SBI PO Prelims Memory Based Paper (Held On: 1 November 2023 Shift 3) (Previous Year Paper)

The correct answer is 'Rescue.'

Key Points

• The given sentence talks about a special team that was formed to save the lost fisherman who was trapped in the freezing lake after dark.
• Therefore, the most appropriate word to be filled in the blank is 'Rescue'.
• Also, the use of the word ''stranded'' in the sentence indicates the use of the word 'rescue' in the blank.
• The word 'Rescue' means To save someone or something from a dangerous situation. (व्‍यकि्त या वस्‍तु को बचाना या का उद्घार करना)
• Example: Firefighters were able to rescue all of the building’s residents but could not save a few of the pets.

Hence, the correct answer is option 1.

Complete Sentence: A special team was formed to rescue the lost fisherman who was stranded on the freezing lake after dark.

Additional Information

• Let us explore the other options:
• Unpleasant means Causing you to have a bad feeling; not nice. (अप्रीतिकर कटु भाव उत्‍पन्‍न करने वाला; अरुचिकर)
• Meditate means To think carefully and deeply, especially for religious reasons or to make your mind calm. (ध्‍यानपूर्वक और गहराई से चिंतन करना, ध्‍यान लगाना)
• Speculate means To guess something. (कुछ अनुमान लगाना; अटकल लगाना)
• Revenue means The money generated from normal business operations, calculated as the average sales price times the number of units sold. (आय)

The correct answer is 'Portray.'

Key Points

• The given sentence says if the media continues to characterize or describe young black men as thugs and gangsters, the standard image of such men will continue to exist in society.
• Therefore, the most appropriate word to be filled in the blank is 'Portray'.
• Also, the use of the word ''media'' in the sentence indicates the use of the word 'portray' in the blank.
• The word 'Portray' means To describe somebody or something in a particular way. (किसी का विशेष प्रकार से वर्णन या चित्रण करना)
• Example: The media is going to portray the killer as a victim of society’s avoidance of mental health issues.

Hence, the correct answer is option 3.

Complete Sentence: If the media continues to portray young black men as thugs and gangsters, the stereotype will continue to persist in society.

Additional Information

• Let us explore the other options:
• Betray means To hurt somebody who trusts you, especially by not being loyal or faithful to him or her. (विश्‍वासघात करना, धोखा देना, किसी के विश्‍वास को तोड़ना)
• Deceive means To try to make somebody believe something that is not true. (बहकाना, भ्रमित करना)
• Request means An act of asking for something. (किसी बात के लिए अनुरोध या निवेदन; प्रार्थना)
• Console means To make somebody happier when he/she is very sad or disappointed. (दुःख या निराशा में धैर्य बाँधाना, दिलासा या सांत्‍वना देना)

The correct answer is 'Recover.'

Key Points

• The given sentence is talking about how the police were able to find a woman’s stolen purse.
• Therefore, the most appropriate word to be filled in the blank is 'Recover'.
• Also, the use of the word ''stolen'' in the sentence indicates the use of the word 'recover' in the blank.
• The word 'Recover' means To find or regain possession of something lost or taken. (खोयी हुई वस्‍तु को ढूँढ़ लेना या चोरी गई वस्‍तु को पुनः पा लेना)
• Example: To recover her lost ID, Richa went to the school office to see if anyone had found it and turned it in.

Hence, the correct answer is option 5.

Complete Sentence: The police were able to recover the woman’s stolen purse after they caught and arrested the thief who had taken it.

Additional Information

• Let us explore the other options:
• Prefer means To choose something rather than something else; to like something better. (एक के स्‍थान पर दूसरे को चुनना; किसी वस्‍तु को अधिक पसंद करना)
• Instruct means To give an order to somebody; to tell somebody to do something. (किसी व्‍यक्ति को आदेश देना; कुछ करने का निर्देश देना)
• Refer means To mention or talk about somebody or something. (व्‍यक्ति या वस्‍तु के विषय में उल्‍लेख या चर्चा करना)
• Obstruct means To stop something from happening or somebody or something from moving, either by accident or deliberately. (किसी के काम में अड़चन डालना या रुकावट पैदा करना)

The correct answer is 'cursory'.

Key Points

• The given sentence talks about the manager urging his team to avoid mistakes and ensure thorough evaluations.
• Therefore, the most appropriate word for the given blank would be 'cursory'.
• 'Cursory' means something done hastily with minimal attention to detail. (सतही, स्पष्ट नहीं)
• Example: Given the time constraints, she gave the report only a cursory glance.
• Hence, the correct answer is 'Option 1'.

The complete sentence would be: The manager urged the team to avoid cursory evaluations and strive for thoroughness.

Additional Information Let's understand the meaning of the other given options:

• Foolishness: Lack of good sense or judgment; acting without wisdom or prudence. (मूर्खता, अबुद्धिमत्ता)
• Precise: Clearly expressed and accurate; exact in detail; definite or specific. (सटीक, निश्चित)
• Attentive: Paying close attention; observant, considerate, and thoughtful. (सतर्क, ध्यानी)
• Thorough: Exhaustive, complete, or detailed; covering all aspects; careful and comprehensive. (पूरा, विस्तृत)

The correct answer is option 2. 

Key Points

• "Everyone" is a singular subject and should be paired with a singular verb.
• Thus, 'were' should be replaced with 'was' to be grammatically correct.

Additional Information

• Subject-Verb Agreement In English, the form of the verb must match the form of the subject in terms of number (singular or plural) and person (first, second, or third). A singular subject should be paired with a singular verb, and a plural subject should be paired with a plural verb.
• In the third sentence, "Everyone at the meeting were surprised," the subject "everyone" is actually singular, even though it refers to a group of people. It should therefore be paired with the singular form of the verb "to be." The correct phrase is "Everyone was surprised," not "Everyone were surprised." This stresses the importance of ensuring proper subject-verb agreement, regardless of whether the semantic meaning of a subject seems to suggest a group.

The correct answer is Option 1.

Key Points

• The error lies in part A because the introductory participial phrase "Running through the park" creates a dangling modifier.
• A participial phrase should clearly modify the person or thing performing the action.
• Here, the phrase incorrectly appears to modify "a squirrel", whereas the intended doer of the action is the narrator ("I").
• Thus, the error originates from the introductory phrase in part A, making it the correct answer.

Therefore, the correct answer is A.

Correct Sentence: "While I was running through the park, a squirrel caught my attention as it was darting up a tree in search of its nest."

Additional Information

• B: "a squirrel caught my attention" – This clause is grammatically correct and does not require any change.
• C: "as it was darting up a tree" – This part correctly describes the squirrel's action.
• D: "in search of its nest" – This phrase is grammatically correct and appropriately modifies the verb "darting."
• No Error – This option is incorrect because the sentence contains a dangling modifier in part A.

The correct answer is option 1.

Key Points

Part A of the sentence i.e. 'As it is to be superior than' is erroneous.

