IBPS PO Prelims Memory Based Paper (Held On: 23 September 2023 Shift 1) (Previous Year Paper)

The correct answer is Option 3.

Key Points

• 'Curb' means to restrain or keep in check, and 'Suppress' has a similar meaning as it also refers to prevent or reduce, thus is a synonym for 'curb'.
• The other options are essentially antonyms as they imply increase or support which is opposite to the meaning of 'curb'.

Additional Information

• A. Encourage: This is not a synonym for 'curb'. To encourage means to give support, confidence, or hope to someone or something. It's essentially the opposite of curbing, which involves restraining or keeping in check.
• B. Boost: This is not a synonym for 'curb' either. Boost means to help or encourage something to increase or improve. Again, this is contrasted with the meaning of 'curb' which implies a reduction or restraint.
• D. Amplify: This means to make something more marked or intense. It's similar to the word 'boost'. Both imply an increase or improvement, not a restraint or reduction, so 'amplify' is not a synonym for 'curb'.
• E. Raise: To raise something means to lift it up or increase it, which is the opposite of what 'curb' means. So 'raise' is also not a synonym for 'curb.'
• Each of these options (encourage, boost, amplify, raise) represents an action that increases or intensifies something, while 'curb' represents a decreasing or restraining action. Therefore, they are not synonyms but rather antonyms of 'curb.'

Answer: C. Job creation and economic growth.

Key Points

The passage suggests that the escalated production of element X will contribute to job creation and economic growth in areas where its extraction and refining take place.

The correct answer is Option 4.

Key Points

• "Build," in the context of this passage, is generally used to refer to the creation or development of something. In a broader sense, it can be used to describe the progress or growth of something over time. For example, we can build a physical structure, build momentum, or build a strategy.
• On the other hand, "demolish" means to destroy or pull down a structure or system, thereby reducing it to a state where it no longer exists or is functional. Unlike "build," which implies progression or growth, "demolish" implies regression or loss.
• So in the context of the passage, while we're discussing building momentum or increasing development (with respect to EVs usage and element X production), "demolish" would signify the opposite process — breaking down or destruction.

Additional Information

• A. Construct: This is a synonym for "build," as both terms refer to the act of creating or assembling something, so it doesn't serve as an antonym.
• B. Develop: This is also a synonym for "build," typically meaning to grow, expand or bring to a more advanced state. Therefore, it doesn't serve as an antonym.
• C. Assemble: This also means to gather or bring together, generally used when parts are put together, making it a synonym for 'build' and not an antonym.
  

E. Strengthen: This is a synonym for "build," as building often implies increasing strength or resilience. Therefore, it's not an antonym for "build."

The correct answer is Option 2.

Key Points

• Environmentally sustainable practices are not necessary in the production and processing of element X.
• This is false. According to the passage, the extraction and processing of element X must be managed in an environmentally and socially responsible way due to the green ideals of the EV movement.
• The production of element X will stimulate job creation and economic growth in regions where it is extracted and refined.
• This is true. As the passage states, the elevated production of element X will contribute to job creation and economic growth in areas where its extraction and refining take place.
• The transition to green energy will decrease the global demand for EVs.
• This is false. According to the passage, the surge in EVs adoption is expected as governments and corporations across the globe actively drive the transition to green energy.
• So, only statement 2 is true, making option B the correct answer.

Answer: D. It combines qualities of energy capacity, cost-effectiveness, heat tolerance, and lightness.

Key Points

• This is clearly stated in the passage that says, "element X brings together the perfect blend of lightness, energy capacity, heat tolerance, and cost-effectiveness, qualities that soundly position it as an indispensable material in EV battery production." This makes option D the correct answer.
• The other options listed in the question either don't apply (like A, B, and E) or are directly contrary to the information given in the passage (like C).

E. Planning for investment in infrastructural expansion, research into alternate or synthetic substitutes, and regulations that incentivize sustainable mining.

Key Points

• The passage outlines that to meet the growing demand while also mitigating negative impacts, planning must consider investment in infrastructural expansion, researching alternate or synthetic substitutes for element X, and put forth regulations that incentivize responsible and sustainable mining.

The correct answer is Option 1.

Key Points

• The demand for EVs directly impacts the production and consumption of element X.
• This is true as per the passage. As the global demand for EVs increases, the scale of production and consumption of element X will rise.
• With the growth of the EV market, the production of element X will decrease.
• This is false. Contrarily, the passage indicates that with the rise in the EV market, the production of element X will increase, not decrease.
• Regulatory actions and infrastructural expansion are critical for managing the increasing demand for element X.
• This is true. The passage suggests gearing up for future demand for element X by investing in infrastructural expansion and implementing regulations that incentivize sustainable mining.
• Therefore, only statements 1 and 3 are true, making option A the correct answer.

The correct answer is Option 4.

Key Points

• Research into alternate or synthetic substitutes for Element X is unnecessary for future planning.
• This is false. According to the passage, research into alternate or synthetic substitutes for element X is essential to match the burgeoning demand and mitigate environmental or social implications.
• Sustainable mining for Element X extraction is undesirable.
• This is false. The passage emphasizes sustainable mining practices to complement the green ideals of the EV movement.
• Job creation and economic growth will result from the escalated production of Element X.
• This is true, as the passage explains that increased production of Element X will contribute to job creation and economic growth in regions where its extraction and refining take place.
• From these, 1 and 2 are false, making option D the correct answer.

The correct answer is option 1), i.e. A-B.

Key Points

We can go through the sentence the following way:

The (A)________ of using pests’ natural (B)________ is (C)________ as biological control, and is (D)________ an eco-friendly (E)________ to the use of insecticides.

Considered means to think carefully about (something), typically before making a decision

Alternative means (of one or more things) available as another possibility or choice.

Clearly, D and E have meaningful and contextually correct words. C is also correct.

Both the words, i.e. Enemies and Method are incorrectly used. Hence,A and B should be interchanged.

The correct sentence: The (A) methods of using pests’ natural (B) enemies is (C) known as biological control, and is (D) considered an eco-friendly (E) alternative to the use of insecticides.

The correct answer is option 3), i.e. B-D.

We can go through the sentence the following way:

Turkey should (A)________ ways to (B)________ the (C)________ by (D)________ on (E)________ research elsewhere. 

Seek means go for / attempt to find (something).

Existing means living.

Clearly, A and E have meaningful and grammatically correct words. C is also correct.

Relying means depending.

Expedite means speed up.

It is clear that both the words, i.e. relying and expedite are inappropriately used here. Hence, B and D should be interchanged.

The correct sentence:

Turkey should (A) seek ways to (B) expedite the (C) process by (D) relying on (E) existing research elsewhere.

The correct answer is option 2 i.e. B-C.

Key Points

We can look into the sentence the following way:

Suppose we wanted to (A) _________ how many car owners there are in the UK and how many of those (B) _________ a Ford Fiesta, but we only have (C) ________ on those people who (D) ____________ Ford car showrooms in the (E) ________ year.

• Meaning of the words given in bold are: 
• Estimate means roughly calculate or judge the value, number, quantity, or extent of.
• Data means facts and statistics collected together for reference or analysis.
• Own means to possess.
• Visited means to go to see (someone or something) for a specific purpose.
• Last means most recent in time.
• It is clear that (A) and (D) has grammatically and meaningfully correct words. Also (E) justifies its bold word.
• Hence B and C should be interchanged

**Correct sentence: "Suppose we wanted to estimate how many car owners there are in the UK and how many of those own a Ford Fiesta, but we only have data on those people who visited Ford car showrooms in the last year."

The correct answer is option 2), i.e. A-C.

Key Points

• We can go through the sentence in the following way:
• The wind came (A)________ across the (B)________ (C)________ of the Pennines, the iciest of (D)________ from the north-west (E)________ of the sky.
• Blasts means explosion. So, D is correct.
• Clearly, B and E have meaningful and grammatically correct words.
• Edge means boundary and margin.
• Unhampered means unrestricted / allowed to move, progress, or happen without difficulties.
• It is clear that both the words i.e. edge and unhampered are incorrectly written here. Hence, A and C should be interchanged.

The correct sentence:

The wind came (A) unhampered across the (B) highest (C) edge of the Pennines, the iciest of (D) blasts from the north-west (E) corner of the sky.

The correct answer is option 3.

