IBPS PO Prelims Memory Based Paper (Held On: 16 October 2022 Shift 2) (Previous Year Paper)

The correct answer is option 3.

Key Points

• Scrutinizing means examining or inspecting closely and thoroughly.
• Sustainable means able to be maintained at a certain rate or level.
• Renewed means giving fresh life or strength to.
• Overhauled means take apart (a piece of machinery or equipment) in order to examine it and repair it if necessary.
• The most appropriate word is renewed as it means that berries gave him strengthening energy.

The correct answer is option 1.

Key Points

• Crude means in a natural or raw state; not yet processed or refined.
• Primitive means relating to, denoting, or preserving the character of an early stage in the evolutionary or historical development of something.
• Improvised means produce or make (something) from whatever is available.
• Unpurified means not made pure.
• The best synonym is crude.

The correct answer is option 5

Key Points

• The correct answer is: Making a narcotic drink
• The passage mentions that before the potential of coffee as a beverage was discovered, people in Arabia used to eat coffee as food and make a drink out of its beans because of its narcotic effects and medicinal value. This indicates that coffee was initially used to brew a narcotic drink before being consumed as a regular beverage.
• Therefore, option 5 "Making a narcotic drink" is the most fitting answer based on the information from the passage.

The correct answer is option 1.

Key Points

• The passage states that out of the approximately 60 species of coffee plants growing wild in various regions, only about ten of them are cultivated
• Of these ten, Coffea Arabica and Coffea Canephora (also known as Robusta) are mentioned as the two species responsible for almost all the coffee produced in the world
• Therefore, option A is the correct answer.

Additional Information

• Option B is incorrect because it incorrectly pairs Coffea Robusta with Coffea Arabica, while the passage specifies Coffea Canephora as the other species responsible for a significant portion of coffee production.
• Option C is incorrect because it pairs Coffea Canephora with Coffea Liberica, which is not mentioned as one of the primary species responsible for coffee production.
• Option D is incorrect because it pairs Coffea Excelsa with Coffea Arabica, while the passage does not mention Coffea Excelsa as one of the

The correct answer is option 2.

Key Points

• Impeded means delay or prevent (someone or something) by obstructing them; hinder.
• Laden means heavily loaded or weighed down.
• Burdened means cause (someone) worry, hardship, or distress.
• Bridled means bring (something) under control; curb.
• The closest and appropriate word should be laden.

The correct answer is option 5.

Key Points

• The last option, 5) Through the cultivation efforts of Arabian farmers, accurately aligns with the passage's narration of how coffee first transitioned from Ethiopia to the Arabian Peninsula. It mentions that coffee berries were transported from Ethiopia to the Arabian Peninsula, where they were first cultivated in present-day Yemen.

Additional Information

• Through the efforts of Venetian trade merchants: The passage mentions that coffee spread to the European continent by means of Venetian trade merchants. However, this event happened after coffee had already reached the Arabian Peninsula.
• By the migration of coffee plants across regions: The passage doesn't speak of any natural migration of coffee plants from one region to another. Instead, the transport and cultivation of coffee are presented as conscious human activities.
• Due to the popularity of coffee houses in Europe: The passage indeed mentions the development and popularity of coffee houses in Europe, but this happened in the 17th Century, long after coffee berries had been transported from Ethiopia to the Arabian Peninsula.
• By the influence of Turkish coffee makers: Turkish coffee makers are mentioned in the passage, but in the context of discovering that roasting coffee beans can produce a delicious drink. The passage doesn't suggest they played a role in the actual transport of coffee from Ethiopia to the Arabian Peninsula.

Key Points

• The correct answer is Eastern Africa (Ethiopia)
• The passage clearly states that coffee was first discovered in Eastern Africa, in an area known today as Ethiopia. Therefore, option C is the correct answer.

Additional Information

• Option A is incorrect because the passage specifies Eastern Africa, not Western Africa, as the location of coffee's first discovery.
• Option B is incorrect because the passage specifies Eastern Africa, not Southern Africa, as the location of coffee's first discovery.
• Option D is incorrect because the passage specifies Eastern Africa, not Northern Africa, as the location of coffee's first discovery.
• Option E is incorrect because the passage specifies Eastern Africa, not Central Africa, as the location of coffee's first discovery

The correct answer is B-C

Key Points

The sentence talks about how Sarah had shifted to a big city and had hopes of becoming a singer, but she was rejected harshly wherever she went.

• Looking at the sentence we can see that:
• Part B talks about 'with successful of becoming'.
• 'Successful' is an adjective - a word used to describe a noun - and unless it is immediately followed by a noun it cannot be preceded by a preposition like 'with' (which is only used with nouns).
• Thus, 'successful' needs to be replaced with a noun.
• Part C talks about 'becoming a dreams'.
• This is incorrect as the article 'a' (used exclusively with nouns) - in this case, an adjective followed by a noun- cannot be used with a noun in its plural form - dreams.
• Thus, 'dreams' needs to be replaced with an adjective as the blank is followed by a noun.
• 'With dreams' and 'becoming a successful' are grammatically and contextually correct.
• Therefore, B will replace C and vice versa.
• Thus, the correct answer is option 1.

The correct sentence will be: Sarah moved to the big city with dreams of becoming a successful singer, but she was met with harsh rejection everywhere.

The correct answer is no rearrangement. 

The sentence requires no rearrangement as all the words are grammatically and contextually correct. 

Thus the correct answer is option 5.

The correct answer is D-A

Key Points

The sentence talks about how although Wesley was adopted by parents who loved him, he still has the curiosity to find out about his birth parents. 

• Looking at the sentence we can see that:
• Part A talks about 'finding by loving parents'.
• This is incorrect given the 'finding' is preceded by 'was' which is in the past tense, meaning that the 'finding' should also have been in the past tense.
• Thus, 'finding' needs to be replaced with a verb in the past tense.
• Part D talks about 'adopted his birth parents', logically it is parents who adopt children and not the other way around.
• Given that Wesley was 'always curious', the verb in Part D should be in the continuous tense.
• Thus, 'adopted' needs to be replaced with a verb in the continuous tense.
• 'Was adopted' and 'about finding his birth parents' are grammatically and contextually correct.
• There A will replace D and vice versa.
• Thus the correct answer is option 1.

The correct sentence will be: While Wesley was adopted by loving parents, he was always curious about finding his birth parents.

The correct answer is A-B

Key Points

The sentence talks about how after being left at the altar by her fiance, Mariam decided to move to a new city and start afresh. 

