SBI PO Prelims Memory Based Paper (Held On: 6 November 2023 Shift 1) (Previous Year Paper)

The correct answer is 'eject, instigating.'

Key Points

• The given sentence is talking about the referees taking action against the hockey players fighting with the other team.
• ​Let us explore the words in the given options:
• 'Eject' means to compel someone to leave a place.
• 'Instigating' means inciting someone to do something, especially something bad.

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Conclusion: The referees shall dismiss the players from the ground for their bad behaviour.

Hence, the correct answer is option 5.

Complete Sentence: The referees shall eject the three players from the hockey game due to instigating a fight with the other team.

Additional Information

• The meaning of other options:
• 'Entertain' means to interest and amuse somebody in order to please him or her.
• 'Lodge' means to become firmly fixed or to make something do this.
• 'Restrain' means to prevent somebody or something from doing something.
• 'Admit' means to agree that something unpleasant is true or that you have done something wrong.
• 'Annoy' means to make somebody angry or slightly angry.
• 'Subdue' means to defeat somebody or something or bring somebody or something under control.
• 'Imitate' means to copy the behavior of somebody or something.
• 'Fabricate' means to invent something false in order to deceive people.

The correct answer is 'chant, motivate.'

Key Points

• The given sentence is talking about something related to the cheerleaders encouraging the team to score a goal.
• ​Let us explore the words in the given options:
• 'Chant' means to say or shout repeatedly in a sing-song tone.
• 'Motivate' means to cause someone to have an interest in or enthusiasm for something.

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Conclusion: The cheerleaders with a repeated loud cheer motivated the team.

Hence, the correct answer is option 3.

Complete Sentence: The cheerleaders offered a chant of encouragement to motivate the team to score a touchdown.

Additional Information

• The meaning of other options:
• 'Calm' means not excited, worried, or angry; quiet.
• 'Troll' means a deliberately offensive or provocative online post.
• 'Pacify' means to make somebody who is angry or upset be calm or quiet.
• 'Trigger' means to make something happen suddenly.
• 'Appease' means to make somebody calmer or less angry by agreeing to what he/she wants.
• 'Harmonize' means to produce a pleasant effect when seen, heard, etc. together.
• 'Anger' means the strong feeling that you have when something has happened or somebody has done something that you do not like.
• 'Vocalize' means to express a thought or emotion in words.

The correct answer is 'sustain, severe.'

Key Points

• The given sentence is talking about something related to Bolt's speed and some type of cramping.
• ​Let us explore the words in the given options:
• 'Sustain' means cause to continue for an extended period or without interruption.
• 'Severe' means extremely bad or serious.

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Conclusion: Bolt's slowing down in the marathon due to some extremely bad or serious cramping.

Hence, the correct answer is option 1.

Complete Sentence: Bolt cannot sustain his speed in the marathon because he is experiencing severe cramping.

Additional Information

• The meaning of other options:
• 'Responsive' means paying attention to somebody or something and reacting in a suitable or positive way.
• 'Refuse' means to say or show that you do not want to do, give, or accept something.
• 'Decline' means to refuse, usually politely.
• 'Willing' means happy to do something; having no reason for not doing something.
• 'Amenable' means happy to accept something; willing to be influenced by somebody or something.
• 'Abstain' means to stop yourself from doing something that you enjoy.
• 'Flexible' means something that can be changed easily.
• 'Combat' means to fight against something; to try to stop or defeat something.

The correct answer is 'maintain, frequently.'

Key Points

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

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

Hence, the correct answer is option 4.

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

Additional Information

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

The correct answer is 'D.'

Key Points

• The correct sequence of the segments after rearrangement is ADEBC.
• The sentence 'A' is independent of any other sentence as it is talking about one of the "consequences of global warming" i.e. the increase in temperatures around the world. Hence, 'A' is the first part.
• Sentence D will come after A as it is giving information about the average increase in the global temperature over the past 100 years.
• Sentence E will come after D as it talks about the hottest year (2016) since record-keeping began in 1895.
• Sentence B will come after E as it further explains that in 2016 Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century.
• The sentence 'C' is the concluding or final part as it says before 2016, 2015 was the warmest year on record.

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Hence, the correct answer is option 5.

Paragraph after rearranging the sentences: One of the most immediate and obvious consequences of global warming is the increase in temperatures around the world. The average global temperature has increased by about 0.8 degrees Celsius over the past 100 years. Since record-keeping began in 1895, the hottest year on record worldwide was 2016, according to NOAA and NASA data. That year Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century. Before 2016, 2015 was the warmest year on record, globally.

Hint

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

The correct answer is 'B.'

Key Points

• The correct sequence of the segments after rearrangement is ADEBC.
• The sentence 'A' is independent of any other sentence as it is talking about one of the "consequences of global warming" i.e. the increase in temperatures around the world. Hence, 'A' is the first part.
• Sentence D will come after A as it is giving information about the average increase in the global temperature over the past 100 years.
• Sentence E will come after D as it talks about the hottest year (2016) since record-keeping began in 1895.
• Sentence B will come after E as it further explains that in 2016 Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century.
• The sentence 'C' is the concluding or final part as it says before 2016, 2015 was the warmest year on record.

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Hence, the correct answer is option 2.

Paragraph after rearranging the sentences: One of the most immediate and obvious consequences of global warming is the increase in temperatures around the world. The average global temperature has increased by about 0.8 degrees Celsius over the past 100 years. Since record-keeping began in 1895, the hottest year on record worldwide was 2016, according to NOAA and NASA data. That year Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century. Before 2016, 2015 was the warmest year on record, globally.

The correct answer is 'A.'

Key Points

• The correct sequence of the segments after rearrangement is ADEBC.
• The sentence 'A' is independent of any other sentence as it is talking about one of the "consequences of global warming" i.e. the increase in temperatures around the world. Hence, 'A' is the first part.
• Sentence D will come after A as it is giving information about the average increase in the global temperature over the past 100 years.
• Sentence E will come after D as it talks about the hottest year (2016) since record-keeping began in 1895.
• Sentence B will come after E as it further explains that in 2016 Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century.
• The sentence 'C' is the concluding or final part as it says before 2016, 2015 was the warmest year on record.

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Hence, the correct answer is option 3.

Paragraph after rearranging the sentences: One of the most immediate and obvious consequences of global warming is the increase in temperatures around the world. The average global temperature has increased by about 0.8 degrees Celsius over the past 100 years. Since record-keeping began in 1895, the hottest year on record worldwide was 2016, according to NOAA and NASA data. That year Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century. Before 2016, 2015 was the warmest year on record, globally.

The correct answer is 'C.'

Key Points

• The correct sequence of the segments after rearrangement is ADEBC.
• The sentence 'A' is independent of any other sentence as it is talking about one of the "consequences of global warming" i.e. the increase in temperatures around the world. Hence, 'A' is the first part.
• Sentence D will come after A as it is giving information about the average increase in the global temperature over the past 100 years.
• Sentence E will come after D as it talks about the hottest year (2016) since record-keeping began in 1895.
• Sentence B will come after E as it further explains that in 2016 Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century.
• The sentence 'C' is the concluding or final part as it says before 2016, 2015 was the warmest year on record.

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Hence, the correct answer is option 4.