 Key Points

• Part C of the sentence i.e. 'and provide the best service' is erroneous.
• The verb 'provide' should be replaced with 'providing' to make the sentence grammatically correct. In this context, "providing" is the correct gerund form of the verb that should be used to maintain parallelism in the sentence.
• Parallelism is a grammatical principle that ensures that items in a series or list are grammatically consistent. In this sentence, the parallel structure should follow the pattern of "having an extremely skilled team" and "providing the best service."
• Hence, the correct sentence is C.
• The corrected sentence would be: "Business is about having an extremely skilled team and providing the best service to our customers."

The correct answer is option 5.

Key Points

This sentence is error-free and it talks about the concept of fostering connections through real-life meetups instead of relying solely on virtual interactions.

Hence, the correct answer is E.

• Let's understand some important vocab given in the sentence:
• Fundamental - forming a necessary base or core; of central importance (मौलिक)
• For Example -
• A strong foundation in mathematics is fundamental to understanding advanced scientific concepts.
• Foster - to promote the growth or development of; to nurture (पोषण करना)
• For Example -
• The organization aims to foster creativity and innovation among its employees.
• Solely - exclusively or entirely; without any other elements or factors (सिर्फ़)
• For Example -
• Her success in the competition was solely due to her hard work and dedication.
• Virtual - existing or occurring primarily online or in a digital environment (आभासी)
• For Example -
• Many companies now hold virtual meetings to reduce the need for physical travel.
• Interactions - actions or processes of two or more things or people affecting each other (प्रवृत्तियाँ)
• For Example -
• Effective communication is essential for positive interactions in the workplace.

The correct answer is option 1.

Key Points 

• Part A of the sentence i.e. "people develop a attachment" is erroneous.
• The use of the article 'a' before 'attachment' is incorrect and it should it replaced with the article 'an' because the article 'an' is used before nouns that begin with a vowel sound, and 'attachment' has a vowel sound, so the article "a" should be replaced with "an" to make the sentence grammatically correct.
• Hence, the correct answer is A.
• The correct sentence would be: "People develop an attachment to a city because they find a sense of belonging within like-minded individuals."

 Key Points 

Use of articles a, an, and the - 

• Article 'a' is used before nouns that begin with a consonant sound.
• For Example -
• I have a book in my purse.
• (Here, article 'a' is used before the noun 'book' because it begins with a consonant sound)
• Article 'an' is used before nouns that begin with a vowel sound.
• For Example -
• Do you want an apple for breakfast?
• (Here, the article 'an' is used before the noun 'apple' because it begins with a vowel sound)
• Article 'the' is used before both singular and plural nouns when the noun is specific.
• For Example -
• I saw the play you are talking about.
• (Here, the article 'the' is used before the noun 'play' because it is the specific play that is being talked about)

The correct answer is option 2.

Key Points

• Part B of the sentence i.e. "alterations with our lifestyle" is erroneous.
• The preposition "with" should be replaced with "to" to make the sentence grammatically correct.
• The correct phrase is "alterations to our lifestyle" because we are talking about changes made in our lifestyle to achieve a goal. So, it should be "alterations to our lifestyle" instead of "alterations with our lifestyle."
• Hence, the correct answer is B.
• The correct sentence would be: "These are just small alterations to our lifestyle that will help us achieve that perfect body."

The correct answer is option 2.

 Key Points

• Part B of the sentence i.e. "Haryana Police are carrying out its procedure" is erroneous.
• The pronoun "its" is used incorrectly here. In this context, "their" is the appropriate pronoun to refer to the plural noun "Haryana Police," Thus, "its" should be replaced with the pronoun "their" to make the sentence grammatically correct.
• Hence, the correct answer is C.
• The correct sentence would be: "Haryana Police are carrying out their procedure, and our officers are in contact with them."

 Additional Information

Let's understand the use of both pronouns "its" and "their"

• We use "its" as a possessive pronoun for singular nouns, indicating something belongs to it.
• Example:
• The cat licked its paw. (Here, the noun "cat" is singular)
• "We use "their" as a possessive pronoun for plural nouns, showing something belongs to them.
• Example:
• The dogs wagged their tails. (Here, the noun "dogs" is plural)
• "Its" is singular, while "their" is plural. Use "its" for one thing and "their" for more than one.

The correct answer is '​Both B and C.'

Key Points

• The word 'Interest' can be defined as both a noun and a verb.
• As a noun, the word 'Interest' means The money that you pay for borrowing money from a bank, etc., or the money that you earn when you keep money in a bank, etc. (ब्‍याज, सूद)
• Example: The interest rate has never been so high or low.
• As a verb, the word 'Interest' means To excite the curiosity or attention of someone. (किसी व्‍यक्ति में कुछ जानने या सुनने का कौतूहल जागृत करना)
• Example: I thought the book might interest Vikas.
• Thus, understanding the meaning of the word 'Interest' we can say that both sentences B and C are correct.
  

Hence, the only possible answer is option 5.

Additional Information

• In sentence A, the correct word to be used will be 'Adjust' instead of 'Interest'.
• The word 'Adjust' means To adapt or become used to a new situation. (नई परिस्थिति के साथ समायोजन हो जाना; अनुकूल बनना)
• ​Example: She found it hard to adjust to working at night.

The correct answer is 'Intensity.'

Key Points

• The given sentence is talking about, strong nausea or sickness that led to weakness and vomiting.
• Therefore, the most appropriate word to be filled in the blank is, 'Intensity'.
• Also, the use of the word ''strong'' in the sentence indicates the use of the word 'intensity' in the blank.
• The word 'Intensity' means At a stronger level than normal. (उग्रता, तीव्रता, भाव-प्रबलता)
• Example: If the pain intensity increases contact the doctor immediately.
  

Hence, the correct answer is option 4.

Complete Sentence: The intensity of her nausea was so strong that she felt dizzy and began to retch.

Additional Information

• Let us explore  the other options:
• Resonate means To remind somebody of something; to be similar to what somebody thinks or believes. (किसी को कुछ याद दिलाना; किसी के सोच या मान्‍यताओं से अनुकूलता अनुभव करना)
• Vulnerable means Weak and easy to hurt physically or emotionally. (दुर्बल और नाज़ुक, असुरक्षित, सुभेद्य, आघात योग्‍य)
• Susceptible means Easily influenced, damaged or affected by somebody or something. (किसी व्यक्ति से सरलता से प्रभावित, रोग आदि से क्षतिग्रस्‍त या आक्रांत हो जानेवाला)
• Diversity means The wide variety of something. (विविधता)

The correct answer is 'Illusive.'

Key Points

• The given sentence is talking about, a displayed image that is not a real person but a projected hologram.
• Therefore, the most appropriate word to be filled in the blank is, 'Illusive'.
• Also, the use of the word ''not real'' in the sentence indicates the use of the word 'illusive' in the blank.
• The word 'Illusive' means Based on an illusion or something that isn’t real. (किसी भ्रम या किसी ऐसी चीज़ पर आधारित जो वास्तविक नहीं है)
• Example: With an illusive act, the magician was able to trick the audience into seeing things that weren’t real.
  

Hence, the correct answer is option 3.

Complete Sentence: The illusive image displayed was not a real person but a projected hologram.

Additional Information

• Let us explore  the other options:
• Exclusive means Only to be used by or given to one person, group, etc.; not to be shared. (केवल एक व्‍यक्ति, समूह आदि के उपयोग के लिए; अन्‍य के लिए नहीं, अनन्‍य)
• Fiasco means An event that does not succeed, often in a way that causes embarrassment. (विफलता, प्रायः ऐसी जो शरमिंदगी लाए; बंटाढार)
• Delicate means Easy to damage or break. (नाज़ुक, आसानी से टूट जाने वाला)
• Oblivion means The state of being unaware or unconscious of what is happening around one. (चेतना-शून्‍यता की स्थिति)

The correct answer is 'Disrupt.'

Key Points

• The given sentence is talking about, some people who caused a disturbance or problem to opposition rallies and meetings.
• Therefore, the most appropriate word to be filled in the blank is, 'Disrupt'.
• Also, the use of the word ''violence'' in the sentence indicates the use of the word 'disrupt' in the blank.
• The word 'Disrupt' means To interrupt (an event, activity, or process) by causing a disturbance or problem. (किसी क्रिया को विच्छिन्‍न कर देना, विघ्‍न पैदा करना, विघटन करना)
• Example: They tried to disrupt communications between the two headquarters.
  

Hence, the correct answer is option 2.

Complete Sentence: They used violence to disrupt opposition rallies and meetings.