• Here, the preposition 'than' used after the adjective 'superior' is incorrect and it should be replaced with the preposition 'to'.
• As per English Grammar rules, the adjectives inferior, superior, senior, junior, prior etc. take the preposition 'to' not 'than'.
• For Example -
• The air hostess asked all the passengers to fasten their seat belts prior to descent.
• You can give this task to someone junior to you.
• Hence, the correct answer is A.
• The correct sentence would be - As it is to be superior to static graphics, animation is being increasingly employed in technology-based learning resources.

​

Additional Information

Let's understand the use of the prepositions 'to' and 'than' - 

To - 

• It is used to indicate the place, person, or thing that someone or something moves toward, or the direction of something.
• For Example -
• We went to the shopping mall.
• It is used to indicate a limit or an ending point.
• For Example -
• The clothes were piled up to the roof in the cupboard.
• It is used to indicate the relationship between two things.
• For Example -
• Your time is very important to us.
• It is also used to indicate a time or a period.
• For Example -
• I work from nine to five on weekdays.

Than - 

• It is used used for comparing and to introduce the second part of a comparison.
• For Example -
• I like cake more than pie.

The correct answer is 'D'.

Key Points 

• There is an error in Part D of the given sentence.
• The word 'valuation' should be replaced by the v+ing form 'valuing'.
• 'Valuation' is a noun but here we need a verb+ ing form because 'for' is used before that.
• The idiom 'silver bullet' means a simple and seemingly magical solution to a complicated problem.
• Hence, as per the context of the given sentence 'valuing' should be there in place of 'valuation'.
• valuing means estimating the monetary worth of.
• Example:- "his estate was valued at £45,000"
• Correct sentence:- Most investors would agree that there is no silver bullet for valuing companies.

Hence, option 4 is the correct answer.

Additional Information

• For -
• It is used to indicate the use of something.
• For Example -
• You can use detergent for washing your dirty clothes.

The correct answer is 'C'.

Key Points 

• There is an error in Part C of the given sentence.
• The word 'high' should be replaced by the adjective 'highly'.
• 'uneven energy landscape' is a complete noun in Part D.
• 'uneven' is an adjective.
• The word that gives more information about adjectives is an adverb.
• Adverb should be there in the place of 'high'.
• 'highly' is an adverb which means at or to a high degree or level. 
• ​Example:- "a highly dangerous substance"
• Correct sentence:- Technical innovation in India's renewable energy policy is deepening a highly uneven energy landscape

Hence, option 3 is the correct answer.

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 'A-R and B-Q.'

Key Points

• From the given options, only the combination of phrases 'A-R and B-Q' creates correct sentences.
• Let's look at the sentences:
• 'A-R' talks about Sophie who was born in France, but shortly after that her family moved (स्‍थान बदलना) to the United States.
• 'Thereafter' means ''after that time''. (उसके बाद; तत्‍पश्‍चात)
• 'B-Q' talks about the recession (मंदी) that blindsided (अंधा करना) a lot of lawyers who at earlier time had taken for granted (किसी चीज़ या किसी को बहुत हल्के में महत्व देना) their comfortable income.
• 'Previously' means ''at a previous or earlier time; before''. (पहले, पूर्व में)

Hence, the correct answer is option 3.

The correct answer is 'B-P and C-Q.'

Key Points

• From the given options, only the combination of phrases 'B-P and C-Q' creates correct sentences.
• Let's look at the sentences:
• 'B-P' talks about those who in business are not, generally, conversant (जानकार या परिचित) with basic scientific principles.
• 'On the whole' means ''generally, but not true in every case''. (सामान्‍य रूप से)
• 'C-Q' talks about someone who is giving advice to the other person to change shampoo and conditioner sometimes to avoid product build-up (समयावधि में हुई वृद्धि).
• 'Once in a while' means ''sometimes but not often''. (कभी-कभी बार-बार नहीं)

Hence, the correct answer is option 2.

The correct answer is 'C-R.'

Key Points

• From the given options, only the combination of phrases 'C-R' creates the correct sentence.
• Let's look at the sentences:
• 'C-R' talks about someone who was jailed for 33 months simultaneously with a sentence (न्‍यायाधीश द्वारा अपराधी को दिया गया दंड) he is already serving (जेल में निश्चित अवधि के लिए अपराध की सज़ा काटना) for burglary (चोरी करने के उद्देश्य से गैर-क़ानूनी रूप से किसी इमारत में घुसने का अपराध).
• 'Concurrently' means ''at the same time; simultaneously''. (समकालिक रूप से)

Hence, the correct answer is option 4.

The correct answer is 'B-R and C-P.'

Key Points

• From the given options, only the combination of phrases 'B-R and C-P' creates correct sentences.
• Let's look at the sentences:
• 'B-R' talks about a project that will instead produce valuable reference material and should be lauded (प्रशंसा करना) for its novelty (नयापन) and foresight (दूरदर्शिता).
• 'On the contrary' means ''the opposite is true; certainly not'' used to intensify a denial of what has just been implied or stated by suggesting that the opposite is the case. (इसके विपरीत; बिलकुल नहीं)
• 'C-P' talks about a man who wore a bathrobe (नहाने का चोगा) and clearly had just come from the bathroom.
• 'Evidently' means ''in a way that is clearly seen or understood; obviously''. (स्‍पष्‍ट रूप से; जो आसानी से दिखाई दे या समझ में आए)

Hence, the correct answer is option 3.

The correct answer is 'Option 3.'

Key Points

• The error lies in the verb form used after "everyone." The subject "everyone" requires the singular form of the verb, which is "comes," not "come."
• "Comes forward" indicates the action of stepping up or volunteering, which aligns with the context of offering help.
• The infinitive "to help him" properly completes the action, indicating the purpose of coming forward.
• Hence, the correct phrase is 'comes forward to help him'.

Therefore, the correct answer is 'Option 3'.

Additional Information

• "came towards him for help": This option uses the past tense "came," which is incorrect because the sentence is in the present tense.
• "comes towards him for help" maintains the present tense, it doesn't convey the sense of proactive action or volunteering that "comes forward" does.
• "comes forward for help him": This option has a grammatical error; the preposition "for" is unnecessary and incorrect. It should be "to help him."

The correct answer is 'Option 3'.

Key Points

• The error lies in the placement and form of the adjective "immediate" modifying "suspension."
• "Immediate" should be used before the noun it modifies, so it should be "immediate suspension."
• The verb "ordered" needs to agree in past tense with the rest of the sentence.
• Hence, the correct phrase is 'ordered immediate'.

Therefore, the correct answer is 'Option 3.'

Additional Information

• "order immediately": This option changes the structure of the sentence. "Order immediately suspension" is not grammatically correct because "immediately" should be modifying "suspension," not "order."
• "order immediate": Similar to the previous option, "order immediate suspension" is grammatically incorrect. It lacks the past tense form of the verb "ordered" and also doesn't include "the" before "immediate suspension."
• "ordering immediate": This option changes the verb tense to present participle form, which is not suitable in this context

The correct answer is "Option 2".