Paragraph after rearranging the sentences: One of the most immediate and obvious consequences of global warming is the increase in temperatures around the world. The average global temperature has increased by about 0.8 degrees Celsius over the past 100 years. Since record-keeping began in 1895, the hottest year on record worldwide was 2016, according to NOAA and NASA data. That year Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century. Before 2016, 2015 was the warmest year on record, globally.

The correct answer is 'E.'

Key Points

• The correct sequence of the segments after rearrangement is ADEBC.
• The sentence 'A' is independent of any other sentence as it is talking about one of the "consequences of global warming" i.e. the increase in temperatures around the world. Hence, 'A' is the first part.
• Sentence D will come after A as it is giving information about the average increase in the global temperature over the past 100 years.
• Sentence E will come after D as it talks about the hottest year (2016) since record-keeping began in 1895.
• Sentence B will come after E as it further explains that in 2016 Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century.
• The sentence 'C' is the concluding or final part as it says before 2016, 2015 was the warmest year on record.

<br>

Hence, the correct answer is option 1.

Paragraph after rearranging the sentences: One of the most immediate and obvious consequences of global warming is the increase in temperatures around the world. The average global temperature has increased by about 0.8 degrees Celsius over the past 100 years. Since record-keeping began in 1895, the hottest year on record worldwide was 2016, according to NOAA and NASA data. That year Earth's surface temperature was 0.99 degrees Celsius warmer than the average across the entire 20th century. Before 2016, 2015 was the warmest year on record, globally.

The correct answer is option 2.

Key Points

To answer this question, let's have a look at all the given sentences as options:

• Option 1: One of the keys to success is maintaining a positive attitude.
• This sentence is grammatically and contextually correct.
• Option 2: Neither of the options are suitable for us.
• This sentence is incorrect because the subject 'Neither of the options' is singular, requiring a singular verb 'is' instead of 'are'.
• The correct sentence would be: "Neither of the options is suitable for us."
• Option 3: We are looking forward to the upcoming seminar.
• This sentence is grammatically and contextually correct.
• Option 4: The teacher asked a series of thought-provoking questions.
• This sentence is grammatically and contextually correct.
• Option 5: Incorrect usage can lead to misunderstandings.
• This sentence is grammatically and contextually correct.

So, out of the given sentences, only option 2 is a grammatically/contextually incorrect sentence.

Therefore, the correct answer is "Neither of the options is suitable for us."

The correct answer is option 2.

Key Points

To answer this question, let's have a look at all the given sentences as options:

• Option 1: The committee has decided to postpone the  meeting to a later date.
• This sentence is grammatically and contextually correct.
• Option 2: The teacher along with her students were excited about the field trip.
• This sentence is incorrect because the main subject 'The teacher' is singular. The verb should therefore also be singular: 'was' instead of 'were'.
• The correct sentence would be: "The teacher along with her students was excited about the field trip."
• Option 3: Investing in education yields long-term benefits for individuals and societies.
• This sentence is grammatically and contextually correct.
• Option 4: A well-organized workspace can significantly enhance productivity.
• This sentence is grammatically and contextually correct.
• Option 5: The colors of the sunset were truly breathtaking.
• This sentence is grammatically and contextually correct.

So, out of the given sentences, only option 2 is a grammatically/contextually incorrect sentence.

Therefore, the correct answer is "The teacher along with her students was excited about the field trip."

The correct answer is option 1.

Key Points

To answer this question, let's have a look at all the given sentences as options:

• Option 1: Each of the players were given a medal for their performance.
• This sentence is incorrect because the subject 'Each of the players' is singular, and the verb should therefore be singular: 'was' instead of 'were'.
• The correct sentence would be: "Each of the players was given a medal for their performance."
• Option 2: Reading scientific journals helps him stay updated on new research.
• This sentence is grammatically and contextually correct.
• Option 3: An apple a day keeps the doctor away.
• This sentence is grammatically and contextually correct.
• Option 4: They have adapted well to the new regulations.
• This sentence is grammatically and contextually correct.
• Option 5: Her understanding of the subject is evident in her discussions.
• This sentence is grammatically and contextually correct.

So, out of the given sentences, only option 1 is a grammatically/contextually incorrect sentence.

Therefore, the correct answer is "Each of the players was given a medal for their performance."

The correct option is option 1 

Key Points

• The passage talks about how pandemic has affected work-life.
• Option 1: normalised means to return to the usual or generally accepted situation
• Example: They hope to normalise relations with the us.
• This word fits the blank correctly and conveys a proper meaning that this pandemic has made working remotely a regular thing which was not the case before.

The correct option is option 2

Key Points

• The passage talks about how pandemic has affected work-life.
• Option 2: hybrid means combining two different things
• Example*: His choreography is described as "a hybrid mix of mime and circus tricks"*
• This word fits the blank correctly and conveys a proper meaning that this pandemic might lead to a combination of in-office working and work from home/ working remotely.

The correct option is option 1

Key Points

• The passage talks about how pandemic has affected work-life.
• Option 1: virtual means not involving people physically going somewhere 
• Example*: Before a virtual meeting, all participants should test the technology and make sure they are comfortable with the major features.*
• The word fits the blank correctly and conveys a proper meaning that the offices might turn completely online and that all the office work would be carried out through the internet only without any physical interactions.

The correct option is option 1

Key Points

• The passage talks about how pandemic has affected work-life.
• Option 1: doubtful means "if you are doubtful about something, you are uncertain about it."
• Example: The teacher is doubtful about having parents working as classroom assistants.
• The word fits the blank correctly and conveys a proper meaning that there is still no surety of the pandemic coming to an end in the near future.

The correct option is option 2

Key Points

• The passage talks about how pandemic has affected work-life.
• Option 1: speculate means "to guess possible answers to a question when you do not have enough information to be certain."
• Example: I don't know why she did it - I'm just speculating
• The word fits the blank correctly and conveys a proper meaning that it is still hard to imagine or predict how the world would get affected once the pandemic ends.

The correct answer is 'C'.

Key Points

• The correct spelling is 'Conqueror'.
• Let's explore the meaning and context of it.
• Conqueror: Someone who is victorious by force of arms
• Ex: The year 1570 brought yet another conqueror, the Ottoman Empire.
• Thus, the correct answer is Option 2.

Additional Information 

• Let's explore the meaning of other options as well.
• Defeated: Disappointingly unsuccessful.
• Cupidity: Extreme greed for material wealth.
• Excessive: Beyond normal limits.

The correct answer is 'A'.

Key Points

• The correct spelling is 'Conflagration'.
• Let's explore the meaning and context of it.
• conflagration: a large fire that burns a lot of buildings, land, forests, etc.
• Ex: The historic tavern burned to the ground in a horrible conflagration.
• Thus the correct answer is Option 2.

Additional Information

• Let's explore the meaning of other options as well.
• Died: to pass from physical life
• Blackened: coated with a mixture of spices (such as garlic powder and cayenne pepper) and fried over extremely high heat
• Embers: a glowing fragment (as of coal) from a fire.

T he correct answer is 'B'.

Key Points 

• The correct spelling is 'Cogent'.
• Let's explore the meaning and context of it.
• Cogent: strongly and clearly expressed in a way that influences what people believe.
• Ex: a cogent argument/reason.
• Thus the correct answer is Option 1.

