IBPS PO Prelims Memory Based Paper (Held On: 30 September 2023 Shift 2) (Previous Year Paper)

The correct answer is D.

Key Points

• The given paragraph is about the dowry system.
• Sentence D is the first sentence as it introduces the topic of the paragraph 'Dowry system' by mentioning its evil effect on society.
• Sentence A is the second sentence as it explains how the dowry system has affected the sacredness of marriage.
• Sentence B is the third sentence as it explains how badly the parents of the bride get affected by the demand for dowry.
• Sentence F is the fourth sentence as it says the parents even become poor or bankrupt to get their daughters married.
• Sentence E is in the correct place so it's the fifth sentence as it explains the ruthless effect of the dowry system on young brides.
• Sentence C is the sixth sentence as it concludes the paragraph by giving the solution of eradicating the dowry system from society.
• The correct sequence is DABFEC.
  

Correct Paragraph: The Dowry system is evil in society. It has reduced the sacred affair of marriage to a business deal. The parents of the brides are often put under inhuman pressure for a handsome dowry. Sometimes they become paupers to get their daughters married. In many cases, young brides are ruthlessly tortured or pushed to suicide. To eradicate this social evil, a total change in the outlook of society is a must.

The correct answer is A.

Key Points

• The given paragraph is about the dowry system.
• Sentence D is the first sentence as it introduces the topic of the paragraph 'Dowry system' by mentioning its evil effect on society.
• Sentence A is the second sentence as it explains how the dowry system has affected the sacredness of marriage.
• Sentence B is the third sentence as it explains how badly the parents of the bride get affected by the demand for dowry.
• Sentence F is the fourth sentence as it says the parents even become poor or bankrupt to get their daughters married.
• Sentence E is in the correct place so it's the fifth sentence as it explains the ruthless effect of the dowry system on young brides.
• Sentence C is the sixth sentence as it concludes the paragraph by giving the solution of eradicating the dowry system from society.
• The correct sequence is DABFEC.
  

Correct Paragraph: The Dowry system is evil in society. It has reduced the sacred affair of marriage to a business deal. The parents of the brides are often put under inhuman pressure for a handsome dowry. Sometimes they become paupers to get their daughters married. In many cases, young brides are ruthlessly tortured or pushed to suicide. To eradicate this social evil, a total change in the outlook of society is a must.

The correct answer is B.

Key Points

• The given paragraph is about the dowry system.
• Sentence D is the first sentence as it introduces the topic of the paragraph 'Dowry system' by mentioning its evil effect on society.
• Sentence A is the second sentence as it explains how the dowry system has affected the sacredness of marriage.
• Sentence B is the third sentence as it explains how badly the parents of the bride get affected by the demand for dowry.
• Sentence F is the fourth sentence as it says the parents even become poor or bankrupt to get their daughters married.
• Sentence E is in the correct place so it's the fifth sentence as it explains the ruthless effect of the dowry system on young brides.
• Sentence C is the sixth sentence as it concludes the paragraph by giving the solution of eradicating the dowry system from society.
• The correct sequence is DABFEC.
  

Correct Paragraph: The Dowry system is evil in society. It has reduced the sacred affair of marriage to a business deal. The parents of the brides are often put under inhuman pressure for a handsome dowry. Sometimes they become paupers to get their daughters married. In many cases, young brides are ruthlessly tortured or pushed to suicide. To eradicate this social evil, a total change in the outlook of society is a must.

The correct answer is F.

Key Points

• The given paragraph is about the dowry system.
• Sentence D is the first sentence as it introduces the topic of the paragraph 'Dowry system' by mentioning its evil effect on society.
• Sentence A is the second sentence as it explains how the dowry system has affected the sacredness of marriage.
• Sentence B is the third sentence as it explains how badly the parents of the bride get affected by the demand for dowry.
• Sentence F is the fourth sentence as it says the parents even become poor or bankrupt to get their daughters married.
• Sentence E is in the correct place so it's the fifth sentence as it explains the ruthless effect of the dowry system on young brides.
• Sentence C is the sixth sentence as it concludes the paragraph by giving the solution of eradicating the dowry system from society.
• The correct sequence is DABFEC.
  

Correct Paragraph: The Dowry system is evil in society. It has reduced the sacred affair of marriage to a business deal. The parents of the brides are often put under inhuman pressure for a handsome dowry. Sometimes they become paupers to get their daughters married. In many cases, young brides are ruthlessly tortured or pushed to suicide. To eradicate this social evil, a total change in the outlook of society is a must.

The correct answer is C.

Key Points

• The given paragraph is about the dowry system.
• Sentence D is the first sentence as it introduces the topic of the paragraph 'Dowry system' by mentioning its evil effect on society.
• Sentence A is the second sentence as it explains how the dowry system has affected the sacredness of marriage.
• Sentence B is the third sentence as it explains how badly the parents of the bride get affected by the demand for dowry.
• Sentence F is the fourth sentence as it says the parents even become poor or bankrupt to get their daughters married.
• Sentence E is in the correct place so it's the fifth sentence as it explains the ruthless effect of the dowry system on young brides.
• Sentence C is the sixth sentence as it concludes the paragraph by giving the solution of eradicating the dowry system from society.
• The correct sequence is DABFEC.
  

Correct Paragraph: The Dowry system is evil in society. It has reduced the sacred affair of marriage to a business deal. The parents of the brides are often put under inhuman pressure for a handsome dowry. Sometimes they become paupers to get their daughters married. In many cases, young brides are ruthlessly tortured or pushed to suicide. To eradicate this social evil, a total change in the outlook of society is a must.

The correct answer is Option (2) i.e. Lies, Distant

Key Points

 Let's look at the meaning of the correct answer:

• Lies - be, remain, or be kept in a specified state.
• ​Example - "The abbey lies in ruins today."
• Distant - a long way away in space or time,
• ​Example - travel to distant parts of the world
• ​From the given meaning we can conclude that the correct answer is lies, distant

Thus the correct sentence is: "The truth lies in every substance of this universe yet it is distant from many.*"*​

Additional Information

 Let's ​discuss the meaning of other options:

• Disappear - to become impossible to see or to find
• Perfuse - permeate or suffuse (something) with a liquid, color, quality, etc
• Persist - to perform a task, etc. or to put a plan into action
• Flourish - to be strong and healthy; to develop in a successful way

The correct answer is Option (3) i.e. Engulfed, Contains 

Key Points

 Let's look at the meaning of the correct answer:

• Engulfed - to cover or surround somebody/something completely
• ​Example - Within a few minutes the factory was engulfed in flames.
• Contains - to have something inside or as part of itself,
• ​Example - Each box contains 24 tins.
• ​From the given meaning we can conclude that the correct answer is engulfed, contains

Thus the correct sentence is: "The poverty-stricken, the penurious are mostly engulfed with indigence that contains nothing but suffering. *"*​

Additional Information

 Let's ​discuss the meaning of other options:

• Languid - weak or faint from illness or fatigue.
• Perfuses - permeate or suffuse with a liquid, colour, or quality.
• Persists - to continue to exist
• Shrink - to become smaller or make something smaller

The correct answer is Option (4) i.e. Push, Goal

Key Points

 Let's look at the meaning of the correct answer:

• Push - to use force to move somebody/something forward or away from you
• ​Example - She pushed him into the water.
• Goal - an idea of the future or desired result that a person or a group of people envision,
• ​Example - The goal is to win at any cost this time.
• ​From the given meaning we can conclude that the correct answer is push, goal.

Thus the correct sentence is: "The Bog-standards never push on the hard work. As their goal is always 'topsy- turvy'. *".*​

Additional Information

 Let's ​discuss the meaning of other options:

• consideration - an act of thinking about something carefully or for a long time
• foundation - the idea, principle, or fact on which something is based
• execution - to perform a task, etc. or to put a plan into action

The correct answer is Option (3) i.e. Cry, catch

Key Points

 Let's look at the meaning of the correct answer:

• cry - to make a noise and produce tears in your eyes, for example, because you are unhappy or have hurt yourself
• ​Example - The baby never stops crying​
• catch - to capture somebody/something that you have been following or looking for,
• ​Example - Two policemen ran after the thief and caught him at the end of the street.
• ​From the given meaning we can conclude that the correct answer is Cry, Catch.

Thus the correct sentence is: "The dolorous cry all the time for something they do not catch on easily. *".*​

Additional Information

 Let's ​discuss the meaning of other options:

• hesitate - to pause before you do something or before you make a decision, usually because you are uncertain or worried
• irritate - to make somebody angry; to annoy
• execute - to perform a task, etc. or to put a plan into action
• portray - to show somebody/something in a picture; to describe somebody/something in a piece of writing
• barge- to push people out of the way in order to get past them

The correct answer is Option (2)Curiosity, Satified.

Key Points

 Let's look at the meaning of the correct answer:

• curiosity - a state in which you want to learn more about something
• ​Example - My fingers tremble with curiosity, confusion, and excitement.​
• satisfied - you’re satisfied, you’re contented,
• ​Example - I patted myself, satisfied that they were flat enough that my uncle would not notice them.
• ​From the given meaning we can conclude that the correct answer is Curiosity, Satisfied.