Key Points

• The correct phrase to be substituted in the above sentence is "most of Europe are increasing".
• The given sentence is in the present tense.
• The subject is "Sub-zero temperatures" (Plural Subject), so a plural verb will be used.
• Hence, "most of Europe are increasing" is the correct phrase to be substituted.

Therefore, the correct answer is "Option 2".

Correct Sentence: "Sub-zero temperatures throughout most of Europe are increasing demand for gas, and several governments have issued calls for conservation."

Additional Information

• "most of Europe were increased" is incorrect because it uses the past tense "were increased,".
• "much of the Europe is increasing" is incorrect because it includes an unnecessary article "the" before "Europe," and it also uses "much of" instead of "most of."
• "much of Europe have been increasing" is incorrect because it uses "much of" instead of "most of."

The correct answer is option B.

Key Points

• To answer this question, let's first understand the meaning of the word "disseminate" in the context of the passage:
• Disseminate - to spread or distribute information widely (फैलाना)
• For Example -
• The organization aims to disseminate health education in rural areas.
• Now, let's consider the options:
• Distribute - to give or deliver something to multiple people (वितरण करना)
• For Example -
• They distributed free meals to the homeless every Sunday.
• Conceal, Withhold, Hide, and Cover all imply not spreading or sharing something, which is opposite of disseminating.
• Therefore, the correct answer is "Distribute," which is synonymous with disseminate as both involve spreading something widely.

The correct answer is option B.

Key Points

• Let's explore the meaning of "empower" in the context used in the passage:
• Empower - to give someone the authority or power to do something (अधिकार देना)
• For Example -
• Education empowers individuals to make informed decisions about their lives.
• Now, examining the options:
• Enable - to make someone able to do something, or to make something possible (सक्षम करना)
• For Example -
• Technology enables quicker communication across long distances.
• Weaken, Prevent, Prohibit, Disable are all terms that reduce power or capability, which are opposite to empowering.
• Therefore, the correct synonym for empower in this context is "Enable."

The correct answer is Option 2) Only B

Key Points

• The passage highlights the role of financial advisory influencers in simplifying complex financial concepts for the general public. Specifically, it mentions that "They simplify the esoteric world of finance, which often seems intimidating to the uninitiated, by breaking down complex concepts into digestible chunks." This approach helps empower individuals to make informed decisions about their finances. Therefore, statement B is true.

Additional Information

• Statement A is incorrect as the passage does not suggest that financial advisory influencers primarily focus on selling their products. Instead, it describes their role as educators who use social media to make financial knowledge more accessible.
• Statement C is also inaccurate based on the passage, which notes the importance of consumers critically evaluating the advice since it may not always be tailored to individual needs or legally binding. The influencers' main role is to educate, not to provide formal financial advisement like certified professionals.

The correct answer is option B.

Key Points

• To answer this question, refer to the first and second paragraphs of the passage:
• "These individuals leverage social media platforms to disseminate knowledge and advice on various financial topics. By breaking down complex concepts into digestible chunks, they empower individuals to make informed decisions about their money."
• From this part of the passage, it's clear that the primary role of financial advisory influencers is to make complex financial information accessible and understandable to the general public, helping them make informed decisions.
• Therefore, the correct answer is 'To simplify complex financial concepts for the general public.'

The correct answer is option B.

Key Points

• Refer to the fourth paragraph of the passage for information on the challenges:
• "The accuracy of the information they provide can vary, and their recommendations might not always be tailored to individual needs."
• The passage does not mention an inability to reach a wide audience as a challenge. Instead, it discusses the variability in information accuracy and the lack of tailored recommendations as challenges.
• Therefore, the correct answer is 'Their inability to reach a wide audience.'

The correct answer is option D.

Key Points

• Understanding the word "complex" as used in the passage:
• Complex - consisting of many different and connected parts; not simple (जटिल)
• For Example -
• Quantum physics is a very complex subject.
• Considering the options:
• Simple - easily understood or done; presenting no difficulty (सरल)
• For Example -</

The correct answer is option C.

Key Points

• Refer to the fourth paragraph of the passage where it discusses evaluating advice:
• "It's essential for consumers to critically evaluate the advice given and consider consulting professional financial advisors for personalized guidance."
• This indicates that not all advice from influencers may be accurate or suitable for every individual, emphasizing the importance of critical evaluation to ensure it fits their personal financial circumstances.
• Therefore, the correct answer is 'Because the advice might not always be accurate or suitable for everyone.'

The correct answer is option 3 i.e. dislike.

Key Points

We have to choose the word which is similar to the emboldened word and replace it. 

• Resent: Feel bitterness towards someone for what they did.
• Dislike: Feel distaste or not like someone for what they did.

Additional Information

Let's take a look at the meaning and usage of all the words given in the question and options-

• Admire: Regard someone with respect
• Agree: To have the same opinion with someone about something
• Welcome: Gladly receive someone

Therefore, from the given options, the best alternative for the emboldened word is 'dislike'.

The correct answer is option 2 i.e. let down.

Explanation:

We have to choose the word which is similar to the emboldened word and can replace it. 

Let's take a look at the meaning and usage of all the words given in the question and options-

• Disappointed: sad, upset and displeased because something didn't meet one's expectations
• Riled up: irritated or annoyed
• Let down: did not meet expectations; disappointed (someone)
• Let go: allowed someone or something to escape or be free
• Give up: stop making an effort

Therefore, from the given options, the best alternative for the 'emboldened' word is ‘let down'.

General solution:

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

Solution:

Number of males visited park in FN on Monday = 120 ×  3/5 = 72

Number of males visited park in AN on Monday = 120 - 72 = 48

Number of males having four wheelers AN on Monday = 48/2 = 24

Total having two wheelers visiting on Monday = (72 + 24) = 96

General solution:

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

Solution:

Number of females visited park on Monday = 150

Number of females visited park on Saturday = 150 ×  (120/100) = 180

Number of married females visiting park on saturday = 180 ×  (3/5) = 108

Number of unmarried females = (180 - 108) = 72

Required percentage = 72/(700) ×  100 = 10.28%

General solution:

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

Solution:

Number of males visited park on Tuesday = 200

Number of males visited park on Thursday = 140

Number of females visited park on Monday = 150

Number of females visited park on Wednesday = 200

Required difference = (350 - 340) = 10

General solution:

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

Solution:

Number of males visiting park below 30 = 120/3 = 40

Number of males visiting park above 30 = (120 - 40) = 80

Number of males visiting park below 30 = 180 ×  2/3 = 120 

Number of males visiting park above 30 = (180 - 120) = 60

Number of females visiting above = (250 - 140) = 110

solution:

Monday:

Number of (males + females) visiting park = 1500 ×  (18/100) = 270

Number of males visiting parks = 800 ×  (15/100) = 120

Number of females visiting parks = (270 - 120) = 150

Tuesday:

Number of (males + females) visiting park = 1500 ×  (22/100) = 330

Number of males visiting parks = 800 ×  (25/100) = 200

Number of females visiting parks = (330 - 200) = 130

Wednesday:

Number of (males + females) visiting park = 1500 ×  (24/100) = 360

Number of males visiting parks = 800 ×  (20/100) = 160

Number of females visiting parks = (360 - 160) = 200

Thursday:

Number of (males + females) visiting park = 1500 ×  (16/100) = 240

Number of males visiting parks = 800 ×  (17.5/100) = 140

Number of females visiting parks = (240 - 140) = 100

Friday:

Number of (males + females) visiting park = 1500 ×  (20/100) = 300

Number of males visiting parks = 800 ×  (22.5/100) = 180

Number of females visiting parks = (300 - 180) = 120

Solution:

Number of males visiting park on Tuesday = 200

Number of males visiting park on Wednesday = 160

Number of females visiting park on Thursday = 100

Number of females visiting park on Friday = 120

Required ratio = (200 + 160): (100 + 120) = 360: 220 = 18: 11

Shortcut Trick

Let the initial average weight of 20 contestants be A.

Weight of contestant who left (L) = 20 × A − 19 × (A + 5.75) = A − 109.25

Weight of contestant who joined (J) = 20 × (A + 5.75 − 2.75) − 19 × (A + 5.75) = A − 49.25

Difference (J − L) = (A − 49.25) − (A − 109.25) = 109.25 − 49.25 = 60 kg.

∴ The correct answer is 60 kg.

Alternate Method

Given: Initial count = 20, Change when 1 left = +5.75 kg (on 19 people), Change when 1 joined = −2.75 kg (on 20 people).

⇒ Total initial weight = 20 × A

⇒ Total weight after 1 leaves = 19 × (A + 5.75) = 19A + 109.25

⇒ Weight of contestant who left (L) = 20A − (19A + 109.25) = A − 109.25

⇒ Total weight after new one joins = 20 × (A + 5.75 − 2.75) = 20 × (A + 3) = 20A + 60

⇒ Weight of contestant who joined (J) = (20A + 60) − (19A + 109.25) = A − 49.25

⇒ Difference = J − L = (A − 49.25) − (A − 109.25) = 109.25 − 49.25

⇒ Difference = 60 kg.

∴ The correct answer is 60 kg.

Additional Information

Average weight Change

When a person leaves, New Avg = (Total Sum − Left Weight) ÷ (n − 1). If the average increases, the person who left was lighter than the average.

Joiner Weight Formula

New Weight = Old Avg + (New count × Change in Avg). This helps in calculating the weight of a person entering a group.

Replacement Logic

If one leaves and one joins, New Weight − Old Weight = Total Strength × Total change in average.

Shortcut Trick Given average speed = 6.4 km/hr and speed a is an integer. Possible values for a must satisfy (a − 1) < 6.4 < a, so a = 7. Speeds are 7 km/hr (snowing) and 6 km/hr (not snowing). Let x be the fraction of distance covered while snowing: 6.4 = 1 / [x/7 + (1−x)/6]. Solving for x gives 7/16. ∴ The correct answer is 7/16. Alternate Method Given: Average speed = 6.4 km/hr, speeds are a and a − 1, where a is an integer. Formula Used: Average Speed = Total Distance ÷ Total Time ⇒ Since average speed (6.4) must lie between the two speeds: a − 1 < 6.4 < a ⇒ a = 7 km/hr and a − 1 = 6 km/hr ⇒ Let total distance be 1 unit and x be the fraction covered at 7 km/hr. ⇒ 6.4 = 1 ÷ [x/7 + (1 − x)/6] ⇒ 6.4 = 1 ÷ [(6x + 7 − 7x)/42] ⇒ 6.4 = 42 ÷ (7 − x) ⇒ 7 − x = 42 ÷ 6.4 ⇒ 7 − x = 420 ÷ 64 = 105 ÷ 16 ⇒ x = 7 − 105/16 = (112 − 105)/16 ⇒ x = 7/16 ∴ The correct answer is 7/16. Additional Information Average Speed Concept Average speed is the total distance divided by the total time. It always lies between the minimum and maximum speeds of the journey segments. Harmonic Mean If equal distances are covered, average speed is the harmonic mean of speeds: 2v1v2/(v1+v2). Integer Constraint When a value is specified as an integer, use the range of the average to narrow down possible values to the nearest whole numbers.

Calculation:

The series follows the following pattern:

⇒ 12 × 0.5 – 0.5 = 5.5

⇒ 5.5 × 1 + 1 = 6.5

⇒ 6.5 × 2 – 2 = 11

⇒ 11 × 4 + 4 = 48

⇒ 48 × 8 – 8 = 376

∴ The value of ? is 48

GIVEN:

930, 812, 506, ?, 272, 156

Calculation: 

⇒ 930 = 31² - 31

⇒ 812 = 292 - 29

⇒ 506 = 232 - 23

⇒ ? = 342 = 192 - 19

⇒ 272 = 172 - 17

⇒ 156 = 132 - 13

∴ The required value of "?" is 342.

Given:

6000, ?, 3000, 4500, 9000, 22500

Calculation:

⇒ 6000 × 0.5 = 3000

⇒ 3000 × 1 = 3000

⇒ 3000 × 1.5 = 4500

⇒ 4500 × 2 = 9000

⇒ 9000 × 2.5 = 22500

∴ ? = 3000

Calculation:

1512 + 12 = 1524

1524 + 16 = 1540

1540 + 23 = 1563

1563 + 33 = 1596

1596 + 46 = 1642

∴ ? = 1596

Given:

290 , ? , 374 , 421 , 474 , 533 

Calculation:

Here the logic follows as,

The series follows the addition of prime numbers from 41

Then, The second term will be,

= 290 + 41 

= 331

$\therefore$ The correct answer is 331.

Shortcut Trick

Effective Rate of Interest for 2 years (compounded annually) = 20 + 20 + (20 × 20)/100 = 44%

Effective Rate of Interest for 1 year (compounded half-yearly) = 10 + 10 + (10 × 10)/100 = 21%

Difference in interest rates = 44% − 21% = 23%

23% of Sum = ₹4,600 → 1% = ₹200 → 100% = ₹20,000

∴ The correct answer is Rs. 20,000.

Alternate Method

Given: Rate (R) = 20% p.a., Difference in Interest = ₹4,600

Formula Used: CI = P[(1 + R/100)ⁿ − 1]

⇒ Case 1 (Annually, 2 yrs): CI₁ = P[(1 + 20/100)² − 1] = P[(1.2)² − 1] = 0.44P

⇒ Case 2 (Half-yearly, 1 yr): R = 10%, n = 2; CI₂ = P[(1 + 10/100)² − 1] = P[(1.1)² − 1] = 0.21P

⇒ Difference = 0.44P − 0.21P = 0.23P

⇒ 0.23P = 4600

⇒ P = 4600 / 0.23 = 20,000

∴ The correct answer is Rs. 20,000.