Additional InformationLet's explore the meaning of other options as well.

• Inevitable: that cannot be avoided or prevented from happening
• Inclusive:  including or containing everything; including the thing mentioned
• Scholarship: an amount of money that is given to a person who has passed an exam or won a competition.

The synonym for 'hostilities' is d. Aggression.

Key Points

• 'Hostilities' refers to acts of warfare or aggressive behavior, which aligns with the meaning of 'aggression'.

Additional Information

• ​​​a. Friendship: This implies a state of being friends, which is the opposite of hostilities.
• b. Cordiality: This refers to sincere affection and kindness, which is also contrary to hostilities.
• c. Cooperation: This means the process of working together to achieve the same end, and is the opposite of hostilities.
• d. Aggression: This is the correct answer. 'Hostilities' refers to acts of warfare or aggressive behavior, which aligns with the meaning of 'aggression'. In the passage, hostilities with China (LAC hostilities) are mentioned, referring to aggressive conflict.
• e. Alliance: This means a union formed for mutual benefit, especially between countries, and is the opposite of hostilities.

Answer: c. 2017

Key Points

• The passage states, "India became a full SCO member in 2017, along with Pakistan."

Answer: d. All of the above

Key Points

• The passage mentions multiple reasons why India's membership in the SCO is beneficial. It talks about the member countries making up a significant portion of global GDP, trade, and reserves of oil and natural gas.
• Additionally, the SCO's focus on regional security and connectivity is also crucial for India's growth. Furthermore, joining the SCO was a significant part of India's ambitions on "multi-alignment" and "strategic autonomy".

Answer: b. Because of the Prime Minister's U.S. State visit

Key Points

• The passage says, "However, India’s decision to postpone the SCO summit due to the Prime Minister’s U.S. State visit."
• This implies that the prime reason for the postponement was the Prime Minister's visit to the United States.

Answer: c. Regional security and connectivity

Key Points

• The passage mentions, "Also important is its focus on regional security and connectivity — areas key to India’s growth."

Answer: a. It joined the revived Quad with the U.S., Japan, and Australia

Key Points

• The passage states, "It seems no coincidence that the Modi government joined the revived Quad with the U.S., Japan, and Australia in the same year that it took up the full SCO membership."

The synonym for 'consensus' is d. Agreement.

Key Points

• 'Consensus' refers to general agreement among a group of people.

Additional Information

• a. Discord: This means a lack of agreement or harmony, which is the opposite of consensus.
• b. Contention: This refers to heated disagreement, which is also contrary to consensus.
• c. Disagreement: This is a state of having differing opinions, and again, is the opposite of consensus.
• d. Agreement: This is the correct answer. 'Consensus' refers to a general agreement or unity of opinion. In the context of the passage, India is trying to find a consensus, or agreement, on certain issues with other SCO members.
• e. Dispute: This means a disagreement or argument, the opposite of consensus.

The antonym for 'revival' is d. Demise.

Key Points

• 'Revival' refers to the process of becoming active or popular again, while 'demise' means the end or failure of something.

Additional Information

• a. Rebirth: This is a synonym of revival. Both imply a resurgence or renewal.
• b. Rejuvenation: This also means becoming fresh or new again, similar to revival.
• c. Resurgence: This is another synonym for revival, implying a renewed growth or rise.
• d. Demise: This is the correct answer. 'Demise' refers to the end or death of something, making it an antonym of 'revival', which implies a resurgence or renewal. In the context of the passage, India joined the "revived" Quad, meaning the Quad that has been renewed or brought back to life.
• e. Restoration: This is a synonym for revival, indicating the action of returning something to a former condition.

The correct answer is: Interface.

Key Points

• b. Interface: This is the correct answer. The passage explicitly states: "The SCO also gives India an interface with Central Asian markets and resources." In this context, 'interface' means a point where two systems or subjects meet and interact.

Additional Information

• a. Opportunity: This word would mean that the SCO provides India with a chance to engage with Central Asian markets and resources. While the meaning could fit, it's not the exact word used in the passage.
• c. Confrontation: This would mean that the SCO leads India into a conflict or hostile situation with Central Asian markets and resources, which does not align with the context of the passage.
• d. Discrepancy: This implies a difference or inconsistency between two things, which does not fit into the context.
• e. Rivalry: This would mean that the SCO initiates a competition or rivalry between India and Central Asian markets and resources, which is not implied in the passage

Answer: 1) True

Key Points

• The passage explicitly states that the Indian government held that joining the SCO was important because member countries of the organization account for a significant proportion of global GDP, trade, oil reserves, and natural gas reserves.
• Additionally, the SCO's focus on regional security and connectivity are areas key to India’s growth and its challenges such as terrorism in Pakistan, Chinese aggressions, and the Belt and Road Initiative.
• Therefore, the statement is true as per the information given in the passage.

General solution:

 

City

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 200

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

Solution:

Number of males below the age of 25 in city D = 250 ×  (20/100) = 50

Number of males below the age of 25 in city E = 480 ×  (25/100) = 120

Number of females below the age of 25 in city D = 200 ×  (40/100) = 80

Number of females below the age of 25 in city E = 270 ×  (33.33/100) = 90

Required sum = (50 + 120 + 80 + 90) = 340

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 200

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

Solution:

Number of males living in city B = 350

Number of females living in city B = 250

Number of males having two wheelers in city B = 350 ×  3/7 = 150

Number of females having two wheelers in city B = 250 ×  2/5 = 100

Number of females having four wheelers in city B = (350 - 150) = 200

Number of females having four wheelers in city B = (250 - 100) = 150

Required difference = (200 ×  4/5 - 150) = (160 - 150) = 10

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 150

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

 

Solution:

Number of males living in the city C = 380

Number of females living in the city C = 280

(380 + x)/(280 + (x - 50)) = 3/2

(760 + 2x) = ( 690 + 3x)

x = 70

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 150

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

 

Solution:

Number of males living in city C = 380

Number of males living in city E = 480

Average number of males living in city C and E = (380 + 480)/2 = 430

Number of males living in city F = (430 + 20) = 450

Number of females living in city A = 240

Number of females living in city C = 280

Average number of females living in city A and C = (240 + 280)/2 = 260

Number of females living in city F = (260 + 40) = 300

Required sum = (450 + 300) = 750

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 150

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

Solution:

Number of males living in city A =300

Number of males living in city B = 350

Number of females living in city C = 280

Number of females living in city E = 270

Required ratio = (300 + 350): (280 + 270) = (650: 550) = 13: 11

General solution:

 

City A 

Number of persons (Male + Female) living in city = 3000 ×  (18/100) = 540

Difference between number of (Male - Females) = 60

M + F = 540

M - F = 60

2M = 600

M = 300

F = 240

 

City B:

 

Number of persons (Male + Female) living in city = 3000 ×  (20/100) = 600

Difference between number of (Male - Females) = 100

M + F = 600

M - F = 100

2M = 700

M = 350

F = 250

 

City C:

 

Number of persons (Male + Female) living in city = 3000 ×  (22/100) = 660

Difference between number of (Male - Females) = 100

M + F = 660

M - F = 100

2M = 760

M = 380

F = 280

 

City D:

 

Number of persons (Male + Female) living in city = 3000 ×  (15/100) = 450

Difference between number of (Male - Females) = 50

M + F = 450

M - F = 50

2M = 500

M = 250

F = 150

 

City E:

 

Number of persons (Male + Female) living in city = 3000 ×  (25/100) = 750

Difference between number of (Male - Females) = 210

M + F = 750

M - F = 210

2M = 960

M = 480

F = 270

 

 

Solution:

Number of literate people in each city if males = 70% and females = 60% literate in all cities.