• Looking at the sentence we can see that:
• Part A talks about 'being jilter by her altar'. This is incorrect because 'jilting' is an action that can only be carried out by living things, an 'altar' cannot 'jilt' (suddenly reject or abandon) someone.
• Also, an 'altar' is usually part of a location - the church of the hall where the wedding is being held - it cannot be possessed or owned by anyone and thus cannot be preceded by the possessive pronoun 'her'.
• Thus, 'altar' needs to be replaced.
• Part B talks about 'at the fiance', this is incorrect because a fiance is a title given to a person in relation to the person they are engaged to, thus it has to be preceded by a possessive pronoun.
• Also, 'at the' implies a physical location and 'fiance' is a label given to a person and cannot be a location.
• Thus. 'fiance' needs to be replaced.
• 'Jilted by her fiance' and 'at the altar' are grammatically and contextually correct.
• Therefore, A will replace B and vice versa.
• Thus, the correct answer is option 2.

The correct sentence will be: After being jilted by her fiancé at the altar, Mariam decided to move to a new city and get a fresh start.

The correct answer is C-D

Key Points

The sentence talks about how Elinor had dreams of moving to America in order to study more, but her parents were insisting on her getting married early.

• Looking at the sentence we can see that:
• Part C talks about 'her married were adamant'.
• 'Married' is a verb - an action - in the past tense and cannot be owned by anyone, and thus cannot be preceded by a possessive pronoun like 'her'.
• It also cannot be plural or singular and thus cannot be followed by a plural verb - were.
• Thus, 'married' needs to be replaced.
• Part D talks about 'getting her parents early'. This would make sense in some other context but 'getting parents early' instead of 'moving to America' makes little contextual sense.
• Thus, 'parents' needs to ve replaced with a verb (against the verb of 'move')
• 'But her parents' and 'getting her married early' make grammatical and contextual sense.
• Therefore, C will replace D and vice versa.
• Thus, the correct answer is option 4.

The correct sentence is: Elinor wanted to move to America in order to pursue further studies, but her parents were adamant about getting her married early.

The correct answer is 'Consent.'

Key Points

• The given sentence is talking about punishing certain sexual acts when done without the permission or mutual agreement.
• Therefore, the most appropriate word to be filled in the blank is 'Consent'.
• Also, the use of the word ''without'' in the sentence indicates the use of the word 'consent' in the blank.
• The word 'Consent' means Permission for something to happen or agreement to do something.
• Example: His parents refused their consent to the marriage.
  

Hence, the correct answer is option 3.

Complete Sentence: The object of the law, he concludes, is to punish certain sexual acts when done without consent.

Additional Information

• Let us explore  the other options:
• Present means Being in a particular place.
• Recent means Having happened, begun, or been done not long ago.
• Insane means Not showing sensible judgment.
• Absent means Not present in a place, at an occasion, or as part of something.

The correct answer is risen.

Key Points

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

• risen - Let's look at the meaning of the correct answer:
• **Example - the sun has just risen.​
• ​From the given meaning we can conclude that the correct answer is risen.

Thus the correct sentence is: *"*According to the latest official estimates, India's literacy rate has risen by approximately 500% since independence". ​

Additional Information

Let's ​discuss the meaning of other options:

• damage - physical harm that impairs the value, usefulness, or normal function of something
• taken - lay hold of (something)
• carry - support and move (someone or something) from one place to another.
• swing - move or cause to move back and forth or from side to side while suspended or on an axis.

The correct answer is boost.

Key Points

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

• A computing machine 20000 times faster can increase the processing power of supercomputers.
• boost - help or encourage (something) to increase or improve.
• ​Example - *We have to adopt a range of measures to boost tourism.*​
• ​From the given meaning we can conclude that the correct answer is boost.

Thus the correct sentence is: *"*China's computing machine is 20000 times faster than its international counterparts and may boost the processing power of supercomputers".

Additional Information

Let's ​discuss the meaning of other options:

• hinder - make it difficult for (someone) to do something or for (something) to happen
• decrease - make or become smaller or fewer in size, amount, intensity, or degree.
• diminish - make or become less.
• destroy - end the existence of (something) by damaging or attacking it.

The correct answer is thought.

Key Points

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

• thought - an idea or opinion produced by thinking, or occurring suddenly in the mind.
• ​Example - *Riha sat deep in the thought.*​
• ​From the given meaning we can conclude that the correct answer is thought

Thus the correct sentence is: "If the thought of investing in the stock market scares you, you are not alone"

Additional Information

Let's ​discuss the meaning of other options:

• song - a short poem or set of words set to music or meant to be sung.
• view - the ability to see something or to be seen from a particular place.
• source - a place, person, or thing from which something originates or can be obtained.
• button - a small disc or knob sewed onto a garment, either to fasten it by being pushed through a slit made for the purpose or for decoration.

The correct answer is Ephemeral.

Key Points

• Ephemeral: lasting for a very short time
• The context talks about Konoha where preparations for war was going on and therefore, the existing peace was short-lived.
• Therefore, the correct answer is: Peace was ephemeral in Konoha as preparations for the upcoming war was being carried out behind the scenes.

Additional Information

• | Word | Meaning | | --- | --- | | Perpetual | continuing forever; everlasting | | Elegant | graceful and stylish in appearance or manner. | | Nadir | the lowest or most unsuccessful point in a situation |

The correct answer is A.

Key Points

• The given paragraph is about the 2022 FIFA World Cup.
• Sentence E is the first sentence as it talks about the 2022 FIFA World Cup, the 22nd running of the FIFA World Cup competition.
• Sentence A is the second sentence as it mentions where (Qatar) the 2022 FIFA World Cup is going to take place.
• Sentence C is in the correct place and it's the third sentence as it informs that the 2022 FIFA World Cup will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after 2002.
• Sentence B is the fourth sentence as it further says the 2022 FIFA World Cup will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament.
• Sentence F is the fifth sentence as it gives information about the first match of the 2022 FIFA World Cup.
• Sentence D is the sixth sentence as it concludes by giving information about the final match of the 2022 FIFA World Cup.
• The correct sequence is EACBFD.
  

Correct Paragraph: The 2022 FIFA World Cup is scheduled to be the 22nd running of the FIFA World Cup competition. It is scheduled to take place in Qatar from 20 November to 18 December 2022. This will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after the 2002 tournament in South Korea and Japan. In addition, the tournament will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament in the United States, Mexico, and Canada. The first match played at the tournament will be contested between Qatar and Ecuador at Al Bayt Stadium, Al Khor. The final is due to be held on 18 December 2022, which also is Qatar National Day.

The correct answer is F.

Key Points

• The given paragraph is about the 2022 FIFA World Cup.
• Sentence E is the first sentence as it talks about the 2022 FIFA World Cup, the 22nd running of the FIFA World Cup competition.
• Sentence A is the second sentence as it mentions where (Qatar) the 2022 FIFA World Cup is going to take place.
• Sentence C is in the correct place and it's the third sentence as it informs that the 2022 FIFA World Cup will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after 2002.
• Sentence B is the fourth sentence as it further says the 2022 FIFA World Cup will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament.
• Sentence F is the fifth sentence as it gives information about the first match of the 2022 FIFA World Cup.
• Sentence D is the sixth sentence as it concludes by giving information about the final match of the 2022 FIFA World Cup.
• The correct sequence is EACBFD.
  