Thus the correct sentence is: "The impatient ragamuffins were the main curiosity of the dictators who were not satisfied with their behaviours.*".*​

Additional Information

 Let's ​discuss the meaning of other options:

• attention - the process whereby a person concentrates on some
• jealous - suspicious or unduly suspicious or fearful of being displaced by a rival
• culprits - someone who perpetrates wrongdoing
• aware - having or showing knowledge or understanding or realization or perception
• Whippersnappers- someone who is unimportant but cheeky and presumptuous
• Upright- in a vertical position; not sloping
• Grumbletonians - A person who is often discontented, thereby taken to grumbling
• convenience- something that makes things easier, quicker or more comfortable

The correct answer is option 3.

 Key Points To answer this question, let's first understand the meanings of the marked words:

• Attendance - the act of being present at a particular place or event (हाजरी)
• For Example -
• The teacher took attendance at the beginning of the class to see which students were present.
• Requiring - demanding or needing something as necessary (आवश्यकता होना)
• For Example -
• She is requiring additional time to complete the project.
• Pandemic - an outbreak of a disease that occurs on a global scale, affecting a large number of people and often crossing international boundaries (महामारी)
• For Example -
• The COVID-19 pandemic had a profound impact on the world's healthcare systems and economies.
• Gradually - in a slow or gradual manner, taking place over a period of time (धीरे-धीरे)
• For Example -
• She gradually improved her language skills by practising a little bit every day.
• After understanding the meanings of the marked words, we can conclude that in the given sentence, "attendance" should be interchanged with "pandemic" to make it grammatically correct because the sentence is about the pandemic's impact on office attendance.
• Similarly, "requiring" should be interchanged with "gradually" to clarify that the increase in office presence is happening slowly over time, making the sentence contextually correct.
• Hence, the correct answer is "C-A, D-B."

 

The correct sentence after the rearrangement would be: "Following the pandemic, the fin-tech firm gradually increased office attendance from one day per week initially to now requiring employees to be present at the physical office for four days each week."

The correct answer is 'C-B.'

Key Points

• The given sentence says that after the troops departed from the country racked or devastated by war, a decline or relapse occurred when the citizens fall back on their unstable form of government.
• Let us explore the meaning of the highlighted words:
• Left - To go away from somewhere. (कहीं से दूर चले जाना)
• Resorted - To turn to and adopt a course of action, especially an extreme or undesirable one so as to resolve a difficult situation. (विवशता में किसी भी अरुचिकर उपाय का सहारा लेना)
• Regression - A return to a former or less developed state. (वापसी, प्रतीपगमन)
• Unstable - Likely to change or fail; not firmly established. (जो कभी भी बदल या गिर सकता है; डाँवाँडोल, अस्थिर)
• Thus, (C) and (B) must be interchanged.
  

Hence, the correct answer is option 2.

Correct Sentence: After our troops left the war-torn country, regression occurred when the citizens resorted to their unstable form of government.

The correct answer is 'No change required.'

Key Points

• The given sentence talks about Iyer who seemed to be getting better after his surgery but started to relapse or worsen today and is now confined to bed.
• Let us explore the meaning of the highlighted words:
• Recovering - To become well again after you have been ill. (बीमारी के बाद स्‍वास्‍थ्‍य लाभ करना)
• Surgery - Medical treatment in which your body is cut open so that part of it can be removed or repaired. (शल्‍य-क्रिया, शल्‍य-चिकित्‍सा, शरीर के रोगग्रस्‍त अंग को काटकर निकाल देना या सुधार देना)
• Regress - To go back to a former condition or a less developed way of behaving. (आचरण या स्थिति की पूर्व या अविकसित अवस्था में लौट जाना, प्रतिगमन करना, बदतर होना, पतन होना)
• Bedridden - Confined to bed by sickness. (बीमारी के कारण बिस्तर पर पड़ा हुआ)
• Thus, no change is required in the sentence.
  

Hence, the correct answer is option 5.

Correct Sentence: While Iyer seemed to be recovering after his surgery last week, he started to regress today and is now bedridden.

The correct answer is 'B-C.'

Key Points

• The given sentence says that when someone's backpack was looted in a foreign country, the importance of her missing passport and visa caused worry since she was not able to leave the country.
• Let us explore the meaning of the highlighted words:
• Stolen - To take something from a person, shop, etc. without permission and without intending to return it or pay for it. (चुराना, चोरी करना)
• Concern - A feeling of worry; something that causes worry. (चिंता; परवाह; चिंताजनक बात)
• Significance - The quality of being worthy of attention; importance. (किसी बात का महत्व)
• Unable - Not able to do something. (असमर्थ, अशक्त)
• Thus, (B) and (C) must be interchanged.
  

Hence, the correct answer is option 1.

Correct Sentence: When my friend’s backpack was stolen in a foreign country, the significance of her missing passport and visa caused concern since she was unable to leave the country.

The correct answer is Option 1.

 

Key Points

• The original sentence placement of "only" can be improved for clarity.
• Moving "only" next to "a little" clarifies that the cost is minimal.
• The best replacement provided is "It would cost India only a little."
• Thus, the error is resolved by choosing Option 1.

Therefore, the correct answer is Option 1.

 

Correct Sentence: "Because the deal cannot enter into force in its current form, India's foreign minister said that signing it would cost India only a little."

 

Additional Information

• Option 2: "It would only cost India little." – Less natural and not as clear.
• Option 3: "It would costing India only a little." – Grammatically incorrect (incorrect verb form).
• Option 4: "It will only cost India little." – Changes tense and lacks clarity.
• Option 5: "No correction required." – Original sentence needed improvement for clarity.

The correct answer is the people reached Mumbai when.

Key Points

• There are two errors in the bold part.
• Firstly, the term ‘people’ is a collective noun. Collective nouns are used in the singular form. Therefore, ‘peoples’ must be replaced by ‘people’ in order to make the sentence correct.
• Secondly, ‘hardly’ and ‘when’ form a pair of coordinating conjunctions. Coordinating conjunctions join phrases, words, etc. of equal ranks. Therefore, ‘when’ should be used instead of ‘than’ in order to make it a grammatically correct sentence.
• Among the choices available, option 3 replaces the bold part most appropriately.
• Hence, option 3 is the correct answer.

The correct sentence is: Hardly had the people reached Mumbai when they were ordered to return to Delhi.

Additional Information

• Hardly -when is used in past perfect tense sentences as follows. Sometimes we use Scarcely-when in place of Hardly-when
• Hardly had the race started when we started cheering.
• Scarcely had you asked a question when he answered it.
• We can use 'no sooner- than' as follows.
• No sooner did we call him than he responded.

The correct answer is were split on whether

Key Points

• If the committee members are unanimous regarding a decision, in that case, the committee is considered as a singular collective noun and a singular verb is used in the context. On the other hand, if a committee has members differing in their views regarding something, the plural form of the verb is used in that case.
• In the given context, the committee members are differing in their opinions and therefore a plural form of the verb should be used. As the tense is correct in the sentence, the correct verb should have been ‘were’.
• This makes option 1 the correct choice among the given options.

The correct sentence is: The committee were split on whether the new regulations for the National Health Protection Scheme should be implemented.

The correct answer is "The backbone of the organization's"

Key Points 

• The correct idiomatic expression in this sentence is ‘the backbone of' and not 'the backing bone in'.
• Be the backbone (Idiom): The part of something that makes it successful or strong.
• Ex: Ordinary volunteers form the backbone of most charitable organizations.
• Hence ‘the backbone of’ should be used in place of ‘the backing bone in’ to make the sentence grammatically correct.
• Among the given choices, only option 3 replaces the given bold part most appropriately.
• Hence the correct answer is Option 3.

The correct sentence is: BJP is the country's only political party with a trained political human resource, which will serve as the backbone of the organization’s workforce in the coming years.

The correct answer is 'Sterile'.

Key Points

• The term 'prolific' means producing many works, results, or offspring, usually with the implication of them being high quality. It implies abundance. (उपजाऊ)
• Example: He was a prolific writer, producing dozens of novels and hundreds of short stories.
• The term 'Sterile' means not able to produce children, young animals, or plant seeds. In a more figurative sense, it might mean unproductive or not producing results. (बांझ)
• Example: The project turned out to be sterile and didn't bring the desired outcomes.
• Hence, the correct antonym for 'prolific' is 'Sterile'.

Therefore, the correct answer is ‘Option 3’.

 Additional Information

• 'Abundant' refers to existing or available in large quantities; plentiful. (प्रचुर)
• 'Fruitful' means producing good or helpful results; productive. (उपजाऊ)
• 'Productive' refers to producing or able to produce large amounts of goods, crops, or other commodities. (उत्पादक)
• 'Plentiful' means existing in or yielding great quantities; abundant. (प्रचुर)

The correct answer is ‘To smooth over the perceived differences between India and Russia.’

Key Points

• The passage specifically notes that a substantial component of Mr. Jaishankar’s mission was to smooth over the perception of differences between the two nations.
• The visit sought to address some of the issues currently affecting the India-Russia relationship, including defence supplies and issues over payment for imports.
• Although other details were discussed during the visit, these were secondary to the primary mission of addressing perceived differences.
• Therefore, it would be accurate to say that the primary rationale for the visit was to "smooth over the perceived differences" as per option 3.

Therefore, the correct answer is ‘Option 3’.

 Additional Information

• Option 1: The negotiation of President Putin's visit to India is not mentioned as a key reason for Mr. Jaishankar’s visit.
• Option 2: While military talks could be a part of discussions, they were not the main focus, as per the passage.
• Option 4: Participation in the BRICS summit is not mentioned as a reason for this visit.
• Option 5: Ensuring swift delivery of S-400 air system units was not noted as the primary objective of the visit.