City A: Literate Males = 210, Literate Females = 144,

Total Literate People = 354

City B: Literate Males = 245, Literate Females = 150,

Total Literate People = 395

City C: Literate Males = 266, Literate Females = 168,

Total Literate People = 434

City D: Literate Males = 175, Literate Females = 120,

Total Literate People = 295

City E: Literate Males = 336, Literate Females = 162,

Total Literate People = 498

Literacy rate in each city = Literate people as a percentage of the total population of the city

City A: Literacy Rate = 65.56%

City B: Literacy Rate = 65.83%

City C: Literacy Rate = 65.76%

City D: Literacy Rate = 65.56%

City E: Literacy Rate = 66.40%

City E has the highest literacy rate with approximately 66.40%.

Shortcut Trick

Area of rectangle = 1260 m². Factors of 1260 with difference 12: 42 × 30.

Length (x) = 42 m, Breadth (x − 12) = 30 m.

Perimeter of rectangle = 2 × (42 + 30) = 144 m.

Cost of fencing = Perimeter × Rate = 144 m × ₹15 per m = ₹2160.

∴ The correct answer is ₹2160.

Alternate Method

Given: Area of rectangular field = 1260 m², Length = x, Breadth = x − 12. Rate = ₹15/m.

Formula Used: Area = Length × Breadth; Perimeter of rectangle = 2(l + b).

⇒ x(x − 12) = 1260

⇒ x² − 12x − 1260 = 0

⇒ x² − 42x + 30x − 1260 = 0

⇒ (x − 42)(x + 30) = 0 ⇒ x = 42 m (Length), Breadth = 30 m

⇒ Perimeter of rectangular field = 2(42 + 30) = 144 m

⇒ Since Perimeters are equal, Fencing length of semi-circular garden = 144 m

⇒ Total Cost = 144 × 15 = ₹2160

∴ The correct answer is ₹2160.

Additional Information

Perimeter of Semi-circle

The total perimeter includes the curved arc and the diameter: P = πr + 2r or r(π + 2).

Cost of Fencing

Total Cost is calculated by multiplying the boundary length (Perimeter) by the rate per unit length.

Area of Semi-circle

The region enclosed is half that of a full circle: Area = (πr²) ÷ 2.

Shortcut Trick

Rate = 10%. Multiplying factors: 3 years = 1.331, 4 years = 1.4641.

CI₁ = 5000 × (1.331 − 1) = 5000 × 0.331 = 1655.

CI₂ = A × (1.4641 − 1) = 0.4641A.

Difference: 0.4641A − 1655 = 2986 ⇒ 0.4641A = 4641 ⇒ A = 10000.

∴ The correct answer is ₹10000.

Alternate Method

Given: Principal₁ = ₹5000, Time₁ = 3 years, Principal₂ = ₹A, Time₂ = 4 years, Rate = 10%.

Formula: CI = P[(1 + R/100)ⁿ − 1]

⇒ CI₁ = 5000[(1 + 10/100)³ − 1]

⇒ CI₁ = 5000[1.1³ − 1] = 5000[1.331 − 1] = 5000 × 0.331 = 1655

⇒ CI₂ = A[(1.1)⁴ − 1] = A[1.4641 − 1] = 0.4641A

⇒ CI₂ − CI₁ = 2986

⇒ 0.4641A − 1655 = 2986

⇒ 0.4641A = 2986 + 1655 = 4641

⇒ A = 4641 ÷ 0.4641 = 10000

∴ The correct answer is ₹10000.

Additional Information

Compound Interest Formula

The amount A = P(1 + r/100)ⁿ. Compound Interest CI = Amount − Principal.

Successive Percentage Method

For 10% rate: 2 years effective rate = 21%, 3 years = 33.1%, 4 years = 46.41%.

Difference between CI and SI

For 2 years, Difference = P(R/100)². For 3 years, Difference = P(R/100)² × (3 + R/100).

Considering the above series,

123, 184, 219, 235, 243, ?

The logic of the series can be explained as:

123 + (128/2 = 64) = 187

187 + (64/2 = 32) = 219

219 + (32/2 = 16) = 235

235 + (16/2 = 8) = 243

By observing the pattern, we can write

⇒ 243 + (8/2 = 4) = ?

⇒ ? = 247

∴ The value of ? is 247.

Considering the above series,

13, 13, 14, 18, 45, 61, ?

The logic of the series can be explained as:

13 + 0² = 13

13 + 1³ = 14

14 + 2² = 18

18 + 3³ = 45

45 + 4² = 61

By observing the pattern, we can write

⇒ 61 + 5³ = ?

⇒ ? = 186

∴ The value of ? is 186.

Calculation:

The series follows following pattern:

⇒ 10 + (1 × 8) = 18

⇒ 18 + (2 × 8) = 34

⇒ 34 + (4 × 8) = 66

⇒ 66 + (8 × 8) = 130

∴ The value of ? is 66

Calculation:

The series follows following pattern:

⇒ 144 + 20 = 164

⇒ 164 + 30 = 194

⇒ 194 + 40 = 234

⇒ 234 + 50 = 284

By observing the pattern, we can write

284 + 60 = 344

⇒ ? = 344

∴ The value of ? is 344.

Calculation:

Considering the above series,

500, 475, 426, 345, 224, ?

The logic of the series can be explained as,

500 – (5)² = 475

475 – (7)² = 426

426 – (9)² = 345

345 – (11)² = 224

By observing the pattern, we can write

224 – (13)² = 55

⇒ ? = 55

∴ The value of ? is 55

Calculation∶

The series follows the following pattern:

⇒ 33 + 288 = 321

⇒ 321 + 144 = 465 , [ 288/2=144]

⇒ 465 + 72 = 537    ,[144/2=72]

⇒ 537 + 36 = 573    ,[72/2=36]

⇒ 573 + 18 = 591    ,[36/2=18]

∴ The value of ? is 591

Note: Best way to approach this type of question is to find the difference from the end where gap between the number is less. here it can be 573 and 537.

Shortcut Trick

Apply Alligation Method on the interest rates since the time period (6 years) is constant for all parts.

Rate 1 (X) = 35%, Rate 2 (Y) = 20%, Combined Rate (X+Y) = 25%.

Difference 1 (X - Combined) = 35 − 25 = 10.

Difference 2 (Combined - Y) = 25 − 20 = 5.

Ratio X : Y = 5 : 10 = 1 : 2.

∴ The correct answer is 1 : 2.

Alternate Method

Given: Principal X at 35%, Principal Y at 20%, Combined Principal (X+Y) at 25%, Time = 6 years.