Correct Paragraph: The 2022 FIFA World Cup is scheduled to be the 22nd running of the FIFA World Cup competition. It is scheduled to take place in Qatar from 20 November to 18 December 2022. This will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after the 2002 tournament in South Korea and Japan. In addition, the tournament will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament in the United States, Mexico, and Canada. The first match played at the tournament will be contested between Qatar and Ecuador at Al Bayt Stadium, Al Khor. The final is due to be held on 18 December 2022, which also is Qatar National Day.

The correct answer is D.

Key Points

• The given paragraph is about the 2022 FIFA World Cup.
• Sentence E is the first sentence as it talks about the 2022 FIFA World Cup, the 22nd running of the FIFA World Cup competition.
• Sentence A is the second sentence as it mentions where (Qatar) the 2022 FIFA World Cup is going to take place.
• Sentence C is in the correct place and it's the third sentence as it informs that the 2022 FIFA World Cup will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after 2002.
• Sentence B is the fourth sentence as it further says the 2022 FIFA World Cup will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament.
• Sentence F is the fifth sentence as it gives information about the first match of the 2022 FIFA World Cup.
• Sentence D is the sixth sentence as it concludes by giving information about the final match of the 2022 FIFA World Cup.
• The correct sequence is EACBFD.
  

Correct Paragraph: The 2022 FIFA World Cup is scheduled to be the 22nd running of the FIFA World Cup competition. It is scheduled to take place in Qatar from 20 November to 18 December 2022. This will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after the 2002 tournament in South Korea and Japan. In addition, the tournament will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament in the United States, Mexico, and Canada. The first match played at the tournament will be contested between Qatar and Ecuador at Al Bayt Stadium, Al Khor. The final is due to be held on 18 December 2022, which also is Qatar National Day.

The correct answer is B.

Key Points

• The given paragraph is about the 2022 FIFA World Cup.
• Sentence E is the first sentence as it talks about the 2022 FIFA World Cup, the 22nd running of the FIFA World Cup competition.
• Sentence A is the second sentence as it mentions where (Qatar) the 2022 FIFA World Cup is going to take place.
• Sentence C is in the correct place and it's the third sentence as it informs that the 2022 FIFA World Cup will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after 2002.
• Sentence B is the fourth sentence as it further says the 2022 FIFA World Cup will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament.
• Sentence F is the fifth sentence as it gives information about the first match of the 2022 FIFA World Cup.
• Sentence D is the sixth sentence as it concludes by giving information about the final match of the 2022 FIFA World Cup.
• The correct sequence is EACBFD.
  

Correct Paragraph: The 2022 FIFA World Cup is scheduled to be the 22nd running of the FIFA World Cup competition. It is scheduled to take place in Qatar from 20 November to 18 December 2022. This will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after the 2002 tournament in South Korea and Japan. In addition, the tournament will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament in the United States, Mexico, and Canada. The first match played at the tournament will be contested between Qatar and Ecuador at Al Bayt Stadium, Al Khor. The final is due to be held on 18 December 2022, which also is Qatar National Day.

The correct answer is E.

Key Points

• The given paragraph is about the 2022 FIFA World Cup.
• Sentence E is the first sentence as it talks about the 2022 FIFA World Cup, the 22nd running of the FIFA World Cup competition.
• Sentence A is the second sentence as it mentions where (Qatar) the 2022 FIFA World Cup is going to take place.
• Sentence C is in the correct place and it's the third sentence as it informs that the 2022 FIFA World Cup will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after 2002.
• Sentence B is the fourth sentence as it further says the 2022 FIFA World Cup will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament.
• Sentence F is the fifth sentence as it gives information about the first match of the 2022 FIFA World Cup.
• Sentence D is the sixth sentence as it concludes by giving information about the final match of the 2022 FIFA World Cup.
• The correct sequence is EACBFD.
  

Correct Paragraph: The 2022 FIFA World Cup is scheduled to be the 22nd running of the FIFA World Cup competition. It is scheduled to take place in Qatar from 20 November to 18 December 2022. This will be the first World Cup ever to be held in the Arab world, and the second World Cup held entirely in Asia after the 2002 tournament in South Korea and Japan. In addition, the tournament will be the last to involve 32 teams, with an increase to 48 teams scheduled for the 2026 tournament in the United States, Mexico, and Canada. The first match played at the tournament will be contested between Qatar and Ecuador at Al Bayt Stadium, Al Khor. The final is due to be held on 18 December 2022, which also is Qatar National Day.

The correct answer is Less than 2 hours is left

Key Points

• In the given sentence, the phrase '2 hours are left' is incorrect.
• When using adjectives like much, less, little and more are used, they are followed by the verb in the singular format. 
• ​In the current scenario, the 'less than 2 hours' refers to a specific time period that will be treated as one and thus is singular.
• Hence, the 'are left' in the sentence will be replaced with 'is left' to make the sentence grammatically correct.

The correct sentence will be: Less than 2 hours is left before the bomb explodes and annihilates the city and its inhabitants. 

Thus, the correct answer is Less than 2 hours is left

Additional Information

Let's look at the meanings of some of the hard words:

The correct answer is Mary and I will be going

Key Points

• In the given sentence 'Mary and me' is the incorrect phrase.
• When it comes to the debate between 'me' and 'I', the answer depends on the subject-object of the sentence.
• If the pronouns are referring to someone who is the subject of the sentence, then 'I' will be used. 
• Example: Sally and I tried really hard to stop Anisha from going, but she wouldn't listen to reason.
• If the pronouns are referring to someone who is the object of the sentence, then 'me' is used. 
• Example: Harsh was very rude when it came to talking to Amar and me.
• Hence, the 'me' in the sentence needs to be replaced with 'I' in order to make the sentence grammatically correct.

The correct sentence will be: Mary and I will be going to the movies after we're done with the marathon.

Thus, the correct answer is Mary and I will be going

The correct answer is 'has been issuing monthly and daily passes'. 

Key Points

• According to the subject-verb agreement rule, If the subject is singular, then the verb must be in singular form and the subject is plural then the verb must be in plural form.
• Examples, 
• The light in the lamppost flickers each night.
• The lights in the lampposts flicker each night.
• In the given sentence, the subject 'corporation' is singular, so it should be followed by the singular verb 'has'.
• 'has been' should be followed by the 'ing' form of the verb (issuing).
• From the given explanation, we can understand that option 1 is the correct answer.

The correct answer is 'can be of'.