Additional Information

Effective Rate for Compounding

For two successive cycles of rate r%, the effective rate is [r + r + (r × r)/100]%. This applies to 2 years annually or 1 year half-yearly.

Compounding Half-yearly

When interest is compounded half-yearly, the Annual Rate is halved (R/2) and the Time period is doubled (2n).

Relationship between CI and SI

Difference between CI and SI for 2 years is P(R/100)². For 1 year, CI and SI are equal if compounded annually.

Shortcut Trick

Equate the total parts of each bag to their LCM (6, 10, 7) = 210, then scale by volume ratios 3 : 5 : 7.

Bag 1 (3 × 210): Lime = 3 × 175 = 525, Silica = 3 × 35 = 105

Bag 2 (5 × 210): Lime = 5 × 147 = 735, Silica = 5 × 63 = 315

Bag 3 (7 × 210): Lime = 7 × 90 = 630, Silica = 7 × 120 = 840

Total Lime : Total Silica = (525 + 735 + 630) : (105 + 315 + 840) = 1890 : 1260 = 3 : 2.

∴ The correct answer is 3 : 2.

Alternate Method

Given: Volume Ratio = 3 : 5 : 7. Ratios (L:S) = 5:1, 7:3, 3:4.

Formula: Total Lime = ∑ (Volume_i × Fraction of Lime_i)

⇒ Total Lime = 3 × (5/6) + 5 × (7/10) + 7 × (3/7)

⇒ Total Lime = 15/6 + 35/10 + 3 = 2.5 + 3.5 + 3 = 9

⇒ Total Silica = 3 × (1/6) + 5 × (3/10) + 7 × (4/7)

⇒ Total Silica = 3/6 + 15/10 + 4 = 0.5 + 1.5 + 4 = 6

⇒ Final Ratio = 9 : 6 = 3 : 2

∴ The correct answer is 3 : 2.

Additional Information

Mixture Balancing

To mix quantities of different ratios, first equalize the total parts by taking the LCM of the sums of the ratio parts before applying the volume weights.

Alligation for Three Components

When three or more mixtures are combined, the final ratio is the sum of the weighted averages of each individual component's concentration.

General solution:

2400 + 5500 + 280X + 32000 ×  X/100 = 15400

2400 + 5500 + 280X + 320X = 15400

600X = 7500

X = 25/2

Village A:

Total population = 2400 

Percentage of females = (50 - 12.5) = 37.5%

Number of females = (2400×  37.5/100) = 900

Number of males = 2400 - 900 = 1500

Village B:

Total population = 5500 

Percentage of females= (19.5 + 12.5) = 32%

Number of females = 5500 ×  (32/100) = 1760

Number of males = (5500 - 1760) = 3740

Village C:

Total population = (280 × 12.5) = 3500

Percentage of females = 40.2%

Number of females = 3500 ×  (40.2/100) = 1407

Number of males = (3500 - 1407) = 2093

Village D: 

Total population = 32000 ×  (12.5/100) = 4000

Percentage of females = 30%

Number of females = 4000 ×  (30/100) = 1200

Number of males = (4000 - 1200) = 2800

Solution:

Total number of males in village D = 2800

Number of graduated males working = 2800 ×   2/7 = 800

Number of non graduated males working = 2800 - 800 = 2000

Number of male job workers = 800 ×  (40/100) = 320

Required difference = (2000 - 320) = 1680

General solution:

2400 + 5500 + 280X + 32000 ×  X/100 = 15400

2400 + 5500 + 280X + 320X = 15400

600X = 7500

X = 25/2

Village A:

Total population = 2400 

Percentage of females = (50 - 12.5) = 37.5%

Number of females = (2400×  37.5/100) = 900

Number of males = 2400 - 900 = 1500

Village B:

Total population = 5500 

Percentage of females= (19.5 + 12.5) = 32%

Number of females = 5500 ×  (32/100) = 1760

Number of males = (5500 - 1760) = 3740

Village C:

Total population = (280 × 12.5) = 3500

Percentage of females = 40.2%

Number of females = 3500 ×  (40.2/100) = 1407

Number of males = (3500 - 1407) = 2093

Village D: 

Total population = 32000 ×  (12.5/100) = 4000

Percentage of females = 30%

Number of females = 4000 ×  (30/100) = 1200

Number of males = (4000 - 1200) = 2800

Solution:

Number of females in village B = 1760

Number of females in village E = 1760 ×  9/8 = 1980

Average number of females in village E and A = (1980 + 900)/2 = 1440

General solution:

2400 + 5500 + 280X + 32000 ×  X/100 = 15400

2400 + 5500 + 280X + 320X = 15400

600X = 7500

X = 25/2

Village A:

Total population = 2400 

Percentage of females = (50 - 12.5) = 37.5%

Number of females = (2400×  37.5/100) = 900

Number of males = 2400 - 900 = 1500

Village B:

Total population = 5500 

Percentage of females= (19.5 + 12.5) = 32%

Number of females = 5500 ×  (32/100) = 1760

Number of males = (5500 - 1760) = 3740

Village C:

Total population = (280 × 12.5) = 3500

Percentage of females = 40.2%

Number of females = 3500 ×  (40.2/100) = 1407

Number of males = (3500 - 1407) = 2093

Village D: 

Total population = 32000 ×  (12.5/100) = 4000

Percentage of females = 30%

Number of females = 4000 ×  (30/100) = 1200

Number of males = (4000 - 1200) = 2800

Solution:

Number of  males in village B = 3740

Number of males in village C = 2093

Number of females in village A = 900

Number of females in village B = 1760

Required difference = (5833 - 2660) = 3173

General solution:

2400 + 5500 + 280X + 32000 ×  X/100 = 15400

2400 + 5500 + 280X + 320X = 15400

600X = 7500

X = 25/2

Village A:

Total population = 2400 

Percentage of females = (50 - 12.5) = 37.5%

Number of females = (2400×  37.5/100) = 900

Number of males = 2400 - 900 = 1500

Village B:

Total population = 5500 

Percentage of females= (19.5 + 12.5) = 32%

Number of females = 5500 ×  (32/100) = 1760

Number of males = (5500 - 1760) = 3740

Village C:

Total population = (280 × 12.5) = 3500

Percentage of females = 40.2%

Number of females = 3500 ×  (40.2/100) = 1407

Number of males = (3500 - 1407) = 2093

Village D: 

Total population = 32000 ×  (12.5/100) = 4000

Percentage of females = 30%

Number of females = 4000 ×  (30/100) = 1200

Number of males = (4000 - 1200) = 2800

Solution:

Number of females in village D = 1200

Number of females in village F is 1200/75 ×  100 = 1600

Total number of males and females in village F = 3400

Number of males in village F = (3400 - 1600) = 1800

General solution:

2400 + 5500 + 280X + 32000 ×  X/100 = 15400

2400 + 5500 + 280X + 320X = 15400

600X = 7500

X = 25/2

Village A:

Total population = 2400 

Percentage of females = (50 - 12.5) = 37.5%

Number of females = (2400×  37.5/100) = 900

Number of males = 2400 - 900 = 1500

Village B:

Total population = 5500 

Percentage of females= (19.5 + 12.5) = 32%

Number of females = 5500 ×  (32/100) = 1760

Number of males = (5500 - 1760) = 3740

Village C:

Total population = (280 × 12.5) = 3500

Percentage of females = 40.2%

Number of females = 3500 ×  (40.2/100) = 1407

Number of males = (3500 - 1407) = 2093

Village D: 

Total population = 32000 ×  (12.5/100) = 4000

Percentage of females = 30%

Number of females = 4000 ×  (30/100) = 1200

Number of males = (4000 - 1200) = 2800

Solution:

Number of males in village B = 3740

Number of married males in village B = 1/5 × 3740 = 748/33

Number of unmarried males in village B = 3740 - 748 = 2992

Number of females in village A = 900

Number of married females in village A = 900/3 = 300

Number of unmarried females in village A = 900 - 300 = 600

Required ratio = 600 : 2992 = 75 : 374

Shortcut Trick

Ratio of investments of A and B is 2 : (5 − 2) = 2 : 3.

Ratio of profits of A and B is (7 − 3) : 3 = 4 : 3.

Profit ratio = (Investment × Time) ratio.

4 : 3 = (2 × 8) : (3 × T_B) ⇒ 4 : 3 = 16 : 3T_B.

12T_B = 48 ⇒ T_B = 4 months.

∴ The correct answer is 4 months.

Alternate Method

Given → Investment of A = 2/5 of Total | Profit of B = 3/7 of Total | Time of A = 8 months. Formulas: Profit_A : Profit_B = (Capital_A × Time_A) : (Capital_B × Time_B)

⇒ Let total investment be 5 units. A's investment = 2 units, B's investment = 5 − 2 = 3 units. ⇒ Let total profit be 7 units. B's profit = 3 units, A's profit = 7 − 3 = 4 units. ⇒ According to partnership rule: (Investment_A × Time_A) / (Investment_B × Time_B) = Profit_A / Profit_B ⇒ (2 × 8) / (3 × T_B) = 4 / 3 ⇒ 16 / 3T_B = 4 / 3 ⇒ 3T_B × 4 = 16 × 3 ⇒ 12T_B = 48 ⇒ T_B = 4 months.

∴ The correct answer is 4 months.

Additional Information

Partnership Basics

In a partnership, the profit sharing ratio is directly proportional to the product of capital invested and the time period of investment.

Variable Ratios

If profits are shared in ratio P₁:P₂ and investments are C₁:C₂, then the time ratio is (P₁/C₁) : (P₂/C₂).

Shortcut Trick

Work done by P in 5 hours = 5/15 = 1/3

Work done by Q in (5 + 3) = 8 hours = 8/20 = 2/5

Work done by R in (5 + 3) = 8 hours = 1 − (1/3 + 2/5) = 1 − 11/15 = 4/15

Efficiency of R = (4/15) ÷ 8 = 1/30

∴ The correct answer is 30 hours.

Alternate Method

Given: P = 15 hours, Q = 20 hours, R = N hours. All worked 5 hrs; P left; Q and R worked 3 more hrs.

⇒ Let efficiency of R be x units/hr.

⇒ Total work completed = 5 × (4 + 3 + x) + 3 × (3 + x) = 60

⇒ 5 × (7 + x) + 3 × (3 + x) = 60

⇒ 35 + 5x + 9 + 3x = 60

⇒ 44 + 8x = 60

⇒ 8x = 16

⇒ x = 2 units/hr

⇒ Time taken by R alone (N) = Total Work ÷ Efficiency of R

⇒ N = 60 ÷ 2 = 30 hours

∴ The correct answer is 30 hours.

Additional Information

Total Work Concept

Total Work is always assumed as the LCM of time taken by individual workers to simplify efficiency calculations.

Efficiency Formula

Efficiency = Total Work ÷ Time taken. Efficiency is inversely proportional to the time taken to complete the work.

Work Left/Remaining

When a person leaves, the remaining work must be divided by the combined efficiency of the remaining workers to find the extra time.

Shortcut Trick

Curved Surface Area of Hemisphere = 2πr² = 882π ⇒ r² = 441 ⇒ r = 21 cm.

Volume of milk in Hemisphere = (2/3)πr³.

Since this fills the Cylinder completely: (2/3)πr³ = πr²h.

Since radii are same: h = (2/3)r = (2/3) × 21 = 14 cm.

∴ The correct answer is 14 cm.

Alternate Method

Given:

Surface area of Hemispherical pot = 882π cm²

Radius of Cylindrical can = Radius of Hemisphere (r)

Formula Used:

1. Curved Surface Area of Hemisphere = 2πr²
2. Volume of Hemisphere = (2/3)πr³
3. Volume of Cylinder = πr²h

Calculations:

⇒ 2πr² = 882π

⇒ r² = 882 ÷ 2 = 441

⇒ r = √441 = 21 cm

As per the question, Volume of Hemisphere = Volume of Cylinder

⇒ (2/3)πr³ = πr²h

⇒ (2/3)r = h

⇒ h = (2/3) × 21

⇒ h = 14 cm

∴ The correct answer is 14 cm.

Additional Information

Total Surface Area of Hemisphere

The total surface area includes the curved part and the flat circular top, calculated as 3πr².

Cylinder Surface Area

Curved Surface Area = 2πrh and Total Surface Area = 2πr(h + r).

Volume Conservation

When a liquid is poured from one container to another, the volume remains constant unless stated otherwise.

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

14.972 × 4.99 ÷ 44.78 + 299.99 ÷ √5624.98 × 12.93 = ?

⇒ 15² × 5 ÷ 45 + 300 ÷ √5625 × 13 = ?

⇒ 225 × 1 ÷ 9 + 300 ÷ 75 × 13 = ?

⇒ 25 + 4 × 13 = ?

⇒ 25 + 52 = ?

⇒ 77 = ?

∴ Required value of ? is 77.

Correct answer  is: 1

Concept used:

1. If the digits after decimal in a given number is less than 5, then the digits after decimal are omitted and the rest number will be the approximate value.

2. If the digits after decimal in a given number is more than 5, then the digits after decimal are omitted and the rest of the number is increased by 1. The obtained number will be the approximate value.

3. The BODMAS rule should be followed to solve the question as per the given table:

Calculation:

{12960.31 ÷ 79.79 × (9.75)2} ÷ 89.89 + √195.79 - 10.23 = ?

⇒ {12960 ÷ 80 × 10²} ÷ 90 + √196 - 10 = ?

⇒ (162 × 100) ÷ 90 + 14 - 10 = ?

