴ The correct answer is 41.

Alternate Method

Given: Largest number of Set A = P, Largest number of Set B = Q.

Equations:

⇒ P + Q = 64 --- (i)

⇒ P = 3Q − 4 --- (ii)

Calculation:

⇒ Put (ii) in (i): (3Q − 4) + Q = 64

⇒ 4Q = 68

⇒ Q = 17 (Largest odd number of Set B)

⇒ P = 64 − 17 = 47 (Largest prime number of Set A)

⇒ Set A contains 3 consecutive primes: 41, 43, 47.

⇒ Smallest number = 41.

∴ The correct answer is 41.

Additional Information

Prime Numbers

A number greater than 1 with exactly two factors: 1 and itself. Consecutive primes after 40 are 41, 43, 47, 53, 59.

Consecutive Odd Numbers

Numbers of the form 2n + 1. The difference between two consecutive odd numbers is always 2.

Linear Equations

Solving systems of equations using substitution or elimination methods to find unknown variables.

Shortcut Trick

Total percentage spent = 40% + 20% + 10% = 70%

Remaining savings percentage = 100% − 70% = 30%

Given, 30% of income = ₹15,000

100% of income = (15,000 ÷ 30) × 100 = ₹50,000

∴ The correct answer is ₹50,000.

Alternate Method

Given:

Expenditure on household items = 40%

Expenditure on clothes = 20%

Investment in recurring deposits (RD) = 10%

Actual savings = ₹15,000

Calculations:

⇒ Total percentage utilized = 40% + 20% + 10% = 70%

⇒ Percentage saved = 100% − 70% = 30%

⇒ Let total income be X.

⇒ 30% of X = 15,000

⇒ (30 ÷ 100) × X = 15,000

⇒ X = (15,000 × 100) ÷ 30

⇒ X = 500 × 100

⇒ X = 50,000

∴ The correct answer is ₹50,000.

Additional Information

Successive Percentage Spending

If a person spends X% and then Y% of the remaining amount, the final value is calculated as Initial × (100−X)/100 × (100−Y)/100.

Income-Expenditure Relationship

Monthly Income = Total Expenditure + Savings. This basic identity is used to solve most percentage-based budget problems.

Fractional Conversions

Convert percentages to fractions to speed up calculations: 20% = 1/5, 40% = 2/5, 10% = 1/10.

Shortcut Trick Evaluate values directly for given a = −3, b = −1, c = 6. Quantity I = (−27 + 1 + 36) ÷ 4 = 10 ÷ 4 = 2.5 Quantity II = −3 ÷ (−27 + 1) = −3 ÷ −26 = 3/26 ≈ 0.115 Since 2.5 > 0.115, Quantity I > Quantity II. ∴ The correct answer is Quantity I > Quantity II. Alternate Method Given: a = −3, b = −1, c = 6 Quantity I Calculation: ⇒ a3 = (−3)3 = −27 ⇒ b2 = (−1)2 = 1 ⇒ c2 = (6)2 = 36 ⇒ Quantity I = (−27 + 1 + 36) ÷ 4 ⇒ Quantity I = 10 ÷ 4 = 2.5 Quantity II Calculation: ⇒ a / (a3 + b2) = −3 / [(−3)3 + (−1)2] ⇒ Quantity II = −3 / (−27 + 1) ⇒ Quantity II = −3 / −26 = 3/26 ≈ 0.115 Comparison: ⇒ 2.5 > 0.115 ∴ The correct answer is Quantity I > Quantity II. Additional Information Power of Negative Numbers A negative number raised to an odd power results in a negative value: (−x)n = −xn. A negative number raised to an even power results in a positive value: (−x)n = xn. Comparison of Quantities Always ensure both quantities are in the same form (decimal or fraction) before comparing. For fractions, cross-multiplication can be used to determine which is larger.

Perimeter of a square = 2 × 2 × (11 + 10) = 84 cm

⇒ Side of the square = 84/4 = 21 cm

Quantity A:

Circumference of the semicircle whose diameter is equal to the side of the square = 21 + 22/7 × 21/2

⇒ 21 + 33 = 54 cm

Quantity B:

Circumference of the circle which is inscribed inside the square = 2 × 22/7 × 21/2 = 66 cm