Key Points

• The error is in the usage of 'could' in the underlined part.
• The sentence talks about health and its varied types.
• The correct word for the underlined part must be 'can' which is used to indicate that something is typically the case. As the sentence is in the present tense, 'can' is the correct word.
• 'could' must be replaced with 'can'.

Thus the correct sentence is - Health can be of varied types; physical, emotional, mental, social, spiritual, and sexual health is some of them.

Important Points

• 'could'(past tense of 'can') is used to indicate possibility and also used in making suggestions or polite requests. 
• ​For example - They could be right, You could always ring him up.
• 'been' is used in the perfect tense. 
• For example - had been, have been, has been.

The correct answer is 'upon one's health​​'.

Key Points

• The error is in the usage of 'into' in the underlined part.
• The sentence talks about health and how it's one's responsibility to improve one's health.
• 'Improve upon (something)' is a phrasal verb which means 'to do something in a better way or with better results than before'.
• 'Into' must be replaced with 'upon'. 
  

Thus the correct sentence is - To improve upon one’s health is one’s own responsibility as a healthy mind can reside only in a healthy body.

Additional Information

• Let us see the meanings of the words in option:
• in - expresses the situation of something that is or appears to be enclosed or surrounded by something else.
• at - expresses the location or arrival in a particular place or position.
• into - to or toward the inside of (something) in the direction of (something)
• to - expresses motion in the direction of (a particular location).

The correct answer is Light pollution could have significant ramifications on the insect population, species or community level.

Key Points

• The sentence 'Light pollution could have significant ramifications at the insect population, species or community level' is grammatically correct.
• We use 'could have' when we try to say that something was possible in the past but that did not take place and it is appropriate for the context of the sentence.
• The word 'significant' is appropriately qualifying the noun 'ramifications'.
• The preposition 'on', which is used to express the position of something, is also appropriate.
• Hence, the sentence is grammatically correct.
• The corrected form of the other sentences are:
• | Option | Grammatical mistake | Corrected sentence | | --- | --- | --- | | 1. | The word 'life' should be replaced with 'lives'. | Artificial light at night can affect every aspect of insects’ lives. | | 2. | The article 'a' should be added before the word 'bulb'. | The most familiar impact of light pollution is moths flapping around a bulb, mistaking it for the moon. | | 3. | The preposition 'on' should be replaced with 'for'. | Insects are important prey for many species. |

• Therefore, option 4) is the answer.

Additional Information

• Ramification: effect

The correct answer is Marine animals can hear across entire ocean basins.

Key Points 

• The sentence 'Marine animals can hear across entire ocean basins.' is grammatically correct.
• The words 'Marine' and 'entire' are appropriately used here to qualify the nouns 'animals' and 'ocean basins'.
• The base form of the verb 'hear' is used with the auxiliary verb 'can' which is appropriate.
• Hence, the sentence is grammatically correct.
• The corrected form of the other sentences are:
• | Option | Grammatical mistake | Corrected sentence | | --- | --- | --- | | 1. | The preposition 'of' should be replaced with 'for'. | The IHR are a legally binding instrument of international law that aims for international collaboration. | | 2. | The verb 'produced' should be replaced with 'produce'. | If productive capacity grows, an economy can produce progressively more goods, which raises the standard of living. | | 4. | The preposition 'to' should be replaced with 'than'. | Underwater sound waves are far more violent than sound waves in air. |

• Therefore, option 3) is the answer.

Additional Information

• Collaboration: working together

The correct answer is International oil companies are used to dealing with industry cycles.

Key Points

• The sentence 'International oil companies are used to dealing with industry cycles.' is grammatically correct.
• The subject 'International oil companies' is plural number hence, 'plural verb' (are) is used here.
• 'Verb+ing' should be used with 'be(am/is/are)+ used to' is used. Hence, 'used to dealing with' is correct.
• Therefore, the sentence is grammatically correct.
• The corrected form of the other sentences are:
• | Option | Grammatical mistake | Corrected sentence | | --- | --- | --- | | 1. | The word 'darker' should be replaced with the word 'darkest'. | The world’s biggest oil companies are preparing to mark an end to the darkest year with a return to profit. | | 2. | The word 'keeping' should be replaced with the word 'keep'. | The Rising demand for oil is likely to keep prices high. | | 4. | The article 'an' should be added before the word 'end'. | The IEA dashed hopes that the coronavirus may have brought an end to the world’s rising appetite for oil. |

• Therefore, the correct answer is option 3).

Additional Information

• Dashed: struck with great force

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

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

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

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

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

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

11.92 + 3(-2.18 × 2.97) - (17.98 ÷ 5.96) = ?

⇒ ? = 12 + 3(-2 × 3) - (18 ÷ 6)

⇒ ? = 12 + 3(-2 × 3) - 3

⇒ ? = 12 + 3(-6) - 3

⇒ ? = 12 - 18 - 3

⇒ ? = - 6 - 3

⇒ ? = -9

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

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

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

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

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

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

2549.99 - [509.99 - {269.97 - (89.9 - 79.9 + 69.9)}] = ?

⇒ ? = 2550 - [510 - {270 - (90 - 80 + 70)}]

⇒ ? = 2550 - [510 - {270 - (90 - 10)}]

⇒ ? = 2550 - [510 - {270 - 80}]

⇒ ? = 2550 - [510 - 190]

⇒ ? = 2550 - 320

∴ ? = 2230

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

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

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

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

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

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

1/3 of 785.99 – 11/8 of 1031.99 = ? – 13/4 of 527.98

⇒ 1/3 of 786 – 11/8 of 1032 = ? – 13/4 of 528

⇒ 262 – 1419 = ? – 1716

⇒ ? = 559

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

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

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

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

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

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

(59.99% of 3499.99) + {(19.92% of 1224.95) ÷ 4.95} = ? 

⇒ (60% of 3500) + {(20% of 1225) ÷ 5} = ?

⇒ (3500 × 60/100) + {(1225 × 20/100) ÷ 5} = ?

⇒ ? = 2100 + {(1225 × 1/5) ÷ 5}

⇒ ? = 2100 + {245 ÷ 5}

⇒ ? = 2100 + 49

⇒ ? = 2149

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

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

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

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

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

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

{44.95 - (16.97 × 2.93 - 2.99 × 1.92)} = ?

⇒ {45 - (17 × 3 - 3 × 2)} = ?

⇒ {45 - (51 - 6)} = ?

⇒ {45 - 45} = ?

⇒ ? = 0

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

Working partner commission = 23/4% of 36000 = 2070.

Remaining profit = 36000 − 2070 = 33930.

Investment ratio (Reshmi:Rahul) = (6000 × 6) : (8000 × 8) = 36 : 64 = 9 : 16.

Rahul profit share = 33930 × (16 ÷ 25) = 21715.20.

Total Rahul profit = 2070 + 21715.20 = 23785.20.

∴ The correct answer is Rs. 23785.20.