The correct answer is ‘India intends to strengthen its relationship with Russia, irrespective of outside pressure.’

Key Points

• The decision by India to continue importing Russian hydrocarbons despite sanctions from the West showcases India's intention to maintain its ties with Russia.
• It displays an effort to strengthen relationships regardless of political influences from the outside.
• The implication of the action indicates India's strategic decision to prioritize its relationship with Russia over Western opposition.
• Although other interpretations could possibly be drawn, Option 2 best reflects the inference that can be made based on the details given.

Therefore, the correct answer is ‘Option 2’.

 Additional Information

• Option 1: Although it is clear that India imports hydrocarbons from Russia, it does not necessarily mean that India is solely reliant on Russia for these imports.
• Option 3: It represents a divergence in policy from the West's approach, but it is not necessarily an outright opposition.
• Option 4: The import decision does not indicate the competence or incompetence of the Indian internal industry.
• Option 5: The action does not necessarily challenge the West's authority; it just highlights India's priorities.

The correct answer is ‘To make less severe or serious’.

Key Points

• In the context of the passage, 'smooth over' refers to Mr. Jaishankar's intention to mitigate the perceived differences or issues between India and Russia.
• Therefore, the idiom 'smooth over' means to make less severe or serious, as per option 3.
• The other options offer meanings that contradict the context in which the idiom is used in the passage.

Therefore, the correct answer is ‘Option 3’.

 Additional Information

• 'To make things worse' or 'to worsen a situation' is the opposite of 'smooth over'.
• 'To ignore or overlook' is not suitable as the context implies direct action to address and lessen issues.
• 'To incite conflict' contradicts the meaning of 'smooth over'.

The correct answer is Option 4.

 

Key Points

• Statement A: Incorrect.
• The passage states that the annual leadership summit between India and Russia has been skipped for two years, breaking the unbroken tradition from 2000-2021.
• Statement B: Correct.
• Mr. Jaishankar assured that imports of Russian hydrocarbons will rise despite the West’s Russian sanctions.
• Statement C: Correct.
• Mr. Jaishankar stated that the India-Russia relationship was the “only constant in world politics” over the last six decades.
• These statements indicate the continuous and strong bilateral relationship between India and Russia.

Therefore, the correct answer is B and C.

 

Additional Information

• Option 1: Only A.
• This is incorrect because statement A is incorrect as per the passage.
• Option 2: Only B.
• This is partially correct but incomplete, as it only includes statement B and omits the also-correct statement C.
• Option 3: A and C.
• This is incorrect because statement A is not accurate according to the passage.
• Option 5: A, B, and C.
• This is incorrect because statement A is inaccurate, even though B and C are correct.

The correct answer is ‘It refers to the alignment of India and Russia's diplomatic policies in a politically turnabout global scenario.’

Key Points

• "Geopolitical and strategic convergence" refers to shared political interests and the alignment of strategic objectives between the two countries.
• The world is "rebalancing" implies a shift in the global political scenario, with power dynamics changing among the countries.
• This suggests that despite geopolitical complexities, both India and Russia are finding common ground and aligning their strategies.
• Option 1 clearly encapsulates these points, offering a more holistic explanation.

Therefore, the correct answer is ‘Option 1’.

 Additional Information

• Option 2: The statement does not suggest a shift in nuclear power.
• Option 3: It has nothing to do with cultural affinity.
• Option 4: The phrase does not necessarily indicate strategizing against a common adversary.
• Option 5: The phrase does not refer to an economic merge.

The correct answer is ‘Eliminate’.

Key Points

• The blank is referring to the efforts by both Russia and India to address and reduce any problems, issues, or 'static' between them.
• The context of the sentence implies that the word should suggest getting rid of or lessening something negative, in this case, the 'static' or issues.
• Hence, the best word to fit in would be 'Eliminate', which speaks to the idea of completely removing or getting rid of something.
• The other options do not fit the context in the most appropriate way.

Therefore, the correct answer is ‘Option 4’.

Complete Sentence: According to Mr. Jaishankar, both Russia and India are working to eliminate any static in their relationship.

Additional Information

• 'Increase' and 'Multiply' would imply intensifying the issues, contrary to the intended meaning.
• 'Avoid' could imply temporary evasion rather than a resolution.
• 'Compmodify' is not a standard word and thus, inappropriate.

The correct answer is ‘India-Russia Relations: Standing against the Tides’.

Key Points

• The primary focus of the passage is the diplomatic efforts of India through Mr. Jaishankar’s visit and its intent to maintain its relationship with Russia despite international complications.
• Option 2, "India-Russia Relations: Standing against the Tides", rightly encapsulates this main thought and is broader to include all the key points discussed in the passage.
• It reflects the issues, intentions, and outcomes of the diplomatic relations between the nations and the strategizing amidst geopolitical dynamics.
• The other options are specific branches of the central theme and, therefore, do not holistically represent the passage.

Therefore, the correct answer is ‘Option 2’.

 Additional Information

• Option 1: The passage is not only about the unresolved issues but also covers diplomatic initiatives, agreements, and future plans.
• Option 3: The visit part is a significant aspect, but the title does not represent the geopolitical dynamics and outcomes completely.
• Option 4 and 5: They are parts of the passage but not the central theme.

The correct answer is 'C' i.e., this part of the sentence has an error.

Key Points

• In the third part of the given sentence, the plural form of the verb 'play' is incorrect.
• The subject 'machine' in the given sentence is singular.
• We know that a singular verb is used with a singular subject and a plural verb with a plural subject.
• Therefore, the singular form of the verb 'plays' should be used with the singular subject 'machine'.
• The singular form of the verb 'plays' should be used in place of the plural form of the verb 'play'.
  

Hence, the correct answer is option 3.

Correct sentence: He bought an answering machine that plays back his messages when he calls.

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Additional Information

• Subjects and verbs must agree with one another in number (singular or plural).
• Thus, if a subject is singular, its verb must also be singular; if the subject is plural, its verb must also be plural.

The correct answer is 'A' i.e., this part of the sentence has an error.

Key Points

• In the given sentence, the noun 'workforce' is not specified.
• The definite article 'the' is used before singular and plural nouns when the noun is specific.
• 'A' and 'an' are indefinite articles, which means that they refer to or introduce an unspecified noun.
• We use 'a' before a consonant sound and 'an' before a vowel sound (here, educated).
• ''No article'' is used when we refer to general ideas, plurals, or uncountable nouns.
• Therefore, the indefinite article 'an' should be used in place of the indefinite article 'a'.

Hence, the correct answer is option 1.

Correct Sentence: Moreover, an educated workforce is argued to be one of the important prerequisites for economic expansion and advancement.

Additional Information

There are three articles: a, an, and the. Articles are used before nouns or noun equivalents and are a type of adjective.

The correct answer is 'A' i.e., this part of the sentence has an error.

Key Points

• In the first part of the given sentence, the use of the preposition 'between' is incorrect.
• We use the preposition 'between' to refer to two things that are separated.
• 'Between' is used when referring to one-to-one relationships.
• Example: Negotiations between the member states collapsed last night.
• 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' means being a member or member of a larger set.
• 'Among' is used when referring to indistinct or nonspecific relationships.
• Example: There wasn’t much unity among the council members.
• Therefore, the preposition 'among' should be used in place of the preposition 'between'.
  

Hence, the correct answer is option 1.

Correct Sentence: Among the big-ticket items, one that is set to put a spell on buyers is Walt Disney’s last will.

The correct answer is 'C' i.e., this part of the sentence has an error.

Key Points

• In the third part of the given sentence, the plural form of the verb 'are' is incorrect.
• The phrase ''One of'' 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'' is always in the plural form (as we are talking of one person/place/thing out of many).
• But the helping verb will always be in the singular form (here, is), as the helping verb agrees with ''one of'' and not with the plural noun in the sentence.
• Therefore, the singular form of the verb 'is' should be used in place of the plural form of the verb 'are'.
  

Hence, the correct answer is option 3.

Correct sentence: One of the most striking and salutary things in American life is the widespread study of law.

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Additional Information

• Subjects and verbs must agree with one another in number (singular or plural).
• Thus, if a subject is singular, its verb must also be singular; if the subject is plural, its verb must also be plural.