Formula Used: SI = (P × R × T) ÷ 100

⇒ Total SI = SI_X + SI_Y

⇒ [(X × 35 × 6) ÷ 100] + [(Y × 20 × 6) ÷ 100] = [(X + Y) × 25 × 6] ÷ 100

⇒ 35X + 20Y = 25(X + Y)

⇒ 35X + 20Y = 25X + 25Y

⇒ 35X − 25X = 25Y − 20Y

⇒ 10X = 5Y

⇒ X ÷ Y = 5 ÷ 10

⇒ X : Y = 1 : 2

∴ The correct answer is 1 : 2.

Additional Information

Simple Interest Property

When the time period is constant, the total interest earned is the sum of interest from individual parts: SI_total = SI₁ + SI₂.

Alligation in SI

Alligation can be used to find the ratio of investments (X and Y) when the overall effective rate of interest is known for a common time period.

Relationship of R and P

For a fixed SI and Time, the Principal and Rate are inversely proportional: P₁ × R₁ = P₂ × R₂.

Shortcut Trick

Total marks of B = 3 × 70 = 210.

Total marks of A = 1.20 × 210 = 252.

Marks of A in English = 252 − (80 + 95) = 252 − 175 = 77.

∴ The correct answer is 77 marks.

Alternate Method

Given:

Average marks of B in 3 subjects = 70

Total marks of A = 120% of B's total marks

Marks of A in Science = 80, Mathematics = 95

Calculations:

⇒ Total marks of B = 70 × 3 = 210

⇒ Total marks of A = 210 × (120/100) = 210 × 1.2 = 252

⇒ Total marks of A = Marks in (Maths + Science + English)

⇒ 252 = 95 + 80 + Marks in English

⇒ 252 = 175 + Marks in English

⇒ Marks in English = 252 − 175 = 77

∴ The correct answer is 77 marks.

Additional Information

Averages

Average = (Sum of all observations) ÷ (Total number of observations). Sum = Average × Count.

Percentage Increase

To increase a value by x%, multiply the original value by (100 + x)/100.

Shortcut Trick

Ratio of Investment × Time equals the Profit Ratio.

For A and B: (20,000 × t) ÷ (30,000 × (t − 4)) = 2 ÷ 2.

Simplified: 2t ÷ 3(t − 4) = 1 ⇒ 2t = 3t − 12 ⇒ t = 12 months.

Time for B = t − 4 = 12 − 4 = 8 months.

Time for C = (t − 4) − 2 = 8 − 2 = 6 months.

∴ The correct answer is 12, 8 and 6 months.

Alternate Method

Given: Investments of A, B, and C are Rs. 20,000, Rs. 30,000, and Rs. 60,000. Profit ratio is 2 : 2 : 3. Formula: Profit Ratio = (I₁ × T₁) : (I₂ × T₂) : (I₃ × T₃)

⇒ Let time for A be t. Then B is t − 4 and C is (t − 4) − 2 = t − 6. ⇒ Ratio of Profit (A:B) = (20,000 × t) : (30,000 × (t − 4)) = 2 : 2. ⇒ 2t ÷ (3t − 12) = 1 ⇒ 2t = 3t − 12 ⇒ t = 12. ⇒ Time for A = 12 months, B = 8 months, C = 6 months. ⇒ Check with C: (30,000 × 8) : (60,000 × 6) = 240,000 : 360,000 = 2 : 3 (Matches).

∴ The correct answer is 12, 8 and 6 months.

Additional Information

Partnership Ratios

In a partnership, profit is distributed based on the product of Capital and Time. If capitals are C₁, C₂ and times are T₁, T₂, then Profit Ratio P₁:P₂ = C₁T₁ : C₂T₂.

Time Calculation

If profit ratios and capitals are known, Time ratio can be found using T = P ÷ C.

General solution:

[2 ×  1.5x ×  (2/5) +2 ×  2.5x ×  (2/5) + 2 × 400 ×  (3/8) + 2 ×  2x ×  (1/2)] = 1340

[1.2x + 2x + 300 + 2x] = 1340

5.2x = 1040

x = 200

Department P:

Total students (Boys + Girls) got graduated = 1.5 ×  2 ×  200 = 600

Number of girls got  graduated = 600 ×  (2/5)= 240

Number of boys got graduated = (600 - 240) = 360

 

Department Q:

Total students (Boys + Girls) got graduated = (250 ×  x/100)  = 2.5 ×  2 ×  200 = 1000

Number of girls got  graduated = 1000 ×  (2/5)= 400

Number of boys got graduated = (1000 - 400) = 600

 

Department R:

Total students (Boys + Girls) got graduated = 400 ×  2 = 800

Number of girls got  graduated = 800 ×  (3/8)= 300

Number of boys got graduated = (800 - 300) = 500

 

Department S:

Total students (Boys + Girls) got graduated = 2 ×  2 ×  200 = 800

Number of girls got  graduated = 800 ×  (1/2) = 400

Number of boys got graduated = (800 - 400) = 400

 

Solution:

Number of boys graduated form department Q = 600

Number of boys graduated from department Q with distinction = 600 ×  3/5 = 360

Number of boys graduated from department Q with first class = (600 - 360) = 240

Number of girls graduated from department Q with first class = (400 ×  5/8) = 250

Required total = (240 + 250) = 490

General solution:

[2 ×  1.5x ×  (2/5) +2 ×  2.5x ×  (2/5) + 2 × 400 ×  (3/8) + 2 ×  2x ×  (1/2)] = 1340

[1.2x + 2x + 300 + 2x] = 1340

5.2x = 1040

x = 200

Department P:

Total students (Boys + Girls) got graduated = 1.5 ×  2 ×  200 = 600

Number of girls got  graduated = 600 ×  (2/5)= 240

Number of boys got graduated = (600 - 240) = 360

 

Department Q:

Total students (Boys + Girls) got graduated = (250 ×  x/100)  = 2.5 ×  2 ×  200 = 1000

Number of girls got  graduated = 1000 ×  (2/5)= 400

Number of boys got graduated = (1000 - 400) = 600

 

Department R:

Total students (Boys + Girls) got graduated = 400 ×  2 = 800

Number of girls got  graduated = 800 ×  (3/8)= 300

Number of boys got graduated = (800 - 300) = 500

 

Department S:

Total students (Boys + Girls) got graduated = 2 ×  2 ×  200 = 800

Number of girls got  graduated = 800 ×  (1/2) = 400

Number of boys got graduated = (800 - 400) = 400

 

Solution:

Number of boys graduated in department Q from hostel = 600 ×  (30/100) = 180

Number of girls  graduated in department R from hostel = 500 ×  (40/100) = 200

Total hostelers graduated from department Q and R = 600

Number of girls graduated in  department Q and R, from the hostel = 600 - (200 + 180) = 220

General solution:

[2 ×  1.5x ×  (2/5) +2 ×  2.5x ×  (2/5) + 2 × 400 ×  (3/8) + 2 ×  2x ×  (1/2)] = 1340

[1.2x + 2x + 300 + 2x] = 1340

5.2x = 1040

x = 200

Department P:

Total students (Boys + Girls) got graduated = 1.5 ×  2 ×  200 = 600

Number of girls got  graduated = 600 ×  (2/5)= 240

Number of boys got graduated = (600 - 240) = 360

 

Department Q:

Total students (Boys + Girls) got graduated = (250 ×  x/100)  = 2.5 ×  2 ×  200 = 1000

Number of girls got  graduated = 1000 ×  (2/5)= 400

Number of boys got graduated = (1000 - 400) = 600

 