∴ Quantity A < Quantity B

Shortcut TrickQuantity A: Speed X = 420/7 = 60 kmph. Ratio 5:3 → Speed Y = (3/5)×60 = 36 kmph. Relative speed = 60 + 36 = 96 kmph. Distance in 3 hrs = 96×3 = 288 km. Initial gap = 100 km. Crossing occurs, then new distance = 288 − 100 = 188 km.Quantity B: Speed = 300/12 = 25 m/s = 25×18/5 = 90 kmph. Distance in 2 hrs = 90×2 = 180 km.Comparison: 188 km > 180 km ⇒ A > B.∴ The correct answer is Quantity A > Quantity B.Alternate MethodQuantity A:⇒ Speed of Train X = 420 km ÷ 7 hours = 60 kmph.⇒ Speed of Train Y = (60 ÷ 5) × 3 = 36 kmph.⇒ Relative Speed (Towards each other) = 60 + 36 = 96 kmph.⇒ Total Distance covered in 3 hours = 96 × 3 = 288 km.⇒ Final Distance between them = |Initial distance − Distance covered| = |100 − 288| = 188 km.Quantity B:⇒ Speed of Bus = 300 m ÷ 12 s = 25 m/s.⇒ Speed in kmph = 25 × (18 ÷ 5) = 90 kmph.⇒ Distance in 2 hours = 90 × 2 = 180 km.⇒ Comparing Quantity A (188 km) and Quantity B (180 km), A > B.∴ The correct answer is Quantity A > Quantity B.Additional InformationRelative SpeedWhen two objects move towards each other, relative speed is the sum of their individual speeds (S1 + S2). If moving in the same direction, it is the difference |S1 − S2|.Unit ConversionTo convert speed from m/s to kmph, multiply by 18/5. To convert kmph to m/s, multiply by 5/18.Distance After CrossingIf objects cover more distance than the initial gap, they cross each other. New distance = |Initial Gap − Relative Distance Covered|.

Seven persons A, B, C, D, E, F, and G are sitting in a straight row. Some of them are facing the north while others face the south direction.

1. Two people sit between B and A, who sit at one of the extreme ends of the row. B is second to the left of E. E and A are facing the same direction. E is not an immediate neighbor of A. 

2. D is sitting second to the right of G. G faces opposite the direction of E. Persons sitting on the extreme ends face opposite directions.

3. C is not sitting on the extreme end and is not the immediate neighbor of F. F is sitting to the right of D but is not an immediate neighbor of the person who faces the south direction. 

Case 1(b) is eliminated because the only possibility is that C and F are immediate neighbors which contradicts the given conditions.

Case 2 is eliminated because the F only be immediate neighbor of E but E is facing south direction which contradicts the given condition.

4. The immediate neighbor of D faces the same direction. Not more than two persons facing north direction sit adjacent to each other.

The final arrangement is:

E sits second to the left of B.

Seven persons A, B, C, D, E, F, and G are sitting in a straight row. Some of them are facing the north while others face the south direction.

1. Two people sit between B and A, who sit at one of the extreme ends of the row. B is second to the left of E. E and A are facing the same direction. E is not an immediate neighbor of A. 

2. D is sitting second to the right of G. G faces opposite the direction of E. Persons sitting on the extreme ends face opposite directions.

3. C is not sitting on the extreme end and is not the immediate neighbor of F. F is sitting to the right of D but is not an immediate neighbor of the person who faces the south direction. 

Case 1(b) is eliminated because the only possibility is that C and F are immediate neighbors which contradicts the given conditions.

Case 2 is eliminated because the F only be immediate neighbor of E but E is facing south direction which contradicts the given condition.

4. The immediate neighbor of D faces the same direction. Not more than two persons facing north direction sit adjacent to each other.

The final arrangement is:

The number of persons sitting right to C is one less than the number of persons sitting to the left of G.

Seven persons A, B, C, D, E, F, and G are sitting in a straight row. Some of them are facing the north while others face the south direction.

1. Two people sit between B and A, who sit at one of the extreme ends of the row. B is second to the left of E. E and A are facing the same direction. E is not an immediate neighbor of A. 

2. D is sitting second to the right of G. G faces opposite the direction of E. Persons sitting on the extreme ends face opposite directions.

3. C is not sitting on the extreme end and is not the immediate neighbor of F. F is sitting to the right of D but is not an immediate neighbor of the person who faces the south direction. 

Case 1(b) is eliminated because the only possibility is that C and F are immediate neighbors which contradicts the given conditions.

Case 2 is eliminated because the F only be immediate neighbor of E but E is facing south direction which contradicts the given condition.

4. The immediate neighbor of D faces the same direction. Not more than two persons facing north direction sit adjacent to each other.

The final arrangement is:

F stands to the right of the one who stands immediately left of G.

Seven persons A, B, C, D, E, F, and G are sitting in a straight row. Some of them are facing the north while others face the south direction.

1. Two people sit between B and A, who sit at one of the extreme ends of the row. B is second to the left of E. E and A are facing the same direction. E is not an immediate neighbor of A. 

2. D is sitting second to the right of G. G faces opposite the direction of E. Persons sitting on the extreme ends face opposite directions.

3. C is not sitting on the extreme end and is not the immediate neighbor of F. F is sitting to the right of D but is not an immediate neighbor of the person who faces the south direction. 

Case 1(b) is eliminated because the only possibility is that C and F are immediate neighbors which contradicts the given conditions.