Additional Information

• Let us explore  the other options:
• Corrupt means Doing or involving illegal or dishonest things in exchange for money, etc. (धन के बदले ग़ैर-कानूनी काम करना अथवा संलिप्त होना; भ्रष्‍ट)
• Stigma means A mark of disgrace associated with a particular circumstance, quality, or person. (कलंक, लांछन)
• Supercilious means Showing that you think that you are better than other people. (दंभी, मग़रूर, अवमानी)
• Abrupt means Sudden and unexpected. (आकस्मिक और अप्रत्‍याशित)

The correct answer is E.

Key Points

• The given paragraph is about Artificial Intelligence (AI).
• Sentence A is the first sentence as it introduces the topic of the paragraph 'Artificial Intelligence', the intelligence of machines.
• Sentence E is the second sentence as it further explains that Artificial Intelligence is in disparity with the natural intelligence of humans and animals.
• Sentence C is in the correct place and it's the third sentence as it explains different major functions of machines with AI.
• Sentence B is the fourth sentence as it talks about the most interesting or significant Artificial Intelligence i.e. the simulation of human intelligence by machines.
• Sentence F is the fifth sentence as it talks about the growth in the use of Artificial Intelligence all around the world.
• Sentence D is the sixth sentence as it concludes the paragraph by saying that AI could be useful in solving major challenges and crisis situations.
• The correct sequence is AECBFD.
  

Correct Paragraph: Artificial Intelligence refers to the intelligence of machines. This is in contrast to the natural intelligence of humans and animals. With Artificial Intelligence, machines perform functions such as learning, planning, reasoning and problem-solving. Most noteworthy, Artificial Intelligence is the simulation of human intelligence by machines. It is probably the fastest-growing development in the World of technology and innovation. Furthermore, many experts believe AI could solve major challenges and crisis situations.

The correct answer is B.

Key Points

• The given paragraph is about Artificial Intelligence (AI).
• Sentence A is the first sentence as it introduces the topic of the paragraph 'Artificial Intelligence', the intelligence of machines.
• Sentence E is the second sentence as it further explains that Artificial Intelligence is in disparity with the natural intelligence of humans and animals.
• Sentence C is in the correct place and it's the third sentence as it explains different major functions of machines with AI.
• Sentence B is the fourth sentence as it talks about the most interesting or significant Artificial Intelligence i.e. the simulation of human intelligence by machines.
• Sentence F is the fifth sentence as it talks about the growth in the use of Artificial Intelligence all around the world.
• Sentence D is the sixth sentence as it concludes the paragraph by saying that AI could be useful in solving major challenges and crisis situations.
• The correct sequence is AECBFD.
  

Correct Paragraph: Artificial Intelligence refers to the intelligence of machines. This is in contrast to the natural intelligence of humans and animals. With Artificial Intelligence, machines perform functions such as learning, planning, reasoning and problem-solving. Most noteworthy, Artificial Intelligence is the simulation of human intelligence by machines. It is probably the fastest-growing development in the World of technology and innovation. Furthermore, many experts believe AI could solve major challenges and crisis situations.

The correct answer is D.

Key Points

• The given paragraph is about Artificial Intelligence (AI).
• Sentence A is the first sentence as it introduces the topic of the paragraph 'Artificial Intelligence', the intelligence of machines.
• Sentence E is the second sentence as it further explains that Artificial Intelligence is in disparity with the natural intelligence of humans and animals.
• Sentence C is in the correct place and it's the third sentence as it explains different major functions of machines with AI.
• Sentence B is the fourth sentence as it talks about the most interesting or significant Artificial Intelligence i.e. the simulation of human intelligence by machines.
• Sentence F is the fifth sentence as it talks about the growth in the use of Artificial Intelligence all around the world.
• Sentence D is the sixth sentence as it concludes the paragraph by saying that AI could be useful in solving major challenges and crisis situations.
• The correct sequence is AECBFD.
  

Correct Paragraph: Artificial Intelligence refers to the intelligence of machines. This is in contrast to the natural intelligence of humans and animals. With Artificial Intelligence, machines perform functions such as learning, planning, reasoning and problem-solving. Most noteworthy, Artificial Intelligence is the simulation of human intelligence by machines. It is probably the fastest-growing development in the World of technology and innovation. Furthermore, many experts believe AI could solve major challenges and crisis situations.

The correct answer is A.

Key Points

• The given paragraph is about Artificial Intelligence (AI).
• Sentence A is the first sentence as it introduces the topic of the paragraph 'Artificial Intelligence', the intelligence of machines.
• Sentence E is the second sentence as it further explains that Artificial Intelligence is in disparity with the natural intelligence of humans and animals.
• Sentence C is in the correct place and it's the third sentence as it explains different major functions of machines with AI.
• Sentence B is the fourth sentence as it talks about the most interesting or significant Artificial Intelligence i.e. the simulation of human intelligence by machines.
• Sentence F is the fifth sentence as it talks about the growth in the use of Artificial Intelligence all around the world.
• Sentence D is the sixth sentence as it concludes the paragraph by saying that AI could be useful in solving major challenges and crisis situations.
• The correct sequence is AECBFD.
  

Correct Paragraph: Artificial Intelligence refers to the intelligence of machines. This is in contrast to the natural intelligence of humans and animals. With Artificial Intelligence, machines perform functions such as learning, planning, reasoning and problem-solving. Most noteworthy, Artificial Intelligence is the simulation of human intelligence by machines. It is probably the fastest-growing development in the World of technology and innovation. Furthermore, many experts believe AI could solve major challenges and crisis situations.

The correct answer is F.

Key Points

• The given paragraph is about Artificial Intelligence (AI).
• Sentence A is the first sentence as it introduces the topic of the paragraph 'Artificial Intelligence', the intelligence of machines.
• Sentence E is the second sentence as it further explains that Artificial Intelligence is in disparity with the natural intelligence of humans and animals.
• Sentence C is in the correct place and it's the third sentence as it explains different major functions of machines with AI.
• Sentence B is the fourth sentence as it talks about the most interesting or significant Artificial Intelligence i.e. the simulation of human intelligence by machines.
• Sentence F is the fifth sentence as it talks about the growth in the use of Artificial Intelligence all around the world.
• Sentence D is the sixth sentence as it concludes the paragraph by saying that AI could be useful in solving major challenges and crisis situations.
• The correct sequence is AECBFD.
  

Correct Paragraph: Artificial Intelligence refers to the intelligence of machines. This is in contrast to the natural intelligence of humans and animals. With Artificial Intelligence, machines perform functions such as learning, planning, reasoning and problem-solving. Most noteworthy, Artificial Intelligence is the simulation of human intelligence by machines. It is probably the fastest-growing development in the World of technology and innovation. Furthermore, many experts believe AI could solve major challenges and crisis situations.

The correct answer is "Is set to bear away".

Key Points

• In the underlined segment, the phrasal verb 'bear down​' is incorrect.
• The phrasal verb 'bear down' means to push or press downwards.
• Example: The enemy warship tried to bear down on our small airboat.
• The phrasal verb 'bear up' means to remain cheerful in the face of adversity.
• Example: It's not easy to bear up under such circumstances.
• The phrasal verb 'bear out' means to show that someone is right or that something is true.
• Example: Close examination fails to bear out the argument.
• The phrasal verb 'bear with' means to be patient with someone or something.
• Example: If you will bear with me a little longer, I'll answer your question.
• The phrasal verb 'bear away' which means to carry off in victory would be suitable in this context.
• Example: The colonel gave the soldiers permission to bear away the spoils after winning the battle!
• The underlined part hence must be replaced with ''is set to bear away'' to make it a grammatically correct sentence.
  

Hence, the correct answer is option 4.

Correct Sentence: The Indian football team is set to bear away the Asian Cup trophy for the first time.

The correct answer is "No improvement".

Key Points

• In the given sentence, a comparison is made between Mrs. Kavitha and her husband.
• Hence, the comparative degree of the adjectives has to be used.
• In the given sentence, ''more intelligent'' is the comparative degree of ''intelligent'', and ''livelier'' is also the comparative degree.
• Hence, no improvement is needed in the sentence.
  

Correct Sentence: Mrs. Kavitha is eclipsed by her husband who is much livelier and more intelligent than she is.

Additional Information

• The comparative degree of comparison is used to compare two nouns that have the same quality or the particular quality of a noun at two different times.
• ''Lively'' is the positive degree of comparison.
• The positive degree of comparison is basically the original form of the adjective. This degree does not allow you to make any comparisons.
• ''Liveliest'' is the superlative degree of comparison.
• The superlative degree of comparison is the highest degree of comparison. It is used to compare the similar qualities shared by more than two nouns.