Alternate Method

Given: Total profit = Rs. 36000, Rahul commission = 23/4%, Reshmi (6000, 6 months), Rahul (8000, 8 months).

Formulas: Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

⇒ Rahul Commission = 36000 × (23 ÷ (4 × 100)) = 36000 × (23 ÷ 400) = 90 × 23 = Rs. 2070.

⇒ Remaining Profit = 36000 − 2070 = Rs. 33930.

⇒ Ratio of Profit = (6000 × 6) : (8000 × 8) = 36000 : 64000 = 9 : 16.

⇒ Sum of Ratios = 9 + 16 = 25.

⇒ Rahul Share from Remaining = (16 ÷ 25) × 33930 = 21715.20.

⇒ Total Rahul Profit = 2070 + 21715.20 = Rs. 23785.20.

∴ The correct answer is Rs. 23785.20.

Additional Information

Working vs Sleeping Partner

A Working Partner manages the business and usually receives a fixed percentage of profit as a salary or commission before the rest is shared.

Partnership Profit Distribution

Profit is divided based on the product of Capital and Time. Formula: P₁:P₂ = C₁T₁:C₂T₂.

Shortcut Trick

Apply Alligation between Expenditure and Savings to find the Income ratio.

% Increase in Expenditure = 20%, % Increase in Savings = 60%, % Increase in Income = 26%.

Ratio of Expenditure : Savings = (60 − 26) : (26 − 20) = 34 : 6 = 17 : 3.

Savings % (x) = [Savings / (Expenditure + Savings)] × 100 = [3 / (17 + 3)] × 100 = 15%.

∴ The correct answer is 15.

Alternate Method

Given:

Let Monthly Income = 100

Savings = x, Expenditure = 100 − x

Formula Used:

Income = Expenditure + Savings

Total Increase in Income = Increase in Expenditure + Increase in Savings

Calculations:

⇒ 26% of 100 = 20% of (100 − x) + 60% of x

⇒ 26 = 0.20 × (100 − x) + 0.60 × x

⇒ 26 = 20 − 0.2x + 0.6x

⇒ 26 − 20 = 0.4x

⇒ 6 = 0.4x

⇒ x = 6 / 0.4 = 60 / 4

⇒ x = 15

∴ The correct answer is 15.

Additional Information

Income, Expenditure and Savings Relationship

The fundamental relation is Income = Expenditure + Savings. Any percentage change in Income is the weighted average of percentage changes in Expenditure and Savings.

Alligation Method for Percentages

If components A and B combine to form C, the ratio of A:B = (% change in B − % change in C) : (% change in C − % change in A).

Percentage Change Calculation

New Value = Old Value × (1 + Percentage Increase/100). Use this to find absolute increases when initial values are assumed.

Shortcut Trick

Average of top 6 = 46

Total of top 7 = 7 × 50 = 350

Total of top 8 = 350 + 34 = 384

Average of top 8 = 384 ÷ 8 = 48

Ratio = 46 : 48 = 23 : 24

∴ The correct answer is 23:24.

Alternate Method

Given: Average of 6 batsmen = 46, Average of 7 batsmen = 50, Score of 8th batsman = 34.

Formula: Average = Total Sum ÷ Number of items

⇒ Total runs of 6 batsmen = 6 × 46 = 276

⇒ Total runs of 7 batsmen = 7 × 50 = 350

⇒ Total runs of 8 batsmen = 350 + 34 = 384

⇒ Average of 8 batsmen = 384 ÷ 8 = 48

⇒ Required Ratio = 46 : 48

⇒ Required Ratio = 23 : 24

∴ The correct answer is 23:24.

Additional Information

Net Deviation Method

Change in sum = (New Average × New Count) − (Old Average × Old Count).

Average Concept

When a new member joins, the change in average is equal to (New Member's Value − Old Average) ÷ New Total Count.

Ratio Simplification

Ratios should always be expressed in their simplest form by dividing both terms by their Highest Common Factor (HCF).

Shortcut Trick

Total distance = Sum of lengths = 100 + 140 = 240 m.

Relative speed (opposite direction) = Sum of speeds = 29 + 43 = 72 km/hour.

Convert speed to m/s: 72 × (5/18) = 20 m/s.

Time = Distance ÷ Relative Speed = 240 ÷ 20 = 12 seconds.

∴ The correct answer is 12 sec.

Alternate Method

Given: Length₁ = 100 m, Length₂ = 140 m, Speed₁ = 29 km/hr, Speed₂ = 43 km/hr.

Formula Used: Time = (L₁ + L₂) ÷ (S₁ + S₂)

⇒ Total distance = 100 + 140 = 240 m

⇒ Relative speed = (29 + 43) × (5/18) m/s

⇒ Relative speed = 72 × (5/18) = 20 m/s

⇒ Crossing time = 240 ÷ 20

⇒ Crossing time = 12 seconds

∴ The correct answer is 12 sec.

Additional Information

Relative Speed Concept

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

Unit Conversion

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

Train Crossing Objects

When a train crosses another moving train, distance is always the sum of both lengths (L₁ + L₂), regardless of direction.

Total number of male Under Graduates in a company = 16000 × 30/100 = 4800

Total number of female Under Graduates in a company = 20000 × 35/100 = 7000

Required average =

= (4800 + 7000)/2 = 5900

Total employees in a company = 16000 + 20000 = 36000

Total number of Male Post graduates in a company = 16000 × 15/100 = 2400

Total number of female Post Graduates in a company = 20000 × 20/100 = 4000

Total Post Graduates in a company = 2400 + 4000 = 6400

Required percentage =

⇒ 6400/36000 × 100

⇒ 17.77% ≈ 18%

Total number of Male Post graduates in a company = 16000 × 15/100 = 2400

Total number of female Post Graduates in a company = 20000 × 20/100 = 4000

Required ratio =

⇒ 4000: 2400

∴ 5: 3

Total number of male Under Graduates in a company = 16000 × 30/100 = 4800

Total number of female Under Graduates in a company = 20000 × 35/100 = 7000

Required percentage =

⇒(7000 – 4800)/7000 × 100%

⇒2200/70

⇒ 31.42% ≈ 31%

Total number of male Graduates in a company = 16000 × 55/100 = 8800

Total number of female Graduates in a company = 20000 × 45/100 = 9000

Required difference =

⇒ 9000 – 8800 = 200

Shortcut Trick

Overall Profit % = (Lending Rate − Borrowing Rate) × Time

Profit % = (15% − 10%) × 3 years = 5% × 3 = 15%

Total Profit = 15% of ₹1500 = 0.15 × 1500 = ₹225

∴ The correct answer is ₹225.