Department R:

Total students (Boys + Girls) got graduated = 400 ×  2 = 800

Number of girls got  graduated = 800 ×  (3/8)= 300

Number of boys got graduated = (800 - 300) = 500

 

Department S:

Total students (Boys + Girls) got graduated = 2 ×  2 ×  200 = 800

Number of girls got  graduated = 800 ×  (1/2) = 400

Number of boys got graduated = (800 - 400) = 400

 

<br>

Solution:

Number of boys graduated from department Q = 600 ×  120/100 = 720

Total number of girls graduated from all the department = (240 + 300 + 400 + 400) = 1340

Required percentage = (720/1340) ×  100 = 53.73%

General solution:

[2 ×  1.5x ×  (2/5) +2 ×  2.5x ×  (2/5) + 2 × 400 ×  (3/8) + 2 ×  2x ×  (1/2)] = 1340

[1.2x + 2x + 300 + 2x] = 1340

5.2x = 1040

x = 200

Department P:

Total students (Boys + Girls) got graduated = 1.5 ×  2 ×  200 = 600

Number of girls got  graduated = 600 ×  (2/5)= 240

Number of boys got graduated = (600 - 240) = 360

 

Department Q:

Total students (Boys + Girls) got graduated = (250 ×  x/100)  = 2.5 ×  2 ×  200 = 1000

Number of girls got  graduated = 1000 ×  (2/5)= 400

Number of boys got graduated = (1000 - 400) = 600

 

Department R:

Total students (Boys + Girls) got graduated = 400 ×  2 = 800

Number of girls got  graduated = 800 ×  (3/8)= 300

Number of boys got graduated = (800 - 300) = 500

 

Department S:

Total students (Boys + Girls) got graduated = 2 ×  2 ×  200 = 800

Number of girls got  graduated = 800 ×  (1/2) = 400

Number of boys got graduated = (800 - 400) = 400

 

Solution:

Average number of girls graduated from the all the college = 335

Average number of all the boys graduated from the ll the departments = (360 + 600 + 500 + 400)/4 = 465

Required difference = (465 - 335) = 130

General solution:

[2 ×  1.5x ×  (2/5) +2 ×  2.5x ×  (2/5) + 2 × 400 ×  (3/8) + 2 ×  2x ×  (1/2)] = 1340

[1.2x + 2x + 300 + 2x] = 1340

5.2x = 1040

x = 200

Department P:

Total students (Boys + Girls) got graduated = 1.5 ×  2 ×  200 = 600

Number of girls got  graduated = 600 ×  (2/5)= 240

Number of boys got graduated = (600 - 240) = 360

 

Department Q:

Total students (Boys + Girls) got graduated = (250 ×  x/100)  = 2.5 ×  2 ×  200 = 1000

Number of girls got  graduated = 1000 ×  (2/5)= 400

Number of boys got graduated = (1000 - 400) = 600

 

Department R:

Total students (Boys + Girls) got graduated = 400 ×  2 = 800

Number of girls got  graduated = 800 ×  (3/8)= 300

Number of boys got graduated = (800 - 300) = 500

 

Department S:

Total students (Boys + Girls) got graduated = 2 ×  2 ×  200 = 800

Number of girls got  graduated = 800 ×  (1/2) = 400

Number of boys got graduated = (800 - 400) = 400

 

Solution:

Number of boys graduated from department Q = 600

Number of boys graduated from department T = (600 + 50) = 650

Number of girls graduated from department P = 240

Number of girls graduated from department T = (240 + 60) = 300

Required difference = (650 ×  2/5 - 300 ×  2/3) = (260 - 200) = 60

Shortcut Trick

Total Marked Price (MP) = Bat MP + Ball MP = (25x × 1.2) + (5x × 2.0) = 30x + 10x = 40x.

Total Selling Price (SP) = Bat SP + Ball SP = (25x × 1.1) + (5x × 1.5) = 27.5x + 7.5x = 35x.

Total Discount = Total MP − Total SP = 40x − 35x = 5x.

Overall Discount % = (Total Discount ÷ Total MP) × 100 = (5x ÷ 40x) × 100 = 12.5%.

∴ The correct answer is 12.5%.

Alternate Method

Given: CP of Bat = 25x, CP of Ball = 5x. Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = CP × (100 + Profit%) ÷ 100 | Discount% = (MP − SP) ÷ MP × 100.

⇒ Bat MP = 25x + 20% of 25x = 25x + 5x = 30x. ⇒ Ball MP = 5x + 100% of 5x = 5x + 5x = 10x. ⇒ Total MP = 30x + 10x = 40x. ⇒ Bat SP = 25x + 10% of 25x = 25x + 2.5x = 27.5x. ⇒ Ball SP = 5x + 50% of 5x = 5x + 2.5x = 7.5x. ⇒ Total SP = 27.5x + 7.5x = 35x. ⇒ Discount = 40x − 35x = 5x. ⇒ Discount Percentage = (5x ÷ 40x) × 100 = 12.5%.

∴ The correct answer is 12.5%.

Additional Information

Marked Price and Discount

Marked Price is the price displayed on the tag, while Discount is always calculated on the MP to arrive at the Selling Price.

Profit and Cost Price

Profit is the extra amount earned over the Cost Price. Profit % = (SP − CP) ÷ CP × 100.

Shortcut Trick

Initial ratio of chemical to water = 11 : 4

Final ratio of chemical to water = 11 : 6

Since chemical remains constant (11 units), the increase in water = 6 − 4 = 2 units.

Total initial units = 11 + 4 = 15 units → 60 L.

1 unit = 4 L ∴ 2 units = 8 L.

∴ The correct answer is 8 L.

Alternate Method

Given: Total solution = 60 L, Ratio (C:W)_initial = 11:4, Ratio (C:W)_final = 11:6

Calculations:

⇒ Total initial parts = 11 + 4 = 15

⇒ Quantity of chemical = (11 ÷ 15) × 60 = 44 L

⇒ Quantity of water = (4 ÷ 15) × 60 = 16 L

⇒ Let water added be x L. New water = 16 + x

⇒ 44 ÷ (16 + x) = 11 ÷ 6

⇒ 11 × (16 + x) = 44 × 6

⇒ 16 + x = 4 × 6 = 24

⇒ x = 24 − 16 = 8 L

∴ The correct answer is 8 L.

Additional Information

Mixture Dilution Rule

When adding only one component to a mixture, the quantity of the other component remains constant. Always equate the constant component to find the new total volume.

Alligation Method

For dilution with pure water, the concentration of the second addition is 0% chemical or 100% water. (Q₁ ÷ Q₂) = (n₂ − n_avg) ÷ (n_avg − n₁).

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:

In this type of question, we are expected to calculate approximate value (not exact value), so we can replace the given numbers by their nearest perfect places which makes the calculation easy.

9.87% of [(299.96)² + (20.24)²] = 999.99% of 4 + ?

Taking approximate value, we get

10% of [(300)² + (20)²] = 1000% of 4 + ?

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

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

Taking approximate value, we get

10% of [(300)² + (20)²] = 1000% of 4 + ?

⇒ (10 ÷ 100) × (90000 + 400) = (1000 ÷ 100) × 4 + ?

⇒ (1 ÷ 10) × (90400) = 10 × 4 + ?