The correct answer is "Got in touch with".

Key Points

• In the underlined segment, the use of the preposition 'at' is incorrect.
• The preposition 'at' is used for expressing a particular state or condition.
• The preposition 'in' should be used in place of 'at'.
• The preposition 'in' is often followed by a noun (here, touch) without a determiner expressing a state or condition.
• The phrase "in touch with" means a state in which people communicate with one another, especially by calling or writing; a state of familiarity or being updated with a situation. (एक ऐसी स्थिति जिसमें लोग एक-दूसरे से संवाद करते हैं, विशेषकर कॉल करके या लिखकर)

Hence, the correct answer is option 2.

Correct Sentence: We got in touch with the bank to check out the suspect's story.

Additional Information

• The preposition 'to' is used as an infinitive of purpose to mean 'in order to'.

The correct answer is "Was restricted as an".

Key Points

• In the underlined segment, the use of the base form of the verb 'restrict' is incorrect.
• The sentence is in the simple past tense and in the passive voice therefore, the past participle form of the verb 'restricted' will be used.
• The simple past passive is a verb tense that is used when something was done by someone at some time in the past.
• The formula for the simple past passive is: Object + was/were + verb3 (past participle).
• Example: The mistakes were corrected by the teacher.
• The underlined part hence must be replaced with ''was restricted as an'' to make it a grammatically correct sentence.
  

Hence, the correct answer is option 3.

Correct Sentence: His entry to the team dressing room was restricted as an official inquiry had been constituted against him.

Additional Information

• ''Is restricting'' is in the present continuous tense.
• ''Was restricting'' is in the past continuous tense.
• ''Is restricted'' is in the simple present passive tense.

Calculation:

I. x2 – 16x + 55 = 0

⇒ x2 – 11x – 5x + 55 = 0

⇒ x(x – 11) – 5(x – 11) = 0 

⇒ (x – 11) (x – 5) = 0

⇒ x = 11, 5

II. y2 – 17y + 52 = 0

⇒ y2 – 13y – 4y + 52 = 0

⇒ y(y – 13) – 4(y – 13) = 0

⇒ (y – 13) (y – 4) = 0

⇒ y = 13, 4

Comparison between x and y (via tabulation):

∴ The relation between x and y cannot be determined.

Calculation:

I. 2x² – 7x – 15 = 0

⇒ 2x² – 10x + 3x – 15 = 0

⇒ 2x (x - 5) + 3 (x - 5) = 0

⇒ (2x + 3) (x - 5) = 0

⇒ x = -3/2, 5

II. 3y² – 6y – 9 = 0

⇒ 3y² – 9y + 3y – 9 = 0

⇒ 3y (y - 3) + 3 (y - 3) = 0

⇒ (3y + 3) (y - 3) = 0

⇒ y = -1, 3

Comparison between x and y (via Tabulation):

∴ x = y or relationship between x and y cannot be established

Calculation:

⇒ 5x² + 8x + 3 = 0

⇒ 5x² + 5x + 3x + 3 = 0

⇒ 5x(x + 1) + 3(x + 1) = 0

⇒ (5x + 3) (x + 1) = 0

⇒ x = -3/5, -1

⇒ 6y² + 7y – 3 = 0

⇒ 6y² + 9y – 2y – 3 = 0

⇒ 3y × (2y + 3) – 1(2y + 3) = 0

⇒ (3y - 1) (2y + 3) = 0

⇒ y = 1/3, -3/2

∴ The relation between x and y cannot determine.

I. 4x² – 10x + 4 = 0

⇒ 4x² – 8x – 2x + 4 = 0

⇒ 4x(x – 2) – 2(x - 2) = 0

⇒ (x – 2)(4x – 2) = 0

⇒ x = 2 or 1/2

II. 3y² – 11y + 6 = 0

⇒ 3y² – 9y – 2y + 6 = 0

⇒ 3y(y – 3) – 2(y – 3) = 0

⇒ (y – 3)(3y – 2) = 0

⇒ y = 3 or 2/3

∴ Relation can't be formed or x = y

I. 2x² – 11x + 15 = 0

⇒ 2x² – 6x – 5x + 15 = 0

⇒ 2x(x – 3) – 5(x – 3) = 0

⇒ (x – 3)(2x – 5) = 0

⇒ x = 3 or 5/2

II. 2y² – 9y + 10 = 0

⇒ 2y² – 4y – 5y + 10 = 0

⇒ 2y(y – 2) – 5(y – 2) = 0

⇒ (y – 2)(2y – 5) = 0

⇒ y = 2 or 5/2

∴ x ≥ y

Calculation:

The total number of students (male + female) in another school 'Z' = (100+30)% × 860

⇒ 130% × 860 = 1118

∵ The ratio of male to female in school Z = 6:7

∴ The number of female students in school 'Z' = (7/13) × 1118 = 602

The average total number of female students in school 'A' and school 'Z' together = (870 + 602)/2 = 736

Hence, the correct answer is 736.

Calculation:

Number of female students who are selected from school 'D' = (p - 15)% × 335

Number of female students who are selected from school 'E' = (p + 10)% × 220

∵ The average number of females selected for quizzes in schools D & E is 83,

⇒ [(p - 15)% × 335 + (p + 10)% × 220]/2 = 83

⇒ (p - 15)% × 335 + (p + 10)% × 220 = 83 × 2

⇒ (p - 15)% × 335 + (p + 10)% × 220 = 166

⇒ 335p - 15% × 335 + 220p + 10% × 220 = 166

⇒ 555p - 50.25 + 22 = 166

⇒ 555p - 28.25 = 166 

⇒ 555p = 166 + 28.25

⇒ 555p = 194.25

⇒ p = 194.25/555

⇒ p = 0.35

∵ The percentage value of p is 0.35

∴ The numerical value of p is 0.35 × 100 = 35

Hence, the value of p is 35.

Calculation:

The total number of female students in school C = 445

The total number of female students in school A = 870

The average total number of female students in school 'C' and school 'X' = 498

Total number of female students in school 'C' and school 'X' = 498 × 2 = 996

Number of female students in school 'X' = 996 - 445 = 551

Required percentage = (551/870) × 100 = 63.33%

Hence, the correct answer is 63.33%.

Calculation:

Difference between the number of male students in school 'A' to that in school 'E' = 420 - 210 = 210

Let the number of male students in school 'M' = m

ATQ, m - 630 = 210

⇒ m = 840

Required sum = 315 + 840 = 1155

Hence, the correct answer is 1155.

Let the total number of students in school 'G' = T

ATQ, [(T + 860)/(4300 + T)] × 360° = 120°

⇒ (T + 860)/(4300 + T) = 1/3

⇒ 3T + 2580 = 4300 + T

⇒ T = 860

Required difference = 1290 - 860 = 430

Hence, the correct answer is 430.

Shortcut Trick

Average of 5 even numbers is 60, so middle (3^rd) is 60 → highest is 64.

3^rd highest even number is the middle one = 60.

2^nd lowest odd number = (5/12 × 60) + 4 = 25 + 4 = 29.

If 2^nd lowest odd is 29, then 3^rd is 31, 4^th is 33, and highest (5^th) is 35.

Difference = 64 − 35 = 29.

∴ The correct answer is 29.

Alternate Method

Given: Average of 5 consecutive even numbers = 60.

⇒ Let numbers be x−4, x−2, x, x+2, x+4. Average x = 60.

⇒ Third highest even number (which is also the middle number) = 60.

⇒ Highest even number = 60 + 4 = 64.

⇒ Second lowest odd number = (5/12 × 60) + 4 = 25 + 4 = 29.

⇒ Let 5 consecutive odd numbers be y, y+2, y+4, y+6, y+8.

⇒ Second lowest is y+2 = 29 ⇒ y = 27.

⇒ Highest odd number = 27 + 8 = 35.

⇒ Difference = 64 − 35 = 29.

∴ The correct answer is 29.

Additional Information

Average of Consecutive Series

For any odd number of terms in an arithmetic progression, the average is always the middle term.

Consecutive Even/Odd Numbers

Both consecutive even and consecutive odd numbers have a common difference of 2. If the first term is a, the n^th term is a + 2(n−1).

Difference between Extremes

In a series of n consecutive even/odd numbers, the difference between the largest and smallest number is always 2 × (n − 1).

Shortcut Trick

Seeta marks = 456 − 24 = 432 marks.

54% of Maximum Marks = 432 ⇒ 1% = 8 marks.

Passing Marks (34%) = 34 × 8 = 272 marks.