Alternate Method

Given: Principal (P) = ₹1500, Time (T) = 3 years, Rate₁ = 10%, Rate₂ = 15%

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100

⇒ Interest paid by A to Bank = (1500 × 10 × 3) ÷ 100

⇒ SI_paid = 15 × 30 = ₹450

⇒ Interest received by A from B = (1500 × 15 × 3) ÷ 100

⇒ SI_received = 15 × 45 = ₹675

⇒ Overall Profit = SI_received − SI_paid

⇒ Overall Profit = 675 − 450 = ₹225

∴ The correct answer is ₹225.

Additional Information

Simple Interest Concept

Simple interest is calculated only on the original principal amount for every period. The interest remains constant each year.

Effective Rate of Interest

When the principal and time are the same, the profit or loss can be directly calculated using the difference in interest rates: Profit = P × (R_high − R_low) × T / 100.

Difference between SI and CI

For the first year, SI and Compound Interest (CI) are the same. From the second year onwards, CI becomes higher as interest is earned on interest.

Shortcut Trick

Initial Ratio (Milk : Water) = 7 : 8

Final Ratio (Water : Milk) = 3 : 2 → (Milk : Water) = 2 : 3

Using Cross-Multiplication Method: (7 × 3 − 8 × 2) units = (10 × 2 − 5 × 3) litres

(21 − 16) units = (20 − 15) litres ⇒ 5 units = 5 litres ⇒ 1 unit = 1 litre

Initial total quantity = (7 + 8) units = 15 units = 15 × 1 = 15 litres.

∴ The correct answer is 15 litres.

Alternate Method

Given: Initial Ratio M:W = 7:8. Let initial milk = 7x and initial water = 8x.

Formula: (Milk + added Milk) / (Water + added Water) = Final Milk / Final Water

⇒ Final Water : Milk = 3 : 2 ⇒ Final Milk : Water = 2 : 3

⇒ (7x + 5) / (8x + 10) = 2 / 3

⇒ 3 × (7x + 5) = 2 × (8x + 10)

⇒ 21x + 15 = 16x + 20

⇒ 21x − 16x = 20 − 15

⇒ 5x = 5 ⇒ x = 1

⇒ Initial quantity = 7x + 8x = 15x

⇒ Initial quantity = 15 × 1 = 15 litres

∴ The correct answer is 15 litres.

Additional Information

Ratio and Proportion Basics

A ratio a:b indicates the relative size of two quantities. The total quantity is the sum of the ratio parts multiplied by a common constant x.

Alligation Method

Used to find the mean value of a mixture when two ingredients of different prices or concentrations are mixed together.

Mixture Replacement Formula

Final Quantity = Initial Quantity × (1 − y/x)ⁿ, where y is the amount replaced and x is the total volume.

Shortcut Trick

Diameter of circle = 70 cm → Radius (r) = 35 cm.

Area of circle = 22/7 × 35 × 35 = 3850 cm².

Area of square = 5450 − 3850 = 1600 cm² → Side (a) = √1600 = 40 cm.

Circumference = 22/7 × 70 = 220 cm; Perimeter = 4 × 40 = 160 cm.

Difference = 220 − 160 = 60 cm.

∴ The correct answer is 60 cm.

Alternate Method

Given: Total Area = 5450 cm², Diameter (d) = 70 cm.

Formula Used: Area of circle = πr²; Area of square = a²; Circumference = 2πr; Perimeter = 4a.

⇒ Radius of circle (r) = 70 ÷ 2 = 35 cm

⇒ Area of circle = (22/7) × 35 × 35 = 22 × 5 × 35 = 3850 cm²

⇒ Area of square = 5450 − 3850 = 1600 cm²

⇒ Side of square (a) = √1600 = 40 cm

⇒ Circumference of circle = 2 × (22/7) × 35 = 220 cm

⇒ Perimeter of square = 4 × 40 = 160 cm

⇒ Required Difference = 220 − 160 = 60 cm

∴ The correct answer is 60 cm.

Additional Information

Circle Properties

Area = πr² and Circumference = 2πr = πd. For r = 7, 14, 21, 35, the circumference and area follow fixed ratios.

Square Properties

Area = side² and Perimeter = 4 × side. The diagonal of a square is side × √2.

Standard Values for π

Always use π ≈ 22/7 for calculations involving multiples of 7 to simplify the division.

Shortcut Trick

Number of people ratio = (Total Amount ratio) ÷ (Amount per person ratio)

Ratio of Men to Women = (5/5) : (4/8) = 1 : (1/2) = 2 : 1

Total ratio parts = 2 + 1 = 3 units → 240 workers

1 unit = 240 ÷ 3 = 80

Number of Men = 2 × 80 = 160

∴ The correct answer is 160.

Alternate Method

Given: Total workers = 240, Total amount = ₹2880, Total Amount Ratio (M:W) = 5:4, Amount per person Ratio (M:W) = 5:8.

⇒ Let number of Men be M and Women be W.

⇒ M × 5x = 5y (where x is per head multiplier, y is total multiplier)

⇒ W × 8x = 4y

⇒ M/W = (5y/5x) / (4y/8x) = 1 / (1/2) = 2/1

⇒ M : W = 2 : 1

⇒ M = (2 / (2+1)) × 240

⇒ M = (2/3) × 240 = 160

∴ The correct answer is 160.

Additional Information

Ratio Product Rule

The ratio of the total value is always equal to the product of the ratio of the number of items and the ratio of value per item.

Compound Ratio

When two or more ratios are multiplied term by term, the resulting ratio is called a compound ratio. In this problem, (Men/Women) × (Amt per Man/Amt per Woman) = (Total Amt Men/Total Amt Women).

Shortcut Trick

Total Capacity (LCM of 60, 75) = 300 units.

Efficiency of Tap A = +5, Efficiency of Tap B = −4.

Initial water = 150 units. Tap B runs for 30 mins: 150 − (4 × 30) = 30 units left.

Remaining to fill = 300 − 30 = 270 units. Time taken by A = 270 ÷ 5 = 54 minutes.

∴ The correct answer is 54 minutes.

Alternate Method

Given: Filling time of Tap A = 60 min, Emptying time of Tap B = 75 min.

Calculations:

⇒ Initial Water in tank = 1/2 × 300 = 150 units.

⇒ Water emptied by Tap B in 30 minutes = 4 × 30 = 120 units.

⇒ Water remaining in tank after 30 minutes = 150 − 120 = 30 units.

⇒ Capacity still remaining to be filled = 300 − 30 = 270 units.

⇒ Time taken by Tap A to fill the rest = 270 ÷ 5 = 54 minutes.

∴ The correct answer is 54 minutes.

Additional Information

Inlet and Outlet Pipes

Inlet pipes add water (positive efficiency), while outlet pipes remove water (negative efficiency). Total work is the volume of the tank.

Efficiency Method

Total capacity is the LCM of individual times. Efficiency = Total Capacity ÷ Individual Time.