⇒ 9040 = 40 + ?

⇒ 9040 -40 = ?

∴ ? = 9000

∴ the approximate value of question mark (?) in the following question is 9000.

Solution:

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

Calculation:

30% of 460 + 25% of 640 + 2 = ? × 6

⇒ (30/100) × 460 + (25/100) × 640 + 2 = ? × 6

⇒ 3 × 46 + (640/4) + 2 = ? × 6

⇒ 138 + 160 + 2 = ? × 6

⇒ 300 = ? × 6

⇒ ? = 300/6

∴ ? = 50

Solution:

We have to follow the BODMAS rule

Calculation:

√1155.91 + √730 + (44.99 ÷ 8.97 -  0.99)^0.49

⇒ √1156 + √730 + (45 ÷ 9 – 1)^0.5

⇒ √1156 + √730 + (5 – 1)^1/2

⇒ √1156 + √730 + 4^1/2

⇒ √1156 + √730 + 2

⇒ 34 + 27 + 2

⇒ 63

∴ 63 will come in place of the question mark

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:

In this type of question, we are expected to calculate approximate value (not exact value), so we can replace the given numbers by their nearest perfect places which makes the calculation easy.

√3.98 + (√((2.22)² + 4.85)) × 5.69 = 24.71% of ?

Taking approximate value, we get

√4 + (√(2² + 5)) × 6 = 25% of ?

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

⇒ √4 + (√ (4 + 5)) × 6 = 25% of ?

⇒ √4 + (√9) × 6 = 25% of ?

⇒ 2 + 18 = 25% of ?

⇒ 2 + 18 = 25% of ? (∵ 1.73 ≈ 2)

⇒ 20 = (25/100) × ?

⇒ 20 × 100 / 25 = ?

? = 80

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:

In this type of question, we are expected to calculate approximate value (not exact value), so we can replace the given numbers by their nearest perfect places which makes the calculation easy.

29² + 34.12 % of 700 ÷ ∛2744.21 = ? + ∛2197

Taking approximate value, we get

29² + 34 % of 700 ÷ ∛2744 = ? + ∛2197

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

⇒ 841 + (34 ÷ 100) × 700 ÷ 14 = ? + 13

⇒ 841 + (238 ÷ 14) = ? + 13

⇒ 841 + 17 = ? + 13

⇒ 858 = ? + 13

⇒ ? = 858 – 13

⇒ ? = 845

∴ The value of ? is 845

Shortcut Trick

Efficiency ratio Ram : Shyam = 6 : 5 (since 20% = 1/5)

Efficiency ratio Rohan : Ram = 5 : 6 (since 16.66% = 1/6)

Combined Efficiency Ram : Shyam : Rohan = 6 : 5 : 5

Total Work = 90 × (6 + 5 + 5) = 1440 units

Target Work = 44.44% of 1440 = 4/9 × 1440 = 640 units

Required Days = 640 ÷ (5 + 5) = 64 days

∴ The correct answer is 64 days.

Alternate Method

Given: Time taken by (Ram + Shyam + Rohan) = 90 days.

Calculations:

⇒ Total Efficiency = 6x + 5x + 5x = 16x

⇒ Total Work = Efficiency × Time = 16x × 90 = 1440x

⇒ Required Work = 44.44% of Total Work = (4/9) × 1440x = 640x

⇒ Efficiency of (Shyam + Rohan) = 5x + 5x = 10x

⇒ Required Days = 640x ÷ 10x = 64 days

∴ The correct answer is 64 days.

Additional Information

Percentage to Fraction Conversion

Significant values used: 16.66% = 1/6 and 44.44% = 4/9. Converting percentages to fractions simplifies ratio calculations.

Work, Time, and Efficiency Relationship

Total Work = (Combined Efficiency of workers) × (Total Time taken). Efficiency is inversely proportional to time for a constant work.

Ratio Balancing

To find a combined ratio like A:B:C, ensure the common term has the same value in both individual ratios (A:B and B:C or A:C).

Shortcut Trick

Let Downstream speed = u and Upstream speed = v.

Case 1: D/u + (D+15)/v = 15 → (D/u + D/v) + 15/v = 15

Case 2: (D−15)/u + (D+10)/v = 13 → (D/u + D/v) − 15/u + 10/v = 13

Subtracting Case 2 from Case 1: 15/u + 5/v = 2. Since Speed of stream = 5, u − v = 10.

By trial/substitution: u = 15, v = 5 fits (15/15 + 5/5 = 2). Then D = 75 km.

Target Time = (75 + 60) ÷ 15 = 135 ÷ 15 = 9 hr. Check constraints or solve for D.

∴ The correct answer is 9 hr.

Alternate Method

Given: Speed of stream (y) = 5 km/hr. Let speed of ship in still water be x km/hr.

⇒ Downstream speed (u) = x + 5, Upstream speed (v) = x − 5.

Equation 1: D/(x+5) + (D+15)/(x−5) = 15

Equation 2: (D−15)/(x+5) + (D+10)/(x−5) = 13

⇒ Subtracting (2) from (1): [D − (D−15)]/(x+5) + [(D+15) − (D+10)]/(x−5) = 15 − 13

⇒ 15/(x+5) + 5/(x−5) = 2

⇒ 15(x−5) + 5(x+5) = 2(x² − 25)

⇒ 15x − 75 + 5x + 25 = 2x² − 50 ⇒ 20x − 50 = 2x² − 50

⇒ 2x² − 20x = 0 ⇒ 2x(x − 10) = 0 ⇒ x = 10 km/hr (since speed cannot be 0)

⇒ u = 10 + 5 = 15 km/hr and v = 10 − 5 = 5 km/hr.

⇒ Substitute x in (1): D/15 + (D+15)/5 = 15 ⇒ D + 3D + 45 = 225 ⇒ 4D = 180 ⇒ D = 45 km.

⇒ Target distance = D + 60 = 45 + 60 = 105 km.

⇒ Time = 105 ÷ 15 = 7 hr.

∴ The correct answer is 7 hr.

Additional Information

Downstream & Upstream Speeds

If boat speed is x and stream speed is y, then Downstream = x + y and Upstream = x − y.

Still Water Speed Calculation

Speed in still water (x) = (Downstream + Upstream) ÷ 2.

Stream Speed Calculation

Speed of stream (y) = (Downstream − Upstream) ÷ 2.

Shortcut Trick

Let the present age of the son be S.

Present age of the mother = 4S.

Given: Father − 3 = Mother + 3 ⇒ Father = Mother + 6 = 4S + 6.

Ratio of Father 2 years ago to Son 4 years after: (4S + 4) ÷ (S + 4) = 10 ÷ 3 ⇒ 12S + 12 = 10S + 40 ⇒ 2S = 28 ⇒ S = 14 years.

Required ratio of Mother after 3 years and Son after 2 years = (4 × 14 + 3) ÷ (14 + 2) = 59 ÷ 16. However, checking if 'the ratio of the ages of the father 2 years [after/ago] and son 4 years after is 10 : 3' means father 2 years after: (4S + 8) ÷ (S + 4) = 10 ÷ 3 ⇒ 12S + 24 = 10S + 40 ⇒ 2S = 16 ⇒ S = 8 years.