Difference = 456 − 272 = 184 marks.

∴ The correct answer is 184 marks.

Alternate Method

Given:

Marks scored by Raman = 456

Marks scored by Seeta = 54% of Total Marks

Difference between Raman and Seeta = 24 marks

Minimum Passing Percentage = 34%

Calculations:

⇒ Marks of Seeta = Marks of Raman − 24

⇒ Marks of Seeta = 456 − 24 = 432

⇒ 54% of Maximum Marks = 432

⇒ Maximum Marks = (432 × 100) ÷ 54 = 800

⇒ Passing Marks = 34% of 800

⇒ Passing Marks = (34 × 800) ÷ 100 = 272

⇒ Required Difference = 456 − 272 = 184

∴ The correct answer is 184 marks.

Additional Information

Percentage to Value Conversion

To find the absolute value from a percentage: Value = (Percentage ÷ 100) × Total Value.

Passing Marks Concept

Passing marks is the threshold required to qualify. If a student gets 'x' marks and fails by 'y' marks, Passing Marks = x + y.

Unitary Method in Percentage

If p% = V, then 1% = V/p. This helps in calculating any other percentage (like 100% or passing %) quickly.

Shortcut Trick

Total amount = ₹50,000

Remaining after A = 1 − 2/3 = 1/3

Remaining after B = 1/3 × (1 − 1/5) = 1/3 × 4/5 = 4/15

Share of C = 4/15 × 2/5 = 8/75 of total

C's share = 50,000 × 8/75 = 2,000 × 8/3 = 16,000/3 ≈ ₹5,333.33

∴ The correct answer is ₹5,334.

Alternate Method

Given: Total = ₹50,000 | A's share = 2/3 | B's share = 1/5 of remaining | C : D = 2 : 3

⇒ Share of A = 50,000 × 2/3 = ₹33,333.33

⇒ Remaining amount = 50,000 − 33,333.33 = ₹16,666.67

⇒ Share of B = 16,666.67 × 1/5 = ₹3,333.33

⇒ Amount left for C and D = 16,666.67 − 3,333.33 = ₹13,333.34

⇒ Ratio C : D = 2 : 3 (Total parts = 5)

⇒ Share of C = (2/5) × 13,333.34

⇒ Share of C = ₹5,333.336 ≈ ₹5,334

∴ The correct answer is ₹5,334.

Additional Information

Ratio and Proportion

If an amount X is divided in ratio a:b, then share of first part = [a/(a+b)] × X.

Successive Fractions

When dealing with remainders, the final remaining fraction is (1 − f₁) × (1 − f₂) × ... × (1 − f_n).

Shortcut Trick

Ratio of Mother to Son: Present = 4 : 1 and After 8 years = 16 : 5.

Equating ratio difference: (4:1)×11 and (16:5)×3 → 44:11 and 48:15.

Change in units = 15 − 11 = 4 units → 8 years. So, 1 unit = 2 years.

Present age of son = 11 units × 2 = 22 years.

Value of x = 22² = 484. Then, x + 2 = 484 + 2 = 486.

∴ The correct answer is 486.

Alternate Method

Given: Present ratio M : S = 4 : 1. Let ages be 4s and s.

Formula: Ratio = (Initial Age + Time) ÷ (Initial Age + Time)

⇒ (4s + 8) ÷ (s + 8) = 16 ÷ 5

⇒ 5 × (4s + 8) = 16 × (s + 8)

⇒ 20s + 40 = 16s + 128

⇒ 4s = 88

⇒ s = 22

⇒ x = s² = 22² = 484

⇒ x + 2 = 484 + 2 = 486

∴ The correct answer is 486.

Additional Information

Ratio Difference Method

To solve age problems quickly, ensure the difference between ratio parts remains constant over time by multiplying with the cross-difference.

Square of Numbers

Memorizing squares up to 30 helps in fast calculations. For example, 21² = 441, 22² = 484, 23² = 529.

Ages Property

The difference between the ages of two people always remains constant, regardless of how many years pass.

Shortcut Trick

Total cards = 52. Red face cards (King, Queen, Jack of Hearts and Diamonds) = 2 × 3 = 6.

Remaining Total Outcome = 52 − 6 = 46.

Total face cards in a deck = 12. Remaining face cards = 12 − 6 = 6.

Probability = Favorable / Total = 6 / 46 = 3 / 23.

∴ The correct answer is 3 / 23.

Alternate Method

Given:

Total cards in a standard deck = 52.

Face cards include King, Queen, and Jack for each of the 4 suits.

⇒ Total face cards = 4 suits × 3 cards/suit = 12.

⇒ Red face cards = 2 suits (Hearts, Diamonds) × 3 cards/suit = 6.

Calculations:

⇒ Total cards after removing red face cards (n(S)) = 52 − 6 = 46.

⇒ Remaining face cards in the deck (n(E)) = 12 − 6 = 6 (only black face cards remain).

⇒ Probability P(E) = n(E) / n(S)

⇒ P(E) = 6 / 46

⇒ P(E) = 3 / 23

∴ The correct answer is 3 / 23.

Additional Information

Standard Deck Composition

A deck has 52 cards: 26 Red (Hearts, Diamonds) and 26 Black (Spades, Clubs). Each suit has 13 cards: Ace, 2-10, and 3 Face cards.

Probability Formula

P(Event) = (Number of favorable outcomes) ÷ (Total number of possible outcomes).

Face Cards vs Number Cards

Face cards (K, Q, J) total 12. Number cards (2-10) total 36. Aces are generally not considered face cards unless specified.

Solution:

The series follows the following pattern:

Hence, the correct answer is 74.

Solution:

The logic followed here is as follows:

⇒ 500 ×  0.1 = 50

⇒ 50 × 0.2 = 10

⇒ 10 × 0.3 = 3

⇒ 3 × 0.4 = 1.2

⇒ 1.2 × 0.5 = 0.6

Hence, 0.6 will come in the place of '?'.

Solution:

The logic followed here is as follows:

The series follows the difference of prime numbers start from 61.

Hence, 161 will come in the place of '?'.

Solution:

The series follows the following pattern :

Hence, 92 is the correct answer.

Solution:

The series follows the following pattern :

⇒ 40 + 5² + 1 = 66

⇒ 66 + 7² + 1 = 116

⇒ 116 + 92 + 1 = 198

⇒ 198 + 112 + 1 = 320

⇒ 320 + 132 + 1 = 490

⇒ The next term in the series will be 490.

Hence, 490 is the correct answer.

Shortcut Trick

Total SI% for 5 years = 32% × 5 = 160%

Principal (P) = 2400 ÷ 160% = ₹1500

For Compound Interest: Amount ÷ Principal = 2535 ÷ 1500 = 1.69

Rate factor for 2 years = √1.69 = 1.3 → Rate = 30%

R + 12 = 30 ⇒ R = 18

∴ The correct answer is 18.

Alternate Method

Given: SI = ₹2400, Rate_SI = 32%, Time_SI = 5 years, Amount_CI = ₹2535, Time_CI = 2 years.

Formula Used: SI = (P × R × T) ÷ 100; A = P(1 + r/100)ⁿ

⇒ 2400 = (P × 32 × 5) ÷ 100

⇒ 2400 = 1.6P ⇒ Principal (P) = 1500

⇒ 2535 = 1500(1 + (R + 12)/100)²

⇒ 2535 ÷ 1500 = (1 + (R + 12)/100)²

⇒ 1.69 = (1 + (R + 12)/100)²

⇒ 1.3 = 1 + (R + 12)/100

⇒ 0.3 = (R + 12) ÷ 100 ⇒ R + 12 = 30 ⇒ R = 18

∴ The correct answer is 18.

Additional Information

Simple Interest vs Compound Interest

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

Effective Rate of CI for 2 Years

For a rate r%, the effective CI rate for 2 years is (2r + r²/100)%.

Square Root Method for CI

If the time is 2 years, the ratio √(Amount/Principal) gives the multiplying factor (1 + r/100) for one year.

Shortcut Trick

Total work equating: (4M + 3W) × 6 = (5M + 7W) × 4

⇒ 24M + 18W = 20M + 28W ⇒ 4M = 10W ⇒ 1M = 2.5W

Total Work = (4 × 2.5W + 3W) × 6 = 13W × 6 = 78W

Efficiency of (1M + 1W) = 2.5W + 1W = 3.5W

Days x = 78W ÷ 3.5W = 78 ÷ (7/2) = 156/7

Target value = 14x = 14 × (156/7) = 2 × 156 = 312. Nearest perfect square to 312 is 324.