General solution:

 

Company A:

Number of two wheelers and four wheelers manufactured = 400

Number of two wheelers and four wheelers sold = 250

Number of two wheelers and four wheelers unsold = (400 - 250) = 150

 

Company B:

Number of two wheelers and four wheelers manufactured = 450

Number of two wheelers and four wheelers sold = 100

Number of two wheelers and four wheelers unsold = (450 - 100) = 350

 

Company C:

Number of two wheelers and four wheelers manufactured = 500

Number of two wheelers and four wheelers sold = 200

Number of two wheelers and four wheelers unsold = (500 - 200) = 300

 

Company D:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 300

Number of two wheelers and four wheelers unsold = (550 - 300) = 250

 

Company E:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 350

Number of two wheelers and four wheelers unsold = (550 - 350) = 200

 

 

Solution:

Average of two wheelers and four wheelers sold = (250 + 100 + 200 + 300 + 350)/5 = 240

Average of two wheelers and four wheelers unsold = (150 + 350 + 300 + 250 + 200)/5 = 250

Required difference = (250 - 240) = 10

General solution:

 

Company A:

Number of two wheelers and four wheelers manufactured = 400

Number of two wheelers and four wheelers sold = 250

Number of two wheelers and four wheelers unsold = (400 - 250) = 150

 

Company B:

Number of two wheelers and four wheelers manufactured = 450

Number of two wheelers and four wheelers sold = 100

Number of two wheelers and four wheelers unsold = (450 - 100) = 350

 

Company C:

Number of two wheelers and four wheelers manufactured = 500

Number of two wheelers and four wheelers sold = 200

Number of two wheelers and four wheelers unsold = (500 - 200) = 300

 

Company D:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 300

Number of two wheelers and four wheelers unsold = (550 - 300) = 250

 

Company E:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 350

Number of two wheelers and four wheelers unsold = (550 - 350) = 200

 

 

Solution:

Number of four wheelers sold in company E = 350/7 ×  4 = 200

Number of two wheelers sold in company E = (350 - 200) = 150

Number of maruti four wheelers sold = 200 ×  30/100 = 60

Number of Tata four wheelers sold = (200 - 60) = 140

Number of  KTM two wheelers sold = 150 ×  (40/100) = 60

Required total = (140 + 60) = 200

General solution:

 

Company A:

Number of two wheelers and four wheelers manufactured = 400

Number of two wheelers and four wheelers sold = 250

Number of two wheelers and four wheelers unsold = (400 - 250) = 150

 

Company B:

Number of two wheelers and four wheelers manufactured = 450

Number of two wheelers and four wheelers sold = 100

Number of two wheelers and four wheelers unsold = (450 - 100) = 350

 

Company C:

Number of two wheelers and four wheelers manufactured = 500

Number of two wheelers and four wheelers sold = 200

Number of two wheelers and four wheelers unsold = (500 - 200) = 300

 

Company D:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 300

Number of two wheelers and four wheelers unsold = (550 - 300) = 250

 

Company E:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 350

Number of two wheelers and four wheelers unsold = (550 - 350) = 200

 

 

Solution:

Number of four wheelers unsold in company D = 70/100 ×  250 = 175

Number of two wheelers unsold in company D = (250 - 175) = 75

Number of four wheelers unsold in company E = (175 + 5) = 180

Number of two wheelers unsold in company E = (200 - 180) = 20

Required sum = (75 + 20) = 95

General solution:

 

Company A:

Number of two wheelers and four wheelers manufactured = 400

Number of two wheelers and four wheelers sold = 250

Number of two wheelers and four wheelers unsold = (400 - 250) = 150

 

Company B:

Number of two wheelers and four wheelers manufactured = 450

Number of two wheelers and four wheelers sold = 100

Number of two wheelers and four wheelers unsold = (450 - 100) = 350

 

Company C:

Number of two wheelers and four wheelers manufactured = 500

Number of two wheelers and four wheelers sold = 200

Number of two wheelers and four wheelers unsold = (500 - 200) = 300

 

Company D:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 300

Number of two wheelers and four wheelers unsold = (550 - 300) = 250

 

Company E:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 350

Number of two wheelers and four wheelers unsold = (550 - 350) = 200

 

 

Solution:

Number of vehicles sold to males  by company B = 100/5 ×  3= 60

Number of vehicles  sold to females  by company B  = (100 - 60) = 40

Number of vehicles sold to males by company C  = 200/5 ×  4 = 160

Number of vehicles sold to females by company C = (200 - 160) = 40

Required difference = (160 + 60): (80) = 220: 80 = 11: 4

General solution:

 

Company A:

Number of two wheelers and four wheelers manufactured = 400

Number of two wheelers and four wheelers sold = 250

Number of two wheelers and four wheelers unsold = (400 - 250) = 150

 

Company B:

Number of two wheelers and four wheelers manufactured = 450

Number of two wheelers and four wheelers sold = 100

Number of two wheelers and four wheelers unsold = (450 - 100) = 350

 

Company C:

Number of two wheelers and four wheelers manufactured = 500

Number of two wheelers and four wheelers sold = 200

Number of two wheelers and four wheelers unsold = (500 - 200) = 300

 

Company D:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 300

Number of two wheelers and four wheelers unsold = (550 - 300) = 250

 

Company E:

Number of two wheelers and four wheelers manufactured = 550

Number of two wheelers and four wheelers sold = 350

Number of two wheelers and four wheelers unsold = (550 - 350) = 200

 

<br>

Solution:

Number of two wheelers sold in company A = 250 ×  (30/100) = 75

Number of four wheelers sold in company A = (250 - 75) = 175

Number of four wheelers unsold in company A = 150 ×  40/100 = 60

Number of two wheelers unsold in company A = (150 - 60) = 90

Number of two wheelers manufactured = (90 + 75) = 165

Number of four wheelers manufactured = (175 + 60) = 235

Required difference = (235 - 165) = 70

Shortcut Trick

Ratio of Height (h) to Radius (r) = 2 : 1. Let h = 2x and r = x.

Total Surface Area (TSA) = 2πr(r + h) = 2 × (22/7) × x × (x + 2x) = 924.

⇒ (44/7) × 3x² = 924 ⇒ x² = 49 ⇒ x = 7 cm.

Volume = πr²h = (22/7) × 7² × 14 = 22 × 7 × 14 = 2156 cm³.

∴ The correct answer is 2156 cm³.

Alternate Method

Given: Ratio of height to radius = 2 : 1, TSA = 924 cm².

Formula Used: TSA = 2πr(h + r); Volume = πr²h

⇒ Let Radius (r) = x and Height (h) = 2x.

⇒ 2 × (22/7) × x × (2x + x) = 924

⇒ 2 × (22/7) × 3x² = 924

⇒ (132/7) × x² = 924

⇒ x² = (924 × 7) ÷ 132

⇒ x² = 7 × 7 = 49 ⇒ x = 7 cm.

⇒ Radius (r) = 7 cm, Height (h) = 14 cm.

⇒ Volume = (22/7) × 7 × 7 × 14

⇒ Volume = 22 × 7 × 14 = 2156 cm³.

∴ The correct answer is 2156 cm³.

Additional Information

Curved Surface Area of Cylinder

The area of the side surface of the cylinder is given by CSA = 2πrh.

Volume of Hollow Cylinder

If R is outer radius and r is inner radius, Volume = π(R² − r²)h.

Base Area of Cylinder

The base of a right circular cylinder is a circle, so Base Area = πr².

Shortcut Trick

Approximate Total mixture = 80 litres, Water = 20%, Milk = 80%.

Mixture remaining after 25% removal = 80 × 0.75 = 60 litres.

Remaining Milk = 80% of 60 = 48 litres; Remaining Water = 20% of 60 = 12 litres.

Final ratio 12:5 means 12 units = 48 litres ⇒ 1 unit = 4 litres.

Required Water = 5 units = 5 × 4 = 20 litres. Added Water = 20 − 12 = 8 litres.

∴ The correct answer is 8 litres.

Alternate Method

Given: Total Mixture ≈ 80 litres, Water ≈ 20.13% ≈ 20%, Removal ≈ 25%.

Step 1: Calculate initial quantities in litres.

⇒ Total mixture = 80 litres.

⇒ Water = 20% of 80 = 16 litres.

⇒ Milk = 80 − 16 = 64 litres.

Step 2: Calculate remaining quantities after taking out 25% of mixture.

⇒ Milk remaining = 64 − (25% of 64) = 64 − 16 = 48 litres.

⇒ Water remaining = 16 − (25% of 16) = 16 − 4 = 12 litres.

Step 3: Let x be the quantity of water added.

⇒ Milk : (Water + x) = 12 : 5

⇒ 48 / (12 + x) = 12 / 5

⇒ 4 / (12 + x) = 1 / 5

⇒ 20 = 12 + x

⇒ x = 20 − 12 = 8 litres.

∴ The correct answer is 8 litres.

Additional Information

Mixture Removal Property

When a portion of a mixture is removed, the ratio of components in the remaining mixture stays the same as the initial ratio.

Mixtures & Alligations

For replacement problems, Quantity left = Initial Quantity × (1 − Removed/Total)ⁿ, where n is the number of operations.

Approximation Rule

In banking exams, values like 79.99 or 20.13% should be rounded to the nearest whole number (80 and 20%) to speed up calculations.

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

12.98 + 417.98 = 34.98 × 19.98 - ?2 - 99.99

13 + 418 = 35 × 20 - ?2 - 100

⇒ 13 + 418 = 700 - ?2 - 100

⇒ 431 = 700 - ?2 - 100

⇒ ?2 = 700 - 431 - 100

⇒ ? = √169 = 13

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

44.99% of 399.99 + 49.99% of 299.99 = ? + 69.99% of 199.99

⇒ 45% of 400 + 50% of 300 = ? + 70% of 200

⇒ 180 + 150 = ? + 140

⇒ 330 = ? + 140

∴ ? = 190

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

[12.935 ÷ 12.984] × [13.033 ÷ 13.136] = 12.83(? – 4)

⇒ [135 ÷ 134] × [133 ÷ 136] = 13(? – 4)

⇒ 13 × 13-3 = 13(? – 4)

⇒ 13-2 = 13(? – 4)

⇒ ? - 4 = -2

⇒ ? = 2

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

(124.95 × 5.98) – (110.02 × 7.96) + 669.95 = ? × 8.99

⇒ (125 × 6) – (110 × 8) + 670 = ? × 9

⇒ 750 – 880 + 670 = ? × 9

⇒ 1420 – 880 = ? × 9

⇒ 540 = ? × 9

∴ ? = 60

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

349.99 – [15.952 – (87.88 + 95.94) ÷ 7.99] = ?