⇒ 16200 ÷ 90 + 14 - 10 = ?

⇒ 180 + 14 - 10 = ?

⇒ ? = 184

∴ The value of ? is 184

Correct  answer is: 4

Concept used:

1. If the digits after decimal in a given number is less than 5, then the digits after decimal are omitted and the rest number will be the approximate value.

2. If the digits after decimal in a given number is more than 5, then the digits after decimal are omitted and the rest of the number is increased by 1. The obtained number will be the approximate value.

3. The BODMAS rule should be followed to solve the question as per the given table:

Calculation:

14.66 × 22.28 - 344.81 ÷ 23.38 + (11.73)2 - 68.87 = ?

⇒ 15 × 22 - 345 ÷ 23 + 12² - 69 = ?

⇒ 15 × 22 - 15 + 144 - 69 =?

⇒ 330 - 15 + 144 -69 =?

⇒ 474 - 84 = ?

⇒ ? = 390

∴ The value of ? is 390

Given:

37.98% of 549.99 + √(49.02) ÷ ? = 7.99 × (2.97)³

Rules of Approximation:

1. If a number has digits to the right of the decimal less than 5, then just drop the digits to the right of the decimal. The number so obtained will be the approximated value.
2. If a number has digits to the right of the decimal more than 5, then just drop the digits to the right of the decimal and raise the remaining number by '1'.The number so obtained will be the approximated value.

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

37.98% of 549.99 + √(49.02) ÷ ? = 7.99 × (2.97)³

⇒ 38% of 550 + √49 ÷ ? = 8 × 3³

⇒ (38/100) × 550 + 7 ÷ ? = 8 × 27

⇒ 209 + 7 ÷ ? = 216

⇒ 7 ÷ ? = 7

⇒ ? = 1

∴ 1 should come in place of the question mark (?).

Given:

9.78% of 79.94 + ?% of 9.67 = 10.94 × 2.99 + √100 × 2.98

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

9.78% of 79.94 + ?% of 9.67 = 10.94 × 2.99 + √100 × 2.98

⇒ 10% of 80 + ?% of 10 = 11 × 3 + √100 × 3

⇒ (10/100) × 80 + (?/100) × 10 = 33 + 10 × 3

⇒ 8 + (?/10) = 33 + 30

⇒ 8 + (?/10) = 63

⇒ (?/10) = 63 - 8 

⇒ (?/10) = 55 

⇒ ? = 55 × 10 = 550

∴ The value of ? is 550.

Given:

Profit = 425%

C.P. = Increase is 5%

S.P. =Constant

Discount = 80% on mark up

Formula used :

Profit = S.P. – C.P.

Calculation:

Quantity I :

Assume the cost price = Rs 100

⇒ Selling price = 100 + 425

⇒ Selling price = 525

⇒ Profit from new C.P. increase = 525 – (100 + (0.05 × 100))

⇒ Profit from new C.P. increase = 525 – 105

⇒ Profit from new C.P. increase = 420%

⇒ New profit margin = (420/105) × 100

⇒ New profit margin % = 400%

Quantity II :

Let the marked price be Rs 100

Selling price = 100 – (0.80 × 100)

⇒ Selling price = 20

⇒ S.P. = C.P. = 20

⇒ Percentage markup = ((100 – 20)/20) × 100

⇒ Percentage markup = 400%

∴ Quantity I = Quantity II

GIVEN:

Payment = Rs 15000

(A + B + C)'s time = 6 days

A's time = 12 days

B's time = 15 days

CONCEPT:

Wages are distributed in the ratio of efficiency.

For a unit work done efficiency is inversely proportional to the time taken.

CALCULATION:

Let the work be 1 unit

A's efficiency = 1/12

B's efficiency = 1/15

(A + B + C)'s efficiency = 1/6

C's efficiency = 1/6 - (1/12 + 1/15)

⇒ (10 - 5 - 4)/60 = 1/60

C's wages = [15000/1(/6)] × 1/60 = Rs 1500

∴ Quantity A = Quantity B

ALTERNATE SOLUTION:

Let the work be 60 (L.C.M of 6, 12, 15)

A's efficiency = 60/12 = 5

B's efficiency = 60/15 = 4

(A + B + C)'s efficiency = 60/6 = 10

C's efficiency = 10 - (5 + 4) = 1

C's wages = [15000/10] × 1 = Rs 1500

∴ Quantity A = Quantity B

GIVEN:

Quantity = 63 l

Initial ratio (alcohol : water) = 5 : 4

Final ratio (alcohol : water) = 3 : 2

EXPLANATION:

Total mixture (ratio) = 5 + 4 = 9 ratio

9 ratio = 63 l

→ 1 ratio = 7 l

∴ Alcohol = 5 ratio = 35 l

and, water = 4 ratio = 28 l

Since the amount of water will remain same,

For final ratio, 2 ratio = 28 l

∴ 3 ratio = 42 l

So, alcohol quantity in the new mixture = 42 l

∴ Quantity A < Quantity B

Quantity I:

Let the present ages of Yash and Kush be 'Y' years and 'K' years respectively.

Difference between the ages of Yash and Kush is 6 years.

Therefore, either Y - K = 6 or K - Y = 6 ... (a)

Three years later, the sum of their ages will be 40 years.

Therefore, Y + 3 + K + 3 = 40

⇒ Y + K = 34 ...(b)

Case (i) when Y - K = 6 and Y + K = 34

Then, 2Y = 40

⇒ Y = 20

4 years ago Yash was = 20 - 4 = 16 years old  

Case (ii) when K - Y = 6 and Y + K = 34

Then, 2Y = 28

⇒ Y = 14

4 years ago Yash was = 14 - 4 = 10 years old  

∴ Quantity I = 16 years or 10 years

Quantity II:

Let the present age of Viru and Veer be 'x' years and 'y' years respectively.  

Two years later, Viru's age will be two - third of Veer's age at that time.  

Therefore, x + 2 = (2/3) × (y + 2)  

⇒ 3x + 6 = 2y + 4  

⇒ -3x + 2y = 2 ...(a) 

Sum of their present ages = 26 years  

So, x + y = 26 ...(b)  

From (a) and (b)  

-3x + 2 × (26 - x) = 2  

⇒ x = 10  

∴ Quantity II = 10 years

Hence, the correct answer is Quantity - I ≥ Quantity - II.

Shortcut Trick

Let the third booth voters be 100 units.

First booth = 52 units, Second booth = 46 units.

Difference (52 − 46) = 6 units → 7686.

Total units = 52 + 46 + 100 = 198 units.

Total voters = (7686 ÷ 6) × 198 = 1281 × 198 = 2,53,638.

∴ The correct answer is 2,53,638 voters.