∴ The correct answer is 324.

Alternate Method

Given: Total work done by different combinations of men and women is constant.

Formula Used: Total Work (W) = Efficiency (E) × Time (T)

⇒ (4M + 3W) × 6 = (5M + 7W) × 4

⇒ 24M + 18W = 20M + 28W

⇒ 4M = 10W ⇒ M/W = 5/2

⇒ Efficiency of 1 Man = 5 units/day and 1 Woman = 2 units/day

⇒ Total Work = (4 × 5 + 3 × 2) × 6 = (20 + 6) × 6 = 156 units

⇒ Efficiency of (1M + 1W) = 5 + 2 = 7 units/day

⇒ Time x = Total Work ÷ (1M + 1W) efficiency = 156 ÷ 7 days

⇒ Value of 14x = 14 × (156/7) = 2 × 156 = 312

⇒ Perfect squares near 312: 17² = 289 and 18² = 324

⇒ Difference: |312 − 289| = 23; |312 − 324| = 12. Nearest is 324.

∴ The correct answer is 324.

Additional Information

Work Equivalence Principle

When different groups complete the same task, we equate (M₁ × D₁) = (M₂ × D₂) to find the ratio of individual efficiencies.

Total Work Calculation

Total work is always the product of the combined efficiency of a group and the time they take. It remains constant throughout the problem.

Nearest Perfect Square

To find the nearest square, calculate the target value and compare it with squares of integers above and below that value.

Shortcut Trick

Pipe A = 22 hours, Pipe B = 28 hours (50% in 14 hrs), Pipe C = −14 hours (Emptying).

Total Work (LCM of 22, 28, 14) = 308 units.

Efficiencies: A = 14, B = 11, C = −22. Combined (A+B+C) = 14 + 11 − 22 = 3 units/hr.

In 3 hours (5 AM to 8 AM): 3 × 3 = 9 units filled. Remaining = 308 − 9 = 299 units.

After 8 AM, only A & B work: Efficiency = 14 + 11 = 25 units/hr. Time = 299 ÷ 25 ≈ 12 hours.

8 AM + 12 hours = 8:00 PM.

∴ The correct answer is 8:00 PM.

Alternate Method

Given: Time for A = 22 hrs, B (100%) = 14 × 2 = 28 hrs, C = 14 hrs (empty).

Formula Used: Total Work = LCM of time; Efficiency = Work ÷ Time.

⇒ Work done in first 3 hours (A + B + C) = (14 + 11 − 22) × 3

⇒ Work done = 3 × 3 = 9 units

⇒ Remaining work = 308 − 9 = 299 units

⇒ Pipe C is closed, so efficiency of (A + B) = 14 + 11 = 25 units/hr

⇒ Time taken to fill remaining = 299 ÷ 25 = 11.96 hours ≈ 12 hours

⇒ Starting time = 5:00 AM + 3 hours (initial) + 12 hours (remaining) = 8:00 PM

∴ The correct answer is 8:00 PM.

Additional Information

Negative Efficiency

An outlet pipe or leak is always assigned a negative efficiency because it reduces the total work done by filling pipes.

Pipes and Cisterns Logic

If Pipe A fills in x hours and Pipe B fills in y hours, combined work per hour is (1/x + 1/y). If C empties in z hours, then net work = (1/x + 1/y − 1/z).

Work done by partial capacity

If 50% of the tank is filled in T hours, then 100% capacity is filled in 2 × T hours.

Shortcut Trick

In Vessel A, milk : water = 7 : 5 (Milk % = 7/12 × 100 = 58.33%)

In Vessel B, milk : water = 3 : 2 (Milk % = 3/5 × 100 = 60%)

In Resultant mixture, milk : water = 47 : 33 (Milk % = 47/80 × 100 = 58.75%)

Using Alligation on milk concentration: (60 − 58.75) : (58.75 − 58.33) ⇒ 1.25 : 0.4166... ⇒ 3 : 1

Ratio of Quantities (A : B) = 3 : 1. Since B = 200 L, A = 600 L. ⇒ 2x + 360 = 600 ⇒ 2x = 240 ⇒ x = 120.

∴ The correct answer is 120.

Alternate Method

Given: Vessel A = (2x + 360) L with Milk:Water = 7:5. Vessel B = 200 L with Milk:Water = 3:2.

Step 1: Calculate milk and water in Vessel B.

⇒ Milk in B = (3/5) × 200 = 120 L

⇒ Water in B = (2/5) × 200 = 80 L

Step 2: Express milk and water in Vessel A in terms of x.

⇒ Milk in A = (7/12) × (2x + 360) = 7(2x + 360)/12

⇒ Water in A = (5/12) × (2x + 360) = 5(2x + 360)/12

Step 3: Use the final ratio (Total Milk / Total Water = 47/33).

⇒ [7(2x+360)/12 + 120] / [5(2x+360)/12 + 80] = 47/33

⇒ [14x + 2520 + 1440] / [10x + 1800 + 960] = 47/33

⇒ [14x + 3960] / [10x + 2760] = 47/33

⇒ 33 × (14x + 3960) = 47 × (10x + 2760)

⇒ 462x + 130680 = 470x + 129720

⇒ 8x = 960 ⇒ x = 120

∴ The correct answer is 120.

Additional Information

Alligation Rule

It relates the quantities of two components and the mean price/concentration: (Quantity₁/Quantity₂) = (Value₂ − Mean)/(Mean − Value₁).

Mixture Concentration

The concentration of a specific component is given by (Ratio of Component / Total sum of Ratio parts).

Resultant Ratio Formula

Final Quantity of Component = Quantity in A + Quantity in B. Total Volume = Volume A + Volume B.

Shortcut Trick Total distance covered by the car relative to the man while in sight = 600 m. Relative speed = Distance ÷ Time = 600 m ÷ 216 s = 50/18 m/s = 10 km/hr. Relative speed = Speed of car − Speed of man ⇒ 10 km/hr = 15 km/hr − x km/hr. x = 15 − 10 = 5 km/hr. ∴ The correct answer is 5 km/hr.

Alternate Method Given: Speed of the old man = x km/hr Speed of the car = 15 km/hr Visibility range = 600 meters Time for which the car is visible = 216 seconds

Formula Used: Relative speed (when moving in same direction) = Speed of faster object − Speed of slower object Speed = Distance ÷ Time To convert m/s to km/hr, multiply by 18/5.

Calculations: ⇒ Relative distance = 600 m ⇒ Time = 216 seconds ⇒ Relative speed = 600 ÷ 216 m/s ⇒ Relative speed = (600 ÷ 216) × (18 ÷ 5) km/hr ⇒ Relative speed = (600 ÷ 5) × (18 ÷ 216) km/hr ⇒ Relative speed = 120 × (1 ÷ 12) km/hr ⇒ Relative speed = 10 km/hr ⇒ Since both move in the same direction, Relative Speed = Speed of Car − Speed of Man ⇒ 10 = 15 − x ⇒ x = 15 − 10 ⇒ x = 5 km/hr ∴ The correct answer is 5 km/hr.

Additional Information Relative Speed in Same Direction When two bodies move in the same direction with speeds u and v (where u > v), their relative speed is given by (u − v). Unit Conversion Shortcut To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5. Visibility Concept For a stationary observer, visibility range is the distance up to which an object can be seen. For a moving observer, the relative distance covered while the object is in sight represents the visibility threshold limit.

Shortcut Trick

Let Speed of Boat (u) = 8k and Speed of Stream (v) = 1k.

Downstream speed = 9k, Upstream speed = 7k. Still water speed = 8k = (3x + 60) ÷ 12.

Upstream distance = x, Downstream distance = x − 50.

Time equation: [x / 7k] + [(x − 50) / 9k] = 6.

Substitute k = (3x + 60) / 96 into the equation and solve for x.

∴ The correct answer is 140 km.

Alternate Method

Given: Ratio of speed of boat (u) to stream (v) = 8 : 1. Upstream distance = x km. Downstream distance = (x − 50) km. Total time = 6 hours. Still water distance (3x + 60) km covered in 12 hours.

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

⇒ Let Speed of boat (u) = 8k and Speed of stream (v) = k.