⇒ 350 – [162 – (88 + 96) ÷ 8] = ?

⇒ 350 – [162 – 184 ÷ 8] = ?

⇒ 350 – [162 – 23] = ?

⇒ 350 – [256 – 23] = ?

⇒ 350 – 233 = ?

∴ ? = 117

Shortcut Trick

Effective Compound Interest rate for 2 years at 11% = 11 + 11 + (11 × 11)/100 = 23.21%.

First Interest amount = 23.21% of ₹20000 = ₹4642.

Simple Interest on second investment = (4642 × 11 × 2) / 100 = 4642 × 0.22 = ₹1021.24.

∴ The correct answer is ₹1021.24.

Alternate Method

Given: Principal (P₁) = ₹20000, Rate (R) = 11%, Time (T) = 2 years.

Formula Used: CI = P[(1 + R/100)^T − 1]; SI = (P × R × T) / 100.

⇒ 1st Interest (CI) = 20000 × [(1 + 11/100)² − 1]

⇒ CI = 20000 × [1.2321 − 1] = 20000 × 0.2321 = ₹4642.

⇒ 2nd Principal (P₂) = 1st Interest = ₹4642.

⇒ SI received = (4642 × 11 × 2) / 100

⇒ SI = (4642 × 22) / 100 = 102124 / 100 = ₹1021.24.

∴ The correct answer is ₹1021.24.

Additional Information

Effective Rate of Compound Interest

For 2 years, the net percentage change formula (x + y + xy/100) provides the effective CI rate relative to the principal.

Simple Interest vs Compound Interest

While SI is calculated only on the principal, CI is calculated on the principal plus the accumulated interest of previous periods.

CI − SI Difference for 2 years

The difference between CI and SI for 2 years is given by the formula P(R/100)².

Shortcut Trick

Difference in percentage marks = 45% − 25% = 20%

Difference in actual marks = 50 − (−25) = 75 marks

20% of Maximum Marks = 75 marks

100% of Maximum Marks = 75 × 5 = 375 marks

∴ The correct answer is 375.

Alternate Method

Given: Ram score = 25%, Shyam score = 45%, Marks gap = 25 (fail) and 50 (extra).

Let Maximum Marks be M.

Passing Marks = 25% of M + 25

Passing Marks = 45% of M − 50

⇒ 25% of M + 25 = 45% of M − 50

⇒ 45% of M − 25% of M = 50 + 25

⇒ 20% of M = 75

⇒ (20/100) × M = 75

⇒ M = (75 × 100) ÷ 20

⇒ M = 375

∴ The correct answer is 375.

Additional Information

Passing Percentage

To find the passing percentage, substitute M back into the passing marks equation: (25% × 375 + 25) ÷ 375 × 100 = 31.66%.

Percentage Change Base

In examination problems, the Maximum Marks always acts as the base (100%) for calculating scored or passing percentages.

Successive Percentage

For problems involving repeated changes, use the net effect formula: a + b + (ab/100).

Solution:

 

School A:

Total number of students (Male + Female) attend interview = 700

Number of female attend interview = 700 ×  (40/100) = 280

Number of males attend interview = (700 - 280) = 420

Number of males selected in interview = 350

Number of males unselected in interview = 420 - 350 = 70

Total number students selected in interview = 500

Number of females selected in interview = 500 - 350 =150

Number of females unselected in interview = 280 - 150 = 130

 

School B:

Total number of students (Male + Female) attend interview = 650

Number of female attend interview = 650 ×  (60/100) = 390

Number of males attend interview = (650 - 390) = 260

Number of males selected in interview = 250

Number of males unselected in interview = 260 - 250 = 10

Total number students selected in interview = 400

Number of females selected in interview = 400 - 250 =150

Number of females unselected in interview = 390 - 150 = 240

 

School C:

Total number of students (Male + Female) attend interview = 750

Number of female attend interview = 750 ×  (30/100) = 225

Number of males attend interview = (750 - 225) = 525

Number of males selected in interview = 300

Number of males unselected in interview = 525 - 300 = 225

Total number students selected in interview = 450

Number of females selected in interview = 450 - 300 =150

Number of females unselected in interview = 225 - 150 = 75

 

School D:

Total number of students (Male + Female) attend interview = 800

Number of female attend interview = 800 ×  (45/100) = 360

Number of males attend interview = (800 - 360) = 440

Number of males selected in interview = 325

Number of males unselected in interview = 440 - 325 = 115

Total number students selected in interview = 550

Number of females selected in interview = 550 - 325 =225

Number of females unselected in interview = 360 - 225 = 135

 

School E:

Total number of students (Male + Female) attend interview = 900

Number of female attend interview = 900 ×  (55/100) = 495

Number of males attend interview = (900 - 495) = 405

Number of males selected in interview = 300

Number of males unselected in interview = 405 - 300 = 105

Total number students selected in interview = 600

Number of females selected in interview = 600 - 300 = 300

Number of females unselected in interview = 495 - 300 = 195

 

 

Solution:

Number of females selected from school A from city P= 150 ×  1/3 = 50

Number of females selected from school A from city Q = (150 - 50) = 100

Number of females selected from school B from city P = 150 ×  1/5 = 30

Number of females selected from school B from city Q = 150 - 30 = 120 

Number of males selected from school A from city Q = 350 ×  1/7 = 50

Number of males selected from school B from city Q = 250 ×  1/10 = 25

Required total = (100 + 120 + 50 + 25) = 295

Solution:

 

School A:

Total number of students (Male + Female) attend interview = 700

Number of female attend interview = 700 ×  (40/100) = 280

Number of males attend interview = (700 - 280) = 420

Number of males selected in interview = 350

Number of males unselected in interview = 420 - 350 = 70

Total number students selected in interview = 500

Number of females selected in interview = 500 - 350 =150

Number of females unselected in interview = 280 - 150 = 130

 

School B:

Total number of students (Male + Female) attend interview = 650

Number of female attend interview = 650 ×  (60/100) = 390

Number of males attend interview = (650 - 390) = 260

Number of males selected in interview = 250

Number of males unselected in interview = 260 - 250 = 10

Total number students selected in interview = 400

Number of females selected in interview = 400 - 250 =150

Number of females unselected in interview = 390 - 150 = 240

 

School C:

Total number of students (Male + Female) attend interview = 750

Number of female attend interview = 750 ×  (30/100) = 225

Number of males attend interview = (750 - 225) = 525

Number of males selected in interview = 300

Number of males unselected in interview = 525 - 300 = 225

Total number students selected in interview = 450

Number of females selected in interview = 450 - 300 =150

Number of females unselected in interview = 225 - 150 = 75

 

School D:

Total number of students (Male + Female) attend interview = 800

Number of female attend interview = 800 ×  (45/100) = 360

Number of males attend interview = (800 - 360) = 440

Number of males selected in interview = 325

Number of males unselected in interview = 440 - 325 = 115

Total number students selected in interview = 550

Number of females selected in interview = 550 - 325 =225

Number of females unselected in interview = 360 - 225 = 135

 

School E:

Total number of students (Male + Female) attend interview = 900

Number of female attend interview = 900 ×  (55/100) = 495

Number of males attend interview = (900 - 495) = 405

Number of males selected in interview = 300

Number of males unselected in interview = 405 - 300 = 105

Total number students selected in interview = 600

Number of females selected in interview = 600 - 300 = 300

Number of females unselected in interview = 495 - 300 = 195

 

Solution:

Average number of males selected = (350 + 250 + 300 + 325 + 300)/5 = 305

Total females selected from all the schools = (150 + 150 + 150 + 225 + 300) = 975

Required percentage = 305/975 × 100 = 31.28%

Solution:

 

School A:

Total number of students (Male + Female) attend interview = 700

Number of female attend interview = 700 ×  (40/100) = 280

Number of males attend interview = (700 - 280) = 420

Number of males selected in interview = 350

Number of males unselected in interview = 420 - 350 = 70

Total number students selected in interview = 500

Number of females selected in interview = 500 - 350 =150

Number of females unselected in interview = 280 - 150 = 130

 

School B:

Total number of students (Male + Female) attend interview = 650

Number of female attend interview = 650 ×  (60/100) = 390

Number of males attend interview = (650 - 390) = 260

Number of males selected in interview = 250

Number of males unselected in interview = 260 - 250 = 10

Total number students selected in interview = 400

Number of females selected in interview = 400 - 250 =150

Number of females unselected in interview = 390 - 150 = 240

 

School C:

Total number of students (Male + Female) attend interview = 750

Number of female attend interview = 750 ×  (30/100) = 225

Number of males attend interview = (750 - 225) = 525

Number of males selected in interview = 300

Number of males unselected in interview = 525 - 300 = 225

Total number students selected in interview = 450

Number of females selected in interview = 450 - 300 =150

Number of females unselected in interview = 225 - 150 = 75

 

School D:

Total number of students (Male + Female) attend interview = 800

Number of female attend interview = 800 ×  (45/100) = 360

Number of males attend interview = (800 - 360) = 440

Number of males selected in interview = 325

Number of males unselected in interview = 440 - 325 = 115

Total number students selected in interview = 550

Number of females selected in interview = 550 - 325 =225

Number of females unselected in interview = 360 - 225 = 135

 

School E:

Total number of students (Male + Female) attend interview = 900

Number of female attend interview = 900 ×  (55/100) = 495

Number of males attend interview = (900 - 495) = 405

Number of males selected in interview = 300

Number of males unselected in interview = 405 - 300 = 105

Total number students selected in interview = 600

Number of females selected in interview = 600 - 300 = 300

Number of females unselected in interview = 495 - 300 = 195

 

 

Solution:

Number of males selected for TCS from school C = 300 ×  1/6 = 50

Number of females selected for TCS from school C = 150 ×  1/5 = 30

Required total = (50 + 30) = 80

Solution:

 

School A:

Total number of students (Male + Female) attend interview = 700

Number of female attend interview = 700 ×  (40/100) = 280

Number of males attend interview = (700 - 280) = 420

Number of males selected in interview = 350

Number of males unselected in interview = 420 - 350 = 70

Total number students selected in interview = 500

Number of females selected in interview = 500 - 350 =150

Number of females unselected in interview = 280 - 150 = 130

 

School B:

Total number of students (Male + Female) attend interview = 650

Number of female attend interview = 650 ×  (60/100) = 390

Number of males attend interview = (650 - 390) = 260

Number of males selected in interview = 250

Number of males unselected in interview = 260 - 250 = 10

Total number students selected in interview = 400

Number of females selected in interview = 400 - 250 =150

Number of females unselected in interview = 390 - 150 = 240

 

School C:

Total number of students (Male + Female) attend interview = 750

Number of female attend interview = 750 ×  (30/100) = 225

Number of males attend interview = (750 - 225) = 525

Number of males selected in interview = 300

Number of males unselected in interview = 525 - 300 = 225

Total number students selected in interview = 450

Number of females selected in interview = 450 - 300 =150

Number of females unselected in interview = 225 - 150 = 75

 

School D:

Total number of students (Male + Female) attend interview = 800

Number of female attend interview = 800 ×  (45/100) = 360

Number of males attend interview = (800 - 360) = 440

Number of males selected in interview = 325

Number of males unselected in interview = 440 - 325 = 115

Total number students selected in interview = 550

Number of females selected in interview = 550 - 325 =225

Number of females unselected in interview = 360 - 225 = 135

 

School E:

Total number of students (Male + Female) attend interview = 900

Number of female attend interview = 900 ×  (55/100) = 495

Number of males attend interview = (900 - 495) = 405

Number of males selected in interview = 300

Number of males unselected in interview = 405 - 300 = 105

Total number students selected in interview = 600

Number of females selected in interview = 600 - 300 = 300

Number of females unselected in interview = 495 - 300 = 195

 

 

Solution:

Average number of unselected females = (130 + 240 + 75 + 135 + 195)/5 = 155

Average number of unselected males = (70 + 10 + 225 + 115 + 105)/5 = 105

Required difference = (155 - 105) = 50

Solution:

 

School A:

Total number of students (Male + Female) attend interview = 700

Number of female attend interview = 700 ×  (40/100) = 280

Number of males attend interview = (700 - 280) = 420

Number of males selected in interview = 350

Number of males unselected in interview = 420 - 350 = 70

Total number students selected in interview = 500

Number of females selected in interview = 500 - 350 =150

Number of females unselected in interview = 280 - 150 = 130

 

School B:

Total number of students (Male + Female) attend interview = 650

Number of female attend interview = 650 ×  (60/100) = 390

Number of males attend interview = (650 - 390) = 260

Number of males selected in interview = 250

Number of males unselected in interview = 260 - 250 = 10

Total number students selected in interview = 400

Number of females selected in interview = 400 - 250 =150

Number of females unselected in interview = 390 - 150 = 240

 

School C:

Total number of students (Male + Female) attend interview = 750

Number of female attend interview = 750 ×  (30/100) = 225

Number of males attend interview = (750 - 225) = 525

Number of males selected in interview = 300

Number of males unselected in interview = 525 - 300 = 225

Total number students selected in interview = 450

Number of females selected in interview = 450 - 300 =150

Number of females unselected in interview = 225 - 150 = 75

 

School D:

Total number of students (Male + Female) attend interview = 800

Number of female attend interview = 800 ×  (45/100) = 360

Number of males attend interview = (800 - 360) = 440

Number of males selected in interview = 325

Number of males unselected in interview = 440 - 325 = 115

Total number students selected in interview = 550

Number of females selected in interview = 550 - 325 =225

Number of females unselected in interview = 360 - 225 = 135

 

School E:

Total number of students (Male + Female) attend interview = 900

Number of female attend interview = 900 ×  (55/100) = 495

Number of males attend interview = (900 - 495) = 405

Number of males selected in interview = 300

Number of males unselected in interview = 405 - 300 = 105

Total number students selected in interview = 600

Number of females selected in interview = 600 - 300 = 300

Number of females unselected in interview = 495 - 300 = 195

 

Solution:

Number of females attending interview from school A from section I = 280 × (2/7) = 80

Number of female selected from school A from section I = 150 × (1/5) = 30

Number of females Unselected from school A from section I = (80 - 30) = 50

Shortcut Trick

Let the number of books read on Tuesday be x.

According to the given deviations: Monday = x + 10 and Wednesday = x − 10.

The Average of these three days is simply the middle value (Tuesday) because they are in an Arithmetic Progression with a common difference of 10.

∴ Tuesday = Average = 20 books.

Monday = 20 + 10 = 30 and Wednesday = 20 − 10 = 10.

∴ The correct answer is 30, 20 and 10.

Alternate Method

Given: Average = 20 books, Days = 3.

Formula Used: Total Sum = Average × Number of entities.

⇒ Total books = 20 × 3 = 60.

⇒ Let books on Tuesday = x.

⇒ Monday = x + 10, Wednesday = x − 10.

⇒ (x + 10) + x + (x − 10) = 60.

⇒ 3x = 60 ⇒ x = 20.

⇒ Monday = 20 + 10 = 30; Tuesday = 20; Wednesday = 20 − 10 = 10.

∴ The correct answer is 30, 20 and 10.

Additional Information

Average in Arithmetic Progression

If terms are in AP, the Average is always the Middle Term (for odd number of terms) or the mean of the two middle terms.

Average Change Rule

If each observation is increased or decreased by a constant k, the Average also increases or decreases by k.

Shortcut Trick

Ratio of Profit Share is determined by the ratio of Investment × Time.

Effective investment of P = (50 × 7) + (30 × 5) = 350 + 150 = 500 units.

Effective investment of Q = (75 × 7) + (80 × 5) = 525 + 400 = 925 units.

Profit ratio P : Q = 500 : 925 = 20 : 37.

Share of P = 20 ÷ (20 + 37) × 1,10,000 = 20 ÷ 57 × 1,10,000 ≈ 38,596.49.

∴ The correct answer is Rs. 38,597.

Alternate Method

Given → P initial = Rs. 50,000; Q initial = Rs. 75,000; Time = 12 months; Total Profit = Rs. 1,10,000. Formulas: Profit Ratio = (I₁ × T₁) : (I₂ × T₂) | Profit Share = (Ratio Part ÷ Total Parts) × Total Profit.

⇒ P total investment units = (50,000 × 7) + (30,000 × 5) = 3,50,000 + 1,50,000 = 5,00,000. ⇒ Q total investment units = (75,000 × 7) + (80,000 × 5) = 5,25,000 + 4,00,000 = 9,25,000. ⇒ Ratio P : Q = 5,00,000 : 9,25,000 = 500 : 925 = 20 : 37. ⇒ Total units = 20 + 37 = 57 units. ⇒ Share of P = (20 ÷ 57) × 1,10,000 ≈ Rs. 38,596.49.

∴ The correct answer is Rs. 38,597.

Additional Information

Partnership Basics

In a compound partnership, the profit is shared based on the product of the capital and the duration of investment.

Active vs Sleeping Partner

An active partner manages the business and may receive a salary or extra profit, while a sleeping partner only provides capital.

Given:

I. x2 – 10x + 25 = 0

II. y2 + 10y + 24 = 0

Calculation:

I. x2 – 10x + 25 = 0

⇒ x^{2 -} 5x - 5x + 25 = 0

⇒ x(x - 5) - 5(x - 5)= 0

⇒ (x - 5)(x - 5) = 0

⇒ x = 5, 5

II. y2 + 10y + 24 = 0

⇒ y² + 6y + 4y + 24 = 0

⇒ y(y + 6) + 4(y + 6) =0

⇒ (y + 6)(y + 4) = 0

⇒ y = (-6), (-4)

 

When we compared the values of ‘x’ and ‘y’ in the table above, we found that there is only ONE relation between X and Y i.e. >. So, a relation between x and y is “x > y”.

∴ After comparison, all the values of x and y the relation is “x > y”.

<br>

Shortcut Trick

I. x2 - 10x + 25 = 0

There are three terms = a, b, and c

Where 'a' = value of x², 'b' = Value of x, 'c' = 25

If value of 'c' is positive value and value of 'b' is negative value, then both the values of x is POSITIVE value.

II. y2 + 10y + 24 = 0

There are also three terms = a, b, and c

Where 'a' = value of y², 'b' = Value of y, 'c' = 24

If the value of 'c' is a positive value and the value of 'b' is also a positive value, then both value of y is NEGATIVE value.

∴ After comparison, all the values of x and y, the relation between x and y is "x > y".