Then, present age of mother = 4 × 8 = 32 years. Mother after 3 years = 35 years. Son after 2 years = 8 + 2 = 10 years. Required ratio = 35 : 10 = 7 : 2.

 ∴ The correct answer is 7 : 2.

Alternate Method

Let the present age of the son be S.

Present age of the mother M = 4S.

Given that: F − 3 = M + 3

⇒ F = M + 6

⇒ F = 4S + 6

Given ratio of father 2 years after and son 4 years after is 10 : 3:

⇒ (F + 2) ÷ (S + 4) = 10 ÷ 3

⇒ (4S + 6 + 2) ÷ (S + 4) = 10 ÷ 3

⇒ (4S + 8) ÷ (S + 4) = 10 ÷ 3

⇒ 3 × (4S + 8) = 10 × (S + 4)

⇒ 12S + 24 = 10S + 40

⇒ 2S = 16

⇒ S = 8 years

Present age of the mother = 4S = 4 × 8 = 32 years.

Age of mother after 3 years = 32 + 3 = 35 years.

Age of son after 2 years = 8 + 2 = 10 years.

Required ratio = 35 ÷ 10 = 7 : 2.

 ∴ The correct answer is 7 : 2.

Additional Information

Ages and Ratios

When solving problems on ages, represent all individual ages in terms of a single variable to simplify calculations.

Ratio Changes Over Time

If the age of a person is x years, then their age after n years is x + n and their age n years ago was x − n.

Given:

For Statement I:

Curved Surface area of cylinder = 352 cm²

Total surface area of cylinder = 2 × 792 cm²

For Statement II:

Radius of cylinder = 1.5 cm more than 4 times height

Calculation:

For Statement I:

Let radius = r. height = h

Curved Surface area of cylinder = 352 cm²

⇒ 352 = 2 × 22 / 7 × r × h

⇒ r × h = 56

Total surface area of cylinder = 2 × 792 cm²

⇒ 2 × 792 = 2 × (22 /7) × (rh + r²)

⇒ rh + r² = 252

⇒ 56 + r² = 252

⇒ r² = 252 - 56

⇒ r² = 196

⇒ r = 14

⇒ r × h = 56

⇒ 14 × h = 56

⇒ h = 4 cm

Statement I is sufficient to answer the question.

For Statement II:

∴ r = 4h + 1.5

Statement II is not sufficient to answer the question.

The correct answer is option 2.

Given:

For Statement I:

Cost price of 2 scarfs = Rs. 2200

Earns = Rs. 55 per scarf

Discount = 23%

For Statement II:

Marks up the C.P = 36%

Earns = Rs. 200

Calculation:

For Statement I:

The cost price of a shirt = Rs. 1100

Selling Price = 1100 + 55

⇒ Rs. 1155

Marked Price = 1155 / 77 × 100

⇒ Rs. 1500

Statement I is sufficient to answer the question.

For Statement II:

Let the cost price be x.

Marked Price = x × 136%

⇒ 1.36x%

Selling Price = x + 200

Statement II is not sufficient to answer the question.

The correct answer is option 1.

Concept Used:

Total work is LCM of work done by all the persons.

Formula Used:

Total Work = Efficiency × Time

Calculations: 

Statement I.

X, Y and Z together can do a piece of work in 19 days.

X and Y together can complete the work in 28.5 days

Y and Z together can complete the work in 38 days.

Total work = LCM of (19, 28.5, 38) = 114

Total Work = Efficiency × Time

114 = (X + Y + Z) × 19

⇒ (X + Y + Z) = 114/19 = 6      ----(1)

Similarly, 114 = (X + Y) × 28.5

⇒ (X + Y) = 114/28.5 = 4      ----(2)

Similarly, 114 = (Y + Z) × 38

⇒ (Y + Z) = 114/38 = 3      ----(3)

Adding (2) and (3) and subtracting (1) from it, we get

(X + 2Y + Z) – (X + Y + Z) = (4 + 3) – 6

⇒ Y = 1

Putting in Y (3), we get

Z = 3 – 1 = 2

Now, Total Work = Efficiency × Time

⇒ 114 = Z × Time

⇒ Time = 114/2 = 57 days

So, statement I alone is sufficient to answer.

Statement II.

Y takes 29 days to complete the work alone.

We cannot find efficiency of Z from this statement alone.

So, statement II alone is not sufficient to answer the question.

∴ The statement I alone is sufficient to answer the question but, statement II alone is not sufficient.

1)  The seminar on Reading is on the even date of the month with 31 days. Three persons have a seminar in between Tina and the one who has a seminar on Reading. 

 

2)  Two persons are going on a seminar between Priya and Deep, who has a seminar in the month 30 days. 

 

3) Rama is going to the seminar before Sejal but not just before. Sejal has a seminar on Diwali. 

 

4)  The seminar on the Environment is not in the month having 30 days. The seminar on the Environment is before Yoga and after the Corruption seminar. Rama does not have a seminar on Yoga. These conditions are not satisfied by Case 2 and Case 3. So, Case 2 and Case 3 are eliminated.

 

The final arrangement is:

 

Rama has a seminar in November. Sejal has a seminar in December. Priya has a seminar on Corruption in August. Hence, the one who has a seminar on corruption is related to August.

1)  The seminar on Reading is on the even date of the month with 31 days. Three persons have a seminar in between Tina and the one who has a seminar on Reading. 

 

2)  Two persons are going on a seminar between Priya and Deep, who has a seminar in the month 30 days. 

 

3) Rama is going to the seminar before Sejal but not just before. Sejal has a seminar on Diwali. 

 

4)  The seminar on the Environment is not in the month having 30 days. The seminar on the Environment is before Yoga and after the Corruption seminar. Rama does not have a seminar on Yoga. These conditions are not satisfied by Case 2 and Case 3. So, Case 2 and Case 3 are eliminated.

 

The final arrangement is:

 

Hence, One person has a seminar between Rama and the one who has a seminar on Diwali.

1)  The seminar on Reading is on the even date of the month with 31 days. Three persons have a seminar in between Tina and the one who has a seminar on Reading. 

 

2)  Two persons are going on a seminar between Priya and Deep, who has a seminar in the month 30 days. 

 

3) Rama is going to the seminar before Sejal but not just before. Sejal has a seminar on Diwali. 

 

4)  The seminar on the Environment is not in the month having 30 days. The seminar on the Environment is before Yoga and after the Corruption seminar. Rama does not have a seminar on Yoga. These conditions are not satisfied by Case 2 and Case 3. So, Case 2 and Case 3 are eliminated.

 

The final arrangement is:

 

Hence, Tina has a seminar on 16th August.

1)  The seminar on Reading is on the even date of the month with 31 days. Three persons have a seminar in between Tina and the one who has a seminar on Reading. 

 

2)  Two persons are going on a seminar between Priya and Deep, who has a seminar in the month 30 days. 

 

3) Rama is going to the seminar before Sejal but not just before. Sejal has a seminar on Diwali. 

 

4)  The seminar on the Environment is not in the month having 30 days. The seminar on the Environment is before Yoga and after the Corruption seminar. Rama does not have a seminar on Yoga. These conditions are not satisfied by Case 2 and Case 3. So, Case 2 and Case 3 are eliminated.

 

The final arrangement is:

 

Hence, Sejal has a seminar on 3rd December.