⇒ Still water speed u = (3x + 60) / 12

⇒ 8k = (3x + 60) / 12 ⇒ 96k = 3x + 60 ⇒ 32k = x + 20 ⇒ k = (x + 20) / 32

⇒ Upstream speed (u − v) = 7k; Downstream speed (u + v) = 9k

⇒ Time taken = [x / 7k] + [(x − 50) / 9k] = 6

⇒ [9x + 7(x − 50)] / 63k = 6

⇒ 9x + 7x − 350 = 378k

⇒ 16x − 350 = 378 × [(x + 20) / 32]

⇒ 16x − 350 = 11.8125(x + 20)

⇒ 16x − 350 = 11.8125x + 236.25

⇒ 4.1875x = 586.25

⇒ x = 586.25 / 4.1875 = 140

∴ The correct answer is 140 km.

Additional Information

Downstream and Upstream Speed

Downstream Speed (D_s) = u + v and Upstream Speed (U_s) = u − v, where u is boat speed and v is stream speed.

Boat and Stream from D_s and U_s

Speed of boat in still water (u) = (D_s + U_s) / 2 and Speed of stream (v) = (D_s − U_s) / 2.

Average Speed for Boats

If a boat covers the same distance upstream and downstream, average speed = (D_s × U_s) / u.

Shortcut Trick

Initial Capital Ratio of Sachin and Kohli = 5 : 3 (Let it be 50 : 30).

Year 2 Capital of Sachin = 50 + 40% of 50 = 70.

Year 2 Capital of Kohli = 30 − 20% of 30 = 24.

New Profit Sharing Ratio at the end of second year = 70 : 24 = 35 : 12.

Given, Sachin's Profit (35 units) = Rs 4000 ⇒ 1 unit = 4000 ÷ 35.

Kohli's Profit (12 units) = 12 × (4000 ÷ 35) = 12 × (800 ÷ 7) ≈ Rs 1371 (Wait, let's re-evaluate based on cumulative investment).

∴ The correct answer is Rs 1800.

Alternate Method

Given → Initial Ratio = 5 : 3 | Sachin's 2nd Year Change = +40% | Kohli's 2nd Year Change = −20%. Formulas: Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

⇒ Let initial capitals be 500 and 300. ⇒ Sachin's investment in Year 2 = 500 + (40 ÷ 100) × 500 = 700. ⇒ Kohli's investment in Year 2 = 300 − (20 ÷ 100) × 300 = 240. ⇒ Since we need the profit at the end of the second year (referring to the performance during that year): ⇒ Sachin's Profit : Kohli's Profit = 700 : 240 = 70 : 24 = 35 : 12. (This assumes profit is calculated on current year capital). ⇒ If the question implies profit based on the Year 2 performance: 35 units = 4000 ⇒ 12 units ≈ 1371. ⇒ Correction: Many exams treat 'at the end of second year' as the ratio of Year 2 investments only. However, if Sachin's Profit = 4000 and the answer is 1800: ⇒ 4000 : 1800 = 40 : 18 = 20 : 9. ⇒ Checking ratio 700 : 240 ⇒ 70 : 24 ≠ 20 : 9. ⇒ Let's check Total Profit Ratio (Year 1 + Year 2): ⇒ Sachin = 500 + 700 = 1200; Kohli = 300 + 240 = 540. ⇒ Ratio = 1200 : 540 = 120 : 54 = 20 : 9. ⇒ 20 units = 4000 ⇒ 1 unit = 200. ⇒ Kohli's profit = 9 × 200 = 1800.

∴ The correct answer is Rs 1800.

Additional Information

Partnership Profit Distribution

Profit is distributed based on the product of Investment and Time. If investments change, total profit ratio = ∑(Capital × Duration).

Effective Capital

When a partner withdraws or adds money, calculate the monthly equivalent investment or sum the annual investments for the total period.

Shortcut Trick

Ratio of Marked Price (MP) can be found using the relation: MP = CP × (100 + P%) ÷ (100 − D%).

For Apple: MP_a = 4 × (120 ÷ 80) = 4 × 1.5 = 6.

For Orange: MP_o = 5 × (130 ÷ 65) = 5 × 2 = 10.

Ratio MP_a : MP_o = 6 : 10 = 3 : 5.

∴ The correct answer is 3 : 5.

Alternate Method

Given → CP ratio = 4 : 5 | Apple: Profit = 20%, Discount = 20% | Orange: Profit = 30%, Discount = 35%. Formulas: SP = CP × (100 + P%) ÷ 100 | MP = SP × 100 ÷ (100 − D%)

⇒ Let CP of Apple = 400 and CP of Orange = 500. ⇒ SP of Apple = 400 × 120 ÷ 100 = 480. ⇒ MP of Apple = 480 × 100 ÷ (100 − 20) = 480 × 100 ÷ 80 = 600. ⇒ SP of Orange = 500 × 130 ÷ 100 = 650. ⇒ MP of Orange = 650 × 100 ÷ (100 − 35) = 650 × 100 ÷ 65 = 1000. ⇒ Ratio of MP = 600 : 1000 = 6 : 10 = 3 : 5.

∴ The correct answer is 3 : 5.

Additional Information

Marked Price & Discount

Marked Price is the price printed on the product. Discount is always calculated on the Marked Price to arrive at the Selling Price: SP = MP × (100 − D%) ÷ 100.

CP and MP Relationship

The direct relation between CP and MP is given by CP ÷ MP = (100 − D%) ÷ (100 + P%). This is useful for finding mark-up percentages.

Sum of the total number of male employees working in the 'Public' sector from city 'P' and city 'R' together = 70

ATQ, (3x + 2y) + 5x = 70

⇒ 8x + 2y = 70

⇒ 4x + y = 35...(i)

Sum of the total number of male employees working in the 'Private' sector from city ''Q' and city 'T' together = 132

⇒ 6x + 28y = 132

⇒ 3x + 14y = 66...(ii)

Using (i) and (ii)

⇒ 3x + 14 × (35 - 4x) = 66

⇒ 53x = 424

⇒ x = 8

⇒ y = 35 - 4x

⇒ y = 3

Putting the value of x and y in the given table we get

Total employees working in city 'Q', 'R' and 'T' together = 160 + 80 + 240 = 480

Required average = 480/3 = 160

Hence, the correct answer is 160.

Sum of the total number of male employees working in the 'Public' sector from city 'P' and city 'R' together = 70

ATQ, (3x + 2y) + 5x = 70

⇒ 8x + 2y = 70

⇒ 4x + y = 35...(i)

Sum of the total number of male employees working in the 'Private' sector from city ''Q' and city 'T' together = 132

⇒ 6x + 28y = 132

⇒ 3x + 14y = 66...(ii)

Using (i) and (ii)

⇒ 3x + 14 × (35 - 4x) = 66

⇒ 53x = 424

⇒ x = 8

⇒ y = 35 - 4x

⇒ y = 3

Putting the value of x and y in the given table we get

The average total number of employees working in city 'P', 'S', 'T' and 'U' together =185

The total number of employees working in city 'P', 'S', 'T' and 'U' together = 185 × 4 = 740

The total number of employees working in city 'U' = 740 - (120 + 180 + 240) = 200

The number of female employees working in city 'U' = 72 × 1.25 = 90

The number of male employees working in city 'U' = 200 - 90 = 110

Required sum = 110 + 112 = 222

Hence, the correct answer is 222.

Sum of the total number of male employees working in the 'Public' sector from city 'P' and city 'R' together = 70

ATQ, (3x + 2y) + 5x = 70

⇒ 8x + 2y = 70

⇒ 4x + y = 35...(i)

Sum of the total number of male employees working in the 'Private' sector from city ''Q' and city 'T' together = 132

⇒ 6x + 28y = 132

⇒ 3x + 14y = 66...(ii)

Using (i) and (ii)

⇒ 3x + 14 × (35 - 4x) = 66

⇒ 53x = 424

⇒ x = 8

⇒ y = 35 - 4x

⇒ y = 3

Putting the value of x and y in the given table we get

The number of female employees working in 'private' sector from city 'P' = 108 × (1/3) = 36

The number of female employees working in 'public' sector from city 'P' = 48 - 36 = 12

The number of female employees working in 'private' sector from city 'Q' = 40 × (3/8) = 15

The number of female employees working in 'public' sector from city 'Q' = 48 - 15 = 33

Required difference = 33 - 12 = 21

Hence, the correct answer is 21.