Given:

I. 7x2 - 4x - 51 = 0

II. y2 - 24y + 143 = 0

Calculation:

From I,

7x2 - 4x - 51 = 0

⇒ 7x2 - 21x + 17x - 51 = 0

⇒ 7x(x - 3) + 17(x - 3) = 0

⇒ (x - 3)(7x + 17) = 0

Taking,

⇒ (x - 3) = 0 or (7x + 17) = 0

⇒ x = 3 or (-17/7)

From II,

y2 - 24y + 143 = 0

⇒ y2 - 11y - 13y + 143 = 0

⇒ y(y - 11) - 13(y - 11) = 0

⇒ (y - 11)(y - 13) = 0

Taking,

⇒ (y - 11) = 0 or (y - 13) = 0

⇒ y = 11 or 13

Comparison between x and y (via Tabulation):

 

∴ x < y.

Given:

I. 2x2 - 17x + 36 = 0

II. y2 + 10y + 24 = 0

Calculation:

From I

2x2 - 17x + 36 = 0

⇒ 2x² - 8x - 9x + 36 = 0

⇒ 2x(x - 4) - 9(x - 4) = 0

⇒ (x - 4)(2x - 9) = 0

⇒ x = 4, 9/2

From II

y2 + 10y + 24 = 0

⇒ y² + 6y + 4y + 24 = 0

⇒ y(y + 6) + 4(y + 6) = 0

⇒ (y + 6)(y + 4) = 0

⇒ y = -6, -4

Comparison between x and y (via Tabulation) 

 

∴ x > y

Important Points

 

Shortcut Trick

If ax2 - bx + c = 0  then roots will be always +ve

If ax2 + bx + c = 0  then roots will be always -ve

So, without solving the equations we can say the answer.

I. 3x² + 2x – 8 = 0

⇒ 3x² + 6x – 4x – 8 = 0

⇒ 3x(x + 2) – 4(x + 2) = 0

⇒ (3x – 4) (x + 2) = 0

⇒ x = 4/3 or -2

II. 3y² – 14y + 16 = 0

⇒ 3y² – 6y – 8y + 16 = 0

⇒ 3y(y – 2) – 8(y – 2) = 0

⇒ (3y – 8) (y – 2) = 0

⇒ y = 8/3 or 2

∴ x < y

Equation I:

x2 – 12x + 11 = 0

⇒ x2 – x – 11x + 11 = 0

⇒ (x – 11) (x – 1) = 0

⇒ x = 11 or x = 1

Equation II:

3y2 + 12y + 9 = 0

⇒ 3y2 + 3y + 9y + 9 = 0

⇒ (3y + 9) (y + 1) = 0

⇒ y = - 3 or y = - 1

Comparing the values of x and y we get,

x > y

Shortcut Trick

Speed = 72 kmph = 72 × 5/18 = 20 m/s.

Distance 1 (T + P) = 20 × 30 = 600 m.

Distance 2 (T + 3P) = 20 × 45 = 900 m.

Subtracting both: (T + 3P) − (T + P) = 2P = 900 − 600 = 300 m ⇒ P = 150 m.

Length of train (T) = 600 − 150 = 450 m.

∴ The correct answer is 450 m.

Alternate Method

Given:

Speed of train = 72 kmph

Time to cross platform 1 (P₁) = 30 sec

Time to cross platform 2 (P₂ = 3P₁) = 45 sec

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Speed in m/s = 72 × (5/18) = 20 m/s

⇒ Let length of train be L and length of first platform be P

⇒ L + P = 20 × 30 = 600 m ----(Eq 1)

⇒ L + 3P = 20 × 45 = 900 m ----(Eq 2)

⇒ (Eq 2) − (Eq 1) ⇒ 2P = 300

⇒ P = 150 m

⇒ Substitute P in Eq 1: L + 150 = 600

⇒ L = 600 − 150 = 450 m

∴ The correct answer is 450 m.

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.

Relative Speed

When two objects move in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Crossing Objects

When a train crosses a platform/bridge, total distance = Length of train + Length of platform.

Shortcut Trick

Total Capacity (LCM of 9, 15, 25) = 225 units.

Efficiencies: A = 25, B = 15, C = −9.

Work done: A (4 hrs) + B (3 hrs) + C (10 hrs) = (25 × 4) + (15 × 3) − (9 × 10).

Filled part = 55 ÷ 225 = 11/45.

∴ The correct answer is 11/45.

Alternate Method

Given:

Pipe A is opened for 4 hours.

Pipe B is closed 1 hour before Pipe A ⇒ 4 − 1 = 3 hours.

Pipe C is opened for 10 hours.

Calculations:

⇒ Water filled by A = 25 × 4 = 100 units

⇒ Water filled by B = 15 × 3 = 45 units

⇒ Water emptied by C = 9 × 10 = 90 units

⇒ Net water filled = 100 + 45 − 90 = 55 units

⇒ Part of tank filled = 55 ÷ 225

⇒ Simplified fraction = 11/45

∴ The correct answer is 11/45.

Additional Information

Pipes and Cisterns Concept

Efficiency of an inlet pipe is taken as positive (+), while the efficiency of an outlet (leakage) pipe is taken as negative (−).

Work-Time Relationship

Total Work = Efficiency × Time. The part filled is the ratio of actual units filled to the total capacity of the tank.

General Solution:

 

Total number of managers (Male + Female) in company X = 90

Number of male managers in company X= 90/9 ×  5 = 50

Number of female managers in company X = 90 - 50 = 40

Number of female clerks working in Company X is 10 less than the total number of managers working in company X 

Number of female clerks working in Company X = (90 - 10) = 80

Number of male clerks working in company X = 80/8 ×  9 = 90

Number of male managers working in company Z = (x + 10)

Number of female managers working in company Z = x

Total number of managers in company Z is the same as the number of female clerks in company X

Number of managers in company Z = 80

x + x + 10 = 80

2x = 70

x = 35

Number of male managers in company Z = (35 + 10) = 45

Number of female managers in company Z = 35

Number of male clerks in company Z is 10 more than the number of male clerks in company X

Number of male clerks in company Z = 90 + 10 = 100

Number of female clerks in company Z = 165 - 100 = 65

Average number of male and female managers in company Z is the same as the number of female clerks in company Y which is 30 less than that of males in the same company.

Number of female clerks in company Y = (45 + 35)/2 = 80/2 = 40

Number of male clerks in company Y = (40 + 30) = 70

Number of male managers to female managers in company Y are in the ratio 4: 5

Number of male managers in company Y = 4 ×  15 = 60

Number of female managers in company Y = 5 ×  15 = 75

 

 

Solution:

Number of male clerks in company X = 90

Number of male clerks in company Y = 70

Total female clerks in all the company = (80 + 40 + 65)

Required percentage = (160/185) ×  100 = 86.48%

General Solution:

 

Total number of managers (Male + Female) in company X = 90

Number of male managers in company X= 90/9 ×  5 = 50

Number of female managers in company X = 90 - 50 = 40

Number of female clerks working in Company X is 10 less than the total number of managers working in company X 

Number of female clerks working in Company X = (90 - 10) = 80

Number of male clerks working in company X = 80/8 ×  9 = 90

Number of male managers working in company Z = (x + 10)

Number of female managers working in company Z = x

Total number of managers in company Z is the same as the number of female clerks in company X

Number of managers in company Z = 80

x + x + 10 = 80

2x = 70

x = 35

Number of male managers in company Z = (35 + 10) = 45

Number of female managers in company Z = 35

Number of male clerks in company Z is 10 more than the number of male clerks in company X

Number of male clerks in company Z = 90 + 10 = 100

Number of female clerks in company Z = 165 - 100 = 65

Average number of male and female managers in company Z is the same as the number of female clerks in company Y which is 30 less than that of males in the same company.

Number of female clerks in company Y = (45 + 35)/2 = 80/2 = 40

Number of male clerks in company Y = (40 + 30) = 70

Number of male managers to female managers in company Y are in the ratio 4: 5

Number of male managers in company Y = 4 ×  15 = 60

Number of female managers in company Y = 5 ×  15 = 75

 

 

Solution:

Male managers in company Z = 45 ×  120/100 = 54

Female managers in company Z = 35 ×  140/100 = 49

Total male managers in all companies = (50 + 60  + 54) = 164

Total female managers in all companies = (40 + 75 + 49) = 164

Required difference = (164 - 164) = 0

General Solution:

 

Total number of managers (Male + Female) in company X = 90

Number of male managers in company X= 90/9 ×  5 = 50

Number of female managers in company X = 90 - 50 = 40

Number of female clerks working in Company X is 10 less than the total number of managers working in company X 

Number of female clerks working in Company X = (90 - 10) = 80

Number of male clerks working in company X = 80/8 ×  9 = 90

Number of male managers working in company Z = (x + 10)

Number of female managers working in company Z = x

Total number of managers in company Z is the same as the number of female clerks in company X

Number of managers in company Z = 80

x + x + 10 = 80

2x = 70

x = 35

Number of male managers in company Z = (35 + 10) = 45

Number of female managers in company Z = 35

Number of male clerks in company Z is 10 more than the number of male clerks in company X

Number of male clerks in company Z = 90 + 10 = 100

Number of female clerks in company Z = 165 - 100 = 65

Average number of male and female managers in company Z is the same as the number of female clerks in company Y which is 30 less than that of males in the same company.

Number of female clerks in company Y = (45 + 35)/2 = 80/2 = 40

Number of male clerks in company Y = (40 + 30) = 70

Number of male managers to female managers in company Y are in the ratio 4: 5

Number of male managers in company Y = 4 ×  15 = 60

Number of female managers in company Y = 5 ×  15 = 75

 

 

Solution:

Number of male managers in company X and Y = (50 + 60) = 110

Number of male clerks in company  and Y = (90 + 70) = 160

Required percentage = 11: 16

Shortcut Trick

Sum of ages after increases = 44 + 4 + 2 = 50 years.