Alternate Method

Given:

Voters in Booth 3 = x

Voters in Booth 1 = 52% of x = 0.52x

Voters in Booth 2 = 46% of x = 0.46x

Calculations:

⇒ Difference = 0.52x − 0.46x = 7686

⇒ 0.06x = 7686

⇒ x = 7686 ÷ 0.06 = 1,28,100

⇒ Total voters = Booth 1 + Booth 2 + Booth 3

⇒ Total = 0.52x + 0.46x + x = 1.98x

⇒ Total = 1.98 × 1,28,100

⇒ Total = 2,53,638

∴ The correct answer is 2,53,638 voters.

Additional Information

Percentage Base Change

When multiple values are compared to a single base (the third booth here), they can be added or subtracted directly as long as the base remains constant.

Unitary Method

Value of 1 unit = (Given Difference) ÷ (Difference in units). Total Value = (1 unit value) × (Total sum of units).

Successive Percentage

If a value changes by a% and then b%, the net change is [a + b + (ab/100)]%. Note: This rule does not apply when values are independent parts of a whole.

Shortcut Trick

Assume Marked Price (MP) = 100.

Cost Price (CP) = 100 × (100 − 20)% = 80.

Selling Price (SP) = 80 × (100 − 10)% = 72.

If CP = MP = 100, then Loss = 100 − 72 = 28.

Loss% = (28 ÷ 100) × 100 = 28%.

∴ The correct answer is 28%.

Alternate Method

Given → Discount = 20% on MP | Loss = 10% on CP | Target = Loss% if CP = MP. Formulas: CP = MP × (100 − D%) ÷ 100 | SP = CP × (100 − L%) ÷ 100 | New Loss% = (MP − SP) ÷ MP × 100.

⇒ Let Marked Price = x. ⇒ Cost Price (CP) = x − 0.20x = 0.80x. ⇒ Selling Price (SP) = 0.80x − (10% of 0.80x) = 0.80x − 0.08x = 0.72x. ⇒ If article was bought at Marked Price, New CP = x. ⇒ Loss = New CP − SP = x − 0.72x = 0.28x. ⇒ Loss Percentage = (0.28x ÷ x) × 100 = 28%. ∴ The correct answer is 28%.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price. SP = MP × (100 − Discount%)/100.

Effective Loss/Gain

When multiple changes occur, the result depends on the sequence of successive percentages applied to the base value.

Calculations:

Let Ramiya’s present age be x.

∴ her age at the time of her marriage is (x - 8) years.

⇒ x = 6/5(x - 8)

⇒ 5x = 6x – 48

⇒ x = 48 years

∴ Ramiya’s brothers age at the time of her marriage = (x – 8) – 10

⇒ 48 – 18

⇒ 30 years

∴ required ratio = 48 : 30

⇒ 8 : 5

The ratio of Ramiya’s present age and her brother’s age at the time of her marriage is 8 : 5.

Shortcut Trick

When two boats move towards each other, one downstream and one upstream, the speed of the stream cancels out.

Relative Speed = Speed of X + Speed of Y = 8 + 7 = 15 km/hr.

Time = Total Distance ÷ Relative Speed = 300 ÷ 15 = 20 hr.

∴ The correct answer is 20 hr.

Alternate Method

Given: Distance = 300 km, Speed of X (u_X) = 8 km/hr, Speed of Y (u_Y) = 7 km/hr.

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

⇒ Let the speed of the stream be v km/hr.

⇒ Speed of Boat X (downstream) = 8 + v km/hr.

⇒ Speed of Boat Y (upstream) = 7 − v km/hr.

⇒ Relative Speed = (8 + v) + (7 − v) = 15 km/hr.

⇒ Time taken to meet = Distance ÷ Relative Speed

⇒ Time = 300 ÷ 15 = 20 hr.

∴ The correct answer is 20 hr.

Additional Information

Relative Speed in Streams

When two boats move towards each other (one up and one down), the stream velocity always cancels out in the relative speed calculation.

Downstream and Upstream

Downstream Speed = u + v and Upstream Speed = u − v, where u is speed in still water and v is stream speed.

Time of Meeting

Time taken to meet = (Initial Distance) ÷ (Relative Speed in opposite direction).

Person: Lata, Uma, Gia, Sana, Tia, Pia, Kate, Hina, Noor, and Ruhi

Month: January, March, April, May, June, July, August, September, October, and December 

1) Tia was born in the month which has 30 days before August. Only four persons were born between Tia and Sana. Uma was born just before Sana. The number of persons born before Uma and after Noor are equal. 

2) Gia was born in a month which has 30 days only. Only three persons were born between Pia and Gia.

3) Pia was born before Gia. Only one person was born between Ruhi and Lata. Ruhi was born before Lata. Less than three people were born between Lata and Hina.

The condition that Pia was born before Gia cannot be fulfilled in Case 1(a) and Case 2.

The final arrangement is:

Hence, Noor was born in the month of March.

Person: Lata, Uma, Gia, Sana, Tia, Pia, Kate, Hina, Noor, and Ruhi

Month: January, March, April, May, June, July, August, September, October, and December 

1) Tia was born in the month which has 30 days before August. Only four persons were born between Tia and Sana. Uma was born just before Sana. The number of persons born before Uma and after Noor are equal. 

2) Gia was born in a month which has 30 days only. Only three persons were born between Pia and Gia.

3) Pia was born before Gia. Only one person was born between Ruhi and Lata. Ruhi was born before Lata. Less than three people were born between Lata and Hina.

The condition that Pia was born before Gia cannot be fulfilled in Case 1(a) and Case 2.

The final arrangement is:

Hence, Tia (the one who is born in the month of June.) is born just after Pia.

Person: Lata, Uma, Gia, Sana, Tia, Pia, Kate, Hina, Noor, and Ruhi

Month: January, March, April, May, June, July, August, September, October, and December 

1) Tia was born in the month which has 30 days before August. Only four persons were born between Tia and Sana. Uma was born just before Sana. The number of persons born before Uma and after Noor are equal. 

2) Gia was born in a month which has 30 days only. Only three persons were born between Pia and Gia.

3) Pia was born before Gia. Only one person was born between Ruhi and Lata. Ruhi was born before Lata. Less than three people were born between Lata and Hina.

The condition that Pia was born before Gia cannot be fulfilled in Case 1(a) and Case 2.

The final arrangement is:

Hence, One person is born between Gia and Hina.

Person: Lata, Uma, Gia, Sana, Tia, Pia, Kate, Hina, Noor, and Ruhi

Month: January, March, April, May, June, July, August, September, October, and December 

1) Tia was born in the month which has 30 days before August. Only four persons were born between Tia and Sana. Uma was born just before Sana. The number of persons born before Uma and after Noor are equal. 

2) Gia was born in a month which has 30 days only. Only three persons were born between Pia and Gia.

3) Pia was born before Gia. Only one person was born between Ruhi and Lata. Ruhi was born before Lata. Less than three people were born between Lata and Hina.

The condition that Pia was born before Gia cannot be fulfilled in Case 1(a) and Case 2.

The final arrangement is:

Hence, Both 1 (Lata was born in April.) and 2( Pia was born before Sana.) are true statements.