Partial Filling/Emptying

Always calculate the current status of the tank before applying the efficiency of the next tap being opened or closed.

I. x² + 2x – 15 = 0

⇒ x² + 5x – 3x – 15 = 0

⇒ x(x + 5) – 3(x + 5) = 0

⇒ (x + 5) (x – 3) = 0

⇒ x = – 5, 3

II. y² + 16y + 55 = 0

⇒ y² + 11y + 5y + 55 = 0

⇒ y(y + 11) + 5(y + 11) = 0

⇒ (y + 11) (y + 5) = 0

⇒ y = –11, –5

∴ x ≥ y

I. x² + 19x + 90 = 0

⇒ x² + 9x + 10x + 90 = 0

⇒ x (x + 9) + 10 (x + 9) = 0

⇒ (x + 9) (x + 10) = 0

⇒ x = - 9, - 10

II. y² + 13y + 36 = 0

⇒ y²   + 4y + 9y + 36 = 0

⇒ y (y + 4) + 9 (y + 4) = 0

⇒ (y + 4) (y + 9) = 0

⇒ y = - 4, - 9 

∴, x ≤ y

i. 2x² + 5x - 3 = 0

⇒ 2x² + 6x - x - 3 = 0

⇒ (2x - 1) (x + 3) = 0

⇒ x = 1 / 2, -3

ii. y² - 14y + 24 = 0

⇒ y^{2 -} 12y - 2y + 24 = 0

⇒ (y - 12) (y - 2) = 0

⇒ y = 12, 2

Hence, x < y.

i. x² - 5x + 6 = 0

⇒ x² - 3x - 2x + 6 = 0

⇒ (x - 3) (x - 2) = 0

⇒ x = 3, 2

ii. 2y² - 32y + 126 = 0

⇒ 2y² - 18y - 14y + 126 = 0

⇒ (2y - 14) (y - 9) = 0

⇒ y = 7, 9

Hence, x < y.

i. x² - 25x + 156 = 0

⇒ x² - 13x - 12x + 156 = 0

⇒ (x - 13) (x - 12) = 0

⇒ x = 12, 13

ii. y² - 20y + 96 = 0

⇒ y² - 12y - 8y + 96 = 0

⇒ (y - 12) (y - 8) = 0

⇒ y = 8, 12

Hence, x ≥ y.

New total number of Golf and Basketball players = 3/2(13% of 1800) + 3/4(8% of 1800) = 351 + 108 = 459

Smart Approach

Percentage of players taking part in Golf = 13%

And, the percentage of players taking part in  Basketball = 8%

Required Ratio = 13% ∶ 8% = 13 ∶ 8

Required Difference = (27 + 17 - 13 - 12)% of 1800 = 19% of 1800 = 342

Required Number of total players = (23 + 27 + 12)% of 1800 = 62% of 1800 = 1116

Number of male players of Boxing = 7/9 × 17/100 × 1800 = 238

Total players of Athletics = 23/100 × 1800 = 414

Required Percentage = 238/414 × 100 = 57.49% ≈ 57%

Shortcut Trick

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

Upstream speed (v) = 10 − 5 = 5 km/hr

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

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

∴ The correct answer is 45 km.

Alternate Method

Given:

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

Speed of stream (y) = 5 km/hr

Total time taken = 12 hours

Formula Used:

Time = Distance ÷ Speed

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

Calculations:

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

⇒ Upstream speed = 10 − 5 = 5 km/hr

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

⇒ 12 = (D ÷ 15) + (D ÷ 5)

⇒ 12 = (D + 3D) ÷ 15

⇒ 12 = 4D ÷ 15

⇒ 4D = 12 × 15

⇒ D = (12 × 15) ÷ 4

⇒ D = 3 × 15 = 45 km

∴ The correct answer is 45 km.

Additional Information

Relative Speed in Water

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

Average Speed for Round Trip

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

Speed Conversion

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

Shortcut Trick

Let the old selling price be 100x and cost price be CP.

Case 1: SP increased by 10% ⇒ 110x = CP × 1.375 ⇒ CP = 110x ÷ 1.375 = 80x.

Case 2: SP increased by 25% ⇒ New SP = 125x.

Profit = New SP − CP ⇒ 125x − 80x = 45x.

Given 45x = 225 ⇒ x = 5.

Cost Price = 80x = 80 × 5 = 400.

∴ The correct answer is ₹ 400.

Alternate Method

Given: Old SP = S, New SP₁ = 1.1S, New SP₂ = 1.25S, Profit₁ = 37.5%, Profit₂ = ₹ 225. Formulas: Profit = SP − CP | SP = CP × (100 + P%) ÷ 100

⇒ Let Cost Price (CP) be 100 units. ⇒ When SP is increased by 10%, Profit = 37.5% ⇒ 1.1 × Old SP = 137.5 units. ⇒ Old SP = 137.5 ÷ 1.1 = 125 units. ⇒ New Selling Price (25% above old) = 125 × 1.25 = 156.25 units. ⇒ Profit in second case = 156.25 − 100 = 56.25 units. ⇒ 56.25 units = 225 ⇒ 1 unit = 225 ÷ 56.25 = 4. ⇒ Cost Price = 100 units = 100 × 4 = 400.

∴ The correct answer is ₹ 400.

Additional Information

Profit Calculation

Profit is always calculated on the Cost Price unless specified otherwise. Formula: Profit % = (Profit ÷ CP) × 100.

Successive Increase

When a value is increased by a% and then by b%, the net increase is not simply a + b, but applies to the updated value.

Shortcut Trick

Let the Principal (P) be 100 units.

A's Amount (SI at 10% for 4 years) = 100 + (10 × 4) = 140 units.

B's Amount (CI at 5% for 2 years) = 100 × (1.05)² = 100 × 1.1025 = 110.25 units.

Total Amount = 140 + 110.25 = 250.25 units → Rs. 20,020.

1 unit = 20,020 ÷ 250.25 = 80.

Principal (100 units) = 100 × 80 = Rs. 8,000.

∴ The correct answer is Rs. 8,000.

Alternate Method

Given: Total Amount = Rs. 20,020, Rate A = 10% (SI), Time A = 4 yrs, Rate B = 5% (CI), Time B = 2 yrs.

Formula: SI Amount = P(1 + RT/100) | CI Amount = P(1 + R/100)^T

⇒ Amount A = P[1 + (10 × 4)/100] = P[1 + 0.4] = 1.4P

⇒ Amount B = P[1 + 5/100]² = P[1.05]² = 1.1025P

⇒ 1.4P + 1.1025P = 20,020

⇒ 2.5025P = 20,020

⇒ P = 20,020 ÷ 2.5025

⇒ P = 8,000

∴ The correct answer is Rs. 8,000.

Additional Information

Simple Interest (SI) Formula

SI = (P × R × T) ÷ 100. The interest remains constant every year on the same principal.