New ratio is 2 ∶ 3 → Total parts = 5.

5 units = 50 ⇒ 1 unit = 10.

New ages: Hrick = 2 × 10 = 20, Oindrila = 3 × 10 = 30.

Present ages: Hrick = 20 − 4 = 16, Oindrila = 30 − 2 = 28.

Original ratio = 16 ∶ 28 = 4 ∶ 7.

∴ The correct answer is 4 ∶ 7.

Alternate Method

Given: Sum of Present Ages = 44 years. New Ratio = 2 ∶ 3 after adding 4 and 2 years respectively.

Calculations:

⇒ Let Hrick's present age be H and Oindrila's be O.

⇒ H + O = 44 — (Equation 1)

⇒ (H + 4) ÷ (O + 2) = 2 ÷ 3

⇒ 3(H + 4) = 2(O + 2)

⇒ 3H + 12 = 2O + 4 ⇒ 3H − 2O = −8 — (Equation 2)

⇒ From (1), O = 44 − H. Substitute in (2):

⇒ 3H − 2(44 − H) = −8

⇒ 3H − 88 + 2H = −8 ⇒ 5H = 80 ⇒ H = 16

⇒ O = 44 − 16 = 28

⇒ Ratio x ∶ y = 16 ∶ 28 = 4 ∶ 7

∴ The correct answer is 4 ∶ 7.

Additional Information

Ratio and Sum Relation

If the sum of two quantities is S and their ratio is a ∶ b, then the quantities are [a ÷ (a+b)] × S and [b ÷ (a+b)] × S.

Age Problems Shift

When ages are increased or decreased, the sum of ages changes by the total number of years added to or subtracted from each individual.

Shortcut Trick

Downstream speed (u) = 10 + 5 = 15 km/hr

Upstream speed (v) = 10 − 5 = 5 km/hr

Distance (D) = [Total Time × (u × v)] ÷ (u + v)

⇒ D = [12 × (15 × 5)] ÷ (15 + 5) = (12 × 75) ÷ 20 = 45 km

∴ The correct answer is 45 km.

Alternate Method

Given:

Speed of boat in still water (x) = 10 km/hr

Speed of stream (y) = 5 km/hr

Total time taken = 12 hours

Formula Used:

Time = Distance ÷ Speed

Downstream Speed = x + y | Upstream Speed = x − y

Calculations:

⇒ Downstream speed = 10 + 5 = 15 km/hr

⇒ Upstream speed = 10 − 5 = 5 km/hr

⇒ Total Time = (Distance ÷ Downstream Speed) + (Distance ÷ Upstream Speed)

⇒ 12 = (D ÷ 15) + (D ÷ 5)

⇒ 12 = (D + 3D) ÷ 15

⇒ 12 = 4D ÷ 15

⇒ 4D = 12 × 15

⇒ D = (12 × 15) ÷ 4

⇒ D = 3 × 15 = 45 km

∴ The correct answer is 45 km.

Additional Information

Relative Speed in Water

When a boat moves with the flow (downstream), speeds are added: U = B + S. Against the flow (upstream), speeds are subtracted: V = B − S.

Average Speed for Round Trip

For a round trip between two points, Average Speed = (2 × U × V) ÷ (U + V). Total Distance = Average Speed × Total Time ÷ 2.

Speed Conversion

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

Shortcut Trick

Let MP of X = 100u, then MP of Y = 140u.

SP of X = 100u × 0.7 = 70u | CP of X = 70u ÷ 0.8 = 87.5u | Loss X = 17.5u.

SP of Y = 140u × 0.85 = 119u | CP of Y = 119u ÷ 1.12 = 106.25u | Profit Y = 12.75u.

Net loss = 17.5u − 12.75u = 4.75u. Given 4.75u = Rs. 228.

1u = 228 ÷ 4.75 = 48. MP of Y = 140 × 48 = Rs. 6720.

∴ The correct answer is Rs. 6720.

Alternate Method

Given: MP_Y = 1.4 × MP_X, Discount_X = 30%, Discount_Y = 15%, Loss%_X = 20%, Profit%_Y = 12%, Total Loss = Rs. 228.

Formulas: SP = MP × (100 − D)% | CP = SP × 100 ÷ (100 ± P/L)% | Profit/Loss = |CP − SP|

⇒ Let Marked Price of X = 100x and Y = 140x.

⇒ Selling Price X = 70x, Selling Price Y = 140x × 0.85 = 119x.

⇒ Cost Price X = 70x ÷ 0.80 = 87.5x. Cost Price Y = 119x ÷ 1.12 = 106.25x.

⇒ Loss on X = 87.5x − 70x = 17.5x. Profit on Y = 119x − 106.25x = 12.75x.

⇒ Total Loss = 17.5x − 12.75x = 4.75x = 228 ⇒ x = 48.

⇒ Marked Price of Y = 140 × 48 = 6720.

∴ The correct answer is Rs. 6720.

Additional Information

Relationship between CP and MP

The ratio of CP to MP can be expressed as CP/MP = (100 − D%)/(100 ± P/L%).

Mark-up Percentage

Mark-up% = [(MP − CP) / CP] × 100. It represents how much higher the MP is compared to the CP.

Shortcut Trick

Ratio of Time taken by P : Q : R = 6 : 3 : 2 (Taking LCM of 1, 2, 3 as 6).

Ratio of Efficiency (Inverse of Time) = 1/6 : 1/3 : 1/2 ⇒ 1 : 2 : 3.

Total Work = Total Efficiency × Total Days = (1 + 2 + 3) × 9 = 54 units.

Time for R = Total Work ÷ Efficiency of R = 54 ÷ 3 = 18 days.

∴ The correct answer is 18 days.

Alternate Method

Given: Time(P) = 2 × Time(Q) = 3 × Time(R). Combined time = 9 days.

Formula Used: Efficiency ∝ 1/Time; Total Work = Combined Efficiency × Time.

⇒ Let the time taken by P be 6x, Q be 3x, and R be 2x.

⇒ One day work of P, Q, and R: 1/6x + 1/3x + 1/2x = 1/9.

⇒ (1 + 2 + 3) / 6x = 1/9.

⇒ 6 / 6x = 1/9 ⇒ 1/x = 1/9 ⇒ x = 9.

⇒ Time taken by R alone = 2x = 2 × 9 = 18 days.

∴ The correct answer is 18 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken. If the ratio of time is a:b, the ratio of efficiency is b:a.

Work and Wages

Wages are distributed in the ratio of efficiency or the ratio of work done by each person.

Combined Work Formula

If A takes 'a' days and B takes 'b' days, together they take (a × b) / (a + b) days to complete the work.

People: Sunil, Raj, Anita, Vanya, Dhruv, and Moksh

Poetry: Life, Wind, Remember, Stars, Alone, and Echo.

Days: Monday to Saturday(of the same week).

1) Anita's interview is scheduled for Wednesday. Remember Poetry is liked by the person who has an interview just a day before the interview of Anita. One person has an interview between the days Anita and Sunil have an interview.

The position of whether Sunil's interview is scheduled before Anita or after is not given. It gives rise to two cases.

 

2) Two persons have an interview scheduled between Vanya and Moksh. Raj likes Echo poetry and his interview is not scheduled for Thursday. 

 

3. The only possibility for Dhruv to have the interview in Case 1 is Thursday and Case 2 is Tuesday. The person who likes Life poetry has an interview just after the person who likes wind poetry. Dhruv does not like Wind and Remember Poetry. 

In Case 2, Dhruv likes to Remember Poetry. It contradicts the condition that Dhruv does not like Remember Poetry. That is why Case 2 is eliminated.

 

4) Vanya and Sunil do not like Stars Poetry. So, the only possibility is that Moksh likes Stars Poetry.

The final arrangement is:

 

Hence, Alone Poetry is liked by the person whose interview is scheduled on Monday.

People: Sunil, Raj, Anita, Vanya, Dhruv, and Moksh

Poetry: Life, Wind, Remember, Stars, Alone, and Echo.

Days: Monday to Saturday(of the same week).

1) Anita's interview is scheduled for Wednesday. Remember Poetry is liked by the person who has an interview just a day before the interview of Anita. One person has an interview between the days Anita and Sunil have an interview.

The position of whether Sunil's interview is scheduled before Anita or after is not given. It gives rise to two cases.

 

2) Two persons have an interview scheduled between Vanya and Moksh. Raj likes Echo poetry and his interview is not scheduled for Thursday. 

 

3. The only possibility for Dhruv to have the interview in Case 1 is Thursday and Case 2 is Tuesday. The person who likes Life poetry has an interview just after the person who likes wind poetry. Dhruv does not like Wind and Remember Poetry. 

In Case 2, Dhruv likes to Remember Poetry. It contradicts the condition that Dhruv does not like Remember Poetry. That is why Case 2 is eliminated.

 

4) Vanya and Sunil do not like Stars Poetry. So, the only possibility is that Moksh likes Stars Poetry.

The final arrangement is:

 

The given pairs represents the set of person and the poetry they like. Vanya likes Remember Poetry but in the given pair Life Poetry is give. That is why Vanya-Life is wrong Pair.

Hence, Vanya-Life doesn't belong to the group.