Case 2 is eliminated because the F only be immediate neighbor of E but E is facing south direction which contradicts the given condition.

4. The immediate neighbor of D faces the same direction. Not more than two persons facing north direction sit adjacent to each other.

The final arrangement is:

D has the third position from the left end.

Seven persons A, B, C, D, E, F, and G are sitting in a straight row. Some of them are facing the north while others face the south direction.

1. Two people sit between B and A, who sit at one of the extreme ends of the row. B is second to the left of E. E and A are facing the same direction. E is not an immediate neighbor of A. 

2. D is sitting second to the right of G. G faces opposite the direction of E. Persons sitting on the extreme ends face opposite directions.

3. C is not sitting on the extreme end and is not the immediate neighbor of F. F is sitting to the right of D but is not an immediate neighbor of the person who faces the south direction. 

Case 1(b) is eliminated because the only possibility is that C and F are immediate neighbors which contradicts the given conditions.

Case 2 is eliminated because the F only be immediate neighbor of E but E is facing south direction which contradicts the given condition.

4. The immediate neighbor of D faces the same direction. Not more than two persons facing north direction sit adjacent to each other.

The final arrangement is:

Three persons are facing the North direction.

We have: R A N D O M 

Therefore, required value = 1 + 2 + 3 + 4 + 2 + 6 = 18

Hence, total is 18.

Given statements: M < T ≤ Q < D; P > A = W ≥ D

On combining: M < T ≤ Q < D ≤ W = A < P

Conclusions:

I. W ≥ T → False (as T ≤ Q < D ≤ W, so it is definite that W is greater than T. It is not possible that W is equal to T.)

II. P > Q → True (as Q < D ≤ W = A < P, so P is greater than Q.)

W is greater than T but not equal to T so the first conclusion doesn't follow. But it is definite that P is greater than Q so the second conclusion follows.

The correct answer is Only II follows.

Given statements: R < V > C ≥ S < N; Q ≥ O > S

On combining: R < V > C ≥ S < O ≤ Q; Q ≥ O > S < N

Conclusions:

I. V > O → False (as V > C ≥ S < O, so no definite relationship can be determined between V and O.)

II. Q > C → False (as C ≥ S < O ≤ Q, so no definite relationship can be determined between Q and C.)

There is no direct relation given between V and O so the first conclusion doesn't follow. Similarly, the second conclusion also doesn't follow.

The correct answer is Neither I nor II follows.

Given statements: C < P = R > N > S; Z < S ≤ O < G

On combining: C < P = R > N > S ≤ O < G; C < P = R > N > S > Z

Conclusions:

I. O > R → False (as R > N > S ≤ O, so no definite relationship can be determined between O and R.)

II. P > Z → True (as P = R > N > S > Z, so P is greater than Z.)

There is no direct relation given between O and R so the first conclusion doesn't follow. P is greater than Z so the second conclusion follows.

The correct answer is Only II follows.

Six person: Meena, Ritu, Karan, Priya, Vivek, and Lalit 

Dates: 5th and 18th

Months: January, March, and April 

ATMs Color: Green, Brown, Yellow, Pink, Orange, and White. 

1. A person visited the white Label ATM on 5th January. Two persons visited in between the persons who visited White and Brown Label ATMs.   Karan and Priya visited the ATM in the same month. Karan visited the ATM before Ritu. 

2. The person visited Pink Label ATM in the month which has 30 days only. Two Persons visited in between Meena and the one who visited the Pink Label ATM. Ritu does not visit Pink Label ATM. Karan visited the ATM before Ritu. 

3. Lalit and Vivek visited the ATM on the same date. Priya and Vivek visited the ATM on different dates. The person visited the Green Label ATM just before the Yellow Label ATM. 

4. Meena does not visit Yellow Label ATM. Lalit does not visit Pink Label ATM. According to the given condition Case 1 is eliminated as in Case 1 Meena visited Yellow Label ATM.

The Final arrangement is:

Karan likes Yellow colour ATM.

Six person: Meena, Ritu, Karan, Priya, Vivek, and Lalit 

Dates: 5th and 18th

Months: January, March, and April 

ATMs Color: Green, Brown, Yellow, Pink, Orange, and White. 

1. A person visited the white Label ATM on 5th January. Two persons visited in between the persons who visited White and Brown Label ATMs.   Karan and Priya visited the ATM in the same month. Karan visited the ATM before Ritu. 

2. The person visited Pink Label ATM in the month which has 30 days only. Two Persons visited in between Meena and the one who visited the Pink Label ATM. Ritu does not visit Pink Label ATM. Karan visited the ATM before Ritu. 

3. Lalit and Vivek visited the ATM on the same date. Priya and Vivek visited the ATM on different dates. The person visited the Green Label ATM just before the Yellow Label ATM.