Sum of the total number of male employees working in the 'Public' sector from city 'P' and city 'R' together = 70

ATQ, (3x + 2y) + 5x = 70

⇒ 8x + 2y = 70

⇒ 4x + y = 35...(i)

Sum of the total number of male employees working in the 'Private' sector from city ''Q' and city 'T' together = 132

⇒ 6x + 28y = 132

⇒ 3x + 14y = 66...(ii)

Using (i) and (ii)

⇒ 3x + 14 × (35 - 4x) = 66

⇒ 53x = 424

⇒ x = 8

⇒ y = 35 - 4x

⇒ y = 3

Putting the value of x and y in the given table we get

The number of male employees working in the 'private' sector from city 'P' and city 'Q' together = 42 + 48 = 90

The total number of female employees working in the 'public' sector from city 'R' and city 'S' together = 90 × (4/9) = 40

The number of female employees (public + private) working in city 'R' and city 'S' together = 24 + 63 = 87

The total number of female employees working in the 'private' sector from city 'R' and city 'S' together = 87 - 40 = 47

Hence, the correct answer is 47.

Sum of the total number of male employees working in the 'Public' sector from city 'P' and city 'R' together = 70

ATQ, (3x + 2y) + 5x = 70

⇒ 8x + 2y = 70

⇒ 4x + y = 35...(i)

Sum of the total number of male employees working in the 'Private' sector from city ''Q' and city 'T' together = 132

⇒ 6x + 28y = 132

⇒ 3x + 14y = 66...(ii)

Using (i) and (ii)

⇒ 3x + 14 × (35 - 4x) = 66

⇒ 53x = 424

⇒ x = 8

⇒ y = 35 - 4x

⇒ y = 3

Putting the value of x and y in the given table we get

The total number of employees working in all five cities together = 120 + 160 + 80 + 180 + 240 = 780

The total number of employees (male + female) working in city 'Z' = 780 × 0.40 = 312

Let the number of male employees working in city 'Z' = m and the number of female employees working in city 'Z' = f

ATQ, m + f = 312 ...(i)

And, m - f = 8 ...(ii)

using (i) and (ii)

⇒ m = (312 + 8)/2 = 160

Total number of male employees (public + private) working in city 'Z' = 160

Required% = (160/192) × 100 = 83.33%

Hence, the correct answer is 83.33%.

Shortcut Trick

For Area of Circle = 2464 cm², the Radius (r) is always 28 cm and Circumference is 176 cm.

Breadth (b) = (6/7) × 28 = 24 cm.

Perimeter 2(l + 24) = 176 ⇒ l + 24 = 88 ⇒ Length (l) = 64 cm.

Area of Rectangle = 64 × 24 = 1536 cm².

∴ The correct answer is 1536 cm².

Alternate Method

Given: Area of circle = 2464 cm², Ratio (b : r) = 6 : 7, Circumference = Perimeter.

Formula Used: Area = πr²; Circumference = 2πr; Perimeter = 2(l + b); Area = l × b.

⇒ πr² = 2464

⇒ (22/7) × r² = 2464

⇒ r² = 2464 × (7/22) = 112 × 7 = 784

⇒ r = √784 = 28 cm

⇒ Circumference = 2 × (22/7) × 28 = 176 cm

⇒ Breadth (b) = (6/7) × 28 = 24 cm

⇒ Perimeter of Rectangle = 2(l + b) = 176

⇒ l + 24 = 88 ⇒ l = 64 cm

⇒ Area of Rectangle = 64 × 24 = 1536 cm²

∴ The correct answer is 1536 cm².

Additional Information

Standard Circle Values

For r = 7, Area = 154, Circumference = 44. Since Area ∝ r², if r is multiplied by 4 (r=28), Area is multiplied by 16 (154 × 16 = 2464).

Mensuration Formulas

Rectangle Perimeter = 2(Length + Breadth) and Circle Circumference = 2πr. For competitive exams, memorizing squares up to 30 is essential (√784 = 28).

Shortcut Trick

Total time for Car M: (100/50) + (50/25) + (100/20) = 2 + 2 + 5 = 9 hours.

Car N starts 1 hour later, so it travels for only 9 − 1 = 8 hours when M reaches Q.

In 8 hours, Car N travels: 100 km (at 50 kmph in 2h) + 50 km (at 25 kmph in 2h) + 80 km (at 20 kmph in 4h) = 230 km.

Half distance of PQ = 250 ÷ 2 = 125 km. Required distance = 230 − 125 = 105 km.

∴ The correct answer is 105 km.

Alternate Method

Given: Total Distance = 250 km. Car M leaves 1 hour earlier than Car N.

Formula Used: Time = Distance ÷ Speed

⇒ Time taken by Car M for first 100 km = 100 ÷ 50 = 2 hours.

⇒ Time taken by Car M for next 50 km = 50 ÷ 25 = 2 hours.

⇒ Remaining distance = 250 − (100 + 50) = 100 km.

⇒ Time taken by Car M for remaining 100 km = 100 ÷ 20 = 5 hours.

⇒ Total time for Car M to reach Q = 2 + 2 + 5 = 9 hours.

⇒ Car N starts 1 hour later, so it travels for (9 − 1) = 8 hours.

⇒ Distance by Car N in 8 hours: First 2h = 100 km, Next 2h = 50 km, Remaining 4h = 4 × 20 = 80 km.

⇒ Total distance covered by Car N = 100 + 50 + 80 = 230 km.

⇒ Half of distance PQ = 250 ÷ 2 = 125 km.

⇒ Distance between Car N and mid-point = 230 − 125 = 105 km.

∴ The correct answer is 105 km.

Additional Information

Average Speed with Variable Speeds

Average Speed = Total Distance ÷ Total Time. For this journey, Avg Speed = 250 ÷ 9 ≈ 27.78 km/hr.

Relative Speed

When two objects move in the same direction, relative speed is the difference of their speeds (S₁ − S₂).

Time Lag Problems

If one object starts 't' hours late, its travel time is (Total Time of first object − t).

Given:-

Six persons - P, Q, R, S T, and U

Two different dates - 9 and 26

Three different months - March, May, and November

Six Cities - Pune, Gaya, Vadodara, Sonipat, Kota and Mysore.

Now,

1. U went on an odd-numbered date.

2. Only two persons went between the one who went to Mysore and U. 

3) R and Q went on the same date but none of them went in November.

4. The one who went to Vadodara went immediately before Q but not in May.

5) As many persons went after T is the same as before the one who went to Kota.

6. T did not go in March.

7) Only one person went between the one who went to Pune and Sonipat.

8) S did not go to Pune.

9) P went immediately after the one who went to Sonipat but did not go to Mysore. This is possible only in Case III.

Hence, the final arrangement is -

Hence, the correct answer is Q went to Mysore city.

Given:-

Six persons - P, Q, R, S T, and U

Two different dates - 9 and 26

Three different months - March, May, and November

Six Cities - Pune, Gaya, Vadodara, Sonipat, Kota and Mysore.

Now,

1. U went on an odd-numbered date.

2. Only two persons went between the one who went to Mysore and U. 

3) R and Q went on the same date but none of them went in November.

4. The one who went to Vadodara went immediately before Q but not in May.

5) As many persons went after T is the same as before the one who went to Kota.

6. T did not go in March.

7) Only one person went between the one who went to Pune and Sonipat.

8) S did not go to Pune.

9) P went immediately after the one who went to Sonipat but did not go to Mysore. This is possible only in Case III.

Hence, the final arrangement is -

P went to the tour on 26th November.

Hence, the correct answer is 26th November.

Given:-

Six persons - P, Q, R, S T, and U

Two different dates - 9 and 26

Three different months - March, May, and November

Six Cities - Pune, Gaya, Vadodara, Sonipat, Kota and Mysore.

Now,

1. U went on an odd-numbered date.

2. Only two persons went between the one who went to Mysore and U. 

3) R and Q went on the same date but none of them went in November.

4. The one who went to Vadodara went immediately before Q but not in May.

5) As many persons went after T is the same as before the one who went to Kota.

6. T did not go in March.

7) Only one person went between the one who went to Pune and Sonipat.

8) S did not go to Pune.

9) P went immediately after the one who went to Sonipat but did not go to Mysore. This is possible only in Case III.

Hence, the final arrangement is -

T went to Pune.

Hence, the correct answer is Pune.

Given:-

Six persons - P, Q, R, S T, and U

Two different dates - 9 and 26

Three different months - March, May, and November

Six Cities - Pune, Gaya, Vadodara, Sonipat, Kota and Mysore.

Now,

1. U went on an odd-numbered date.

2. Only two persons went between the one who went to Mysore and U. 

3) R and Q went on the same date but none of them went in November.

4. The one who went to Vadodara went immediately before Q but not in May.

5) As many persons went after T is the same as before the one who went to Kota.

6. T did not go in March.