Compound Interest (CI) Effective Rate

For 2 years, effective CI rate = x + y + (xy ÷ 100). For 5%, it is 5 + 5 + (25 ÷ 100) = 10.25%.

Relationship between SI and CI

For the first year, SI and CI on the same principal and rate are always equal. Difference for 2 years = P(R/100)².

Shortcut Trick

Total Work = LCM(10, 20, 30, 15) = 60 units.

Efficiency of A = 6, B = 3, C = 2 (Positive work).

Efficiency of D = −4 (Negative work).

Combined Efficiency = 6 + 3 + 2 − 4 = 7 units/day.

Time = Total Work ÷ Combined Efficiency = 60/7 days.

∴ The correct answer is 60/7 days.

Alternate Method

Given: Time taken by A = 10 days, B = 20 days, C = 30 days. Time taken by D to destroy = 15 days.

Formula Used: Efficiency = Total Work ÷ Time; Combined Time = Total Work ÷ Sum of Efficiencies.

⇒ Net efficiency of (A + B + C + D) = 6 + 3 + 2 − 4

⇒ Net efficiency = 11 − 4 = 7 units/day

⇒ Time taken to complete the work = Total Work ÷ Net efficiency

⇒ Time taken = 60 ÷ 7 days

∴ The correct answer is 60/7 days.

Additional Information

Negative Work Concept

In Time and Work, any person destroying or emptying work is assigned a negative efficiency value.

Pipes and Cisterns

This problem follows the same logic as an inlet and outlet pipe system where the leak (outlet) reduces the net filling rate.

Work and Wages

Wages are always distributed in the ratio of the actual work done by each individual, which is Efficiency × Time.

Shortcut Trick

Speed of Passenger Train in m/s = 60 × 5/18 = 50/3 m/s.

Total distance (Train + Platform) = 18 × 50/3 = 300 m. Platform = 300 − 180 = 120 m.

Goods Train Speed = (150 + 120) / 27 = 270 / 27 = 10 m/s = 10 × 18/5 = 36 kmph.

Relative Speed (Same direction) = 60 − 36 = 24 kmph.

∴ The correct answer is 24 kmph.

Alternate Method

Given: Length of Passenger Train (L₁) = 180 m, Speed (S₁) = 60 kmph, Time (T₁) = 18 sec. Length of Goods Train (L₂) = 150 m, Time (T₂) = 27 sec.

Formula Used: Speed = Distance / Time; Distance = Length of Train + Length of Platform.

⇒ S₁ in m/s = 60 × 5/18 = 50/3 m/s

⇒ Total Distance = S₁ × T₁ = (50/3) × 18 = 300 m

⇒ Platform Length (P) = 300 − 180 = 120 m

⇒ S₂ (Goods Train Speed) = (L₂ + P) / T₂ = (150 + 120) / 27 = 270 / 27 = 10 m/s

⇒ S₂ in kmph = 10 × 18/5 = 36 kmph

⇒ Relative Speed (Same direction) = S₁ − S₂ = 60 − 36 = 24 kmph

∴ The correct answer is 24 kmph.

Additional Information

Relative Speed Concepts

When two objects move in the same direction, Relative Speed = S₁ − S₂. When they move in the opposite direction, Relative Speed = S₁ + S₂.

Unit Conversion

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

Train Crossing Objects

When a train crosses a stationary object with length (platform/bridge), total distance = Length of train + Length of object.

1. Box G is at the bottom and box C is immediately above box G. 2. Three boxes are placed between box A and box L. 3. Box L is placed at an even-numbered position.

4. Box Z is between box L and box P. 5. Only one box is in between box L and box P.  6. Box P is below box A. 7. Box M is immediately below box A.

8. Box J is between box M and box Q. 9. Box Q is above box P but not at the top.

(The only place left for box D is immediately above box C.)

The second box is immediately below the first box except “Box G, D”.

Hence, Box G and Box D did not belong to the group.

1. Box G is at the bottom and box C is immediately above box G. 2. Three boxes are placed between box A and box L. 3. Box L is placed at an even-numbered position.

4. Box Z is between box L and box P. 5. Only one box is in between box L and box P.  6. Box P is below box A. 7. Box M is immediately below box A.

8. Box J is between box M and box Q. 9. Box Q is above box P but not at the top.

(The only place left for box D is immediately above box C.)

Hence, Box C is in the middle of box D and box G.

1. Box G is at the bottom and box C is immediately above box G. 2. Three boxes are placed between box A and box L. 3. Box L is placed at an even-numbered position.

4. Box Z is between box L and box P. 5. Only one box is in between box L and box P.  6. Box P is below box A. 7. Box M is immediately below box A.

8. Box J is between box M and box Q. 9. Box Q is above box P but not at the top.

(The only place left for box D is immediately above box C.)

Hence, 4 boxes are between box G and box L.

1. Box G is at the bottom and box C is immediately above box G. 2. Three boxes are placed between box A and box L. 3. Box L is placed at an even-numbered position.

4. Box Z is between box L and box P. 5. Only one box is in between box L and box P.  6. Box P is below box A. 7. Box M is immediately below box A.

8. Box J is between box M and box Q. 9. Box Q is above box P but not at the top.

(The only place left for box D is immediately above box C.)

Hence, Box L is placed exactly between Box Z and Box Q.

1. Box G is at the bottom and box C is immediately above box G. 2. Three boxes are placed between box A and box L. 3. Box L is placed at an even-numbered position.

4. Box Z is between box L and box P. 5. Only one box is in between box L and box P.  6. Box P is below box A. 7. Box M is immediately below box A.

8. Box J is between box M and box Q. 9. Box Q is above box P but not at the top.

(The only place left for box D is immediately above box C.)

Hence, Boxes L and Z are placed in the middle of the arrangement.

Given statements: M = N ≥ O; J < O; A ≥ J > P

On combining: M = N ≥ O > J ≤ A; J > P

Conclusions:

I.  M > P → True (as M = N ≥ O > J > P → M > P)

II. O > P → True (as O > J > P → O > P)

Hence, both I and II are True.

Given statements : M > A ≥ T > F = Y ≤ S < P 

Conclusions: 

I: F < P → True ( as F = Y ≤ S < P → F < P )

II: A > S → False ( as A ≥ T > F = Y ≤ S → A > Y and Y ≤ S ) → thus clear relation between A and S cannot be determined

Therefore, only conclusion I is True.

Given statements: U ≤ W ≥ R > S ; T > S = V

on combining : U ≤ W ≥ R > S = V < T

Conclusions:

I. W < V → False (as W ≥ R > S = V) it is clear that W is greater than V

II. T < V → False (as S = V < T) V is shorter than T

Both statements not follow the given statement as per statement W ≥ R > S = V it is clear W > V while in conclusion it is given 

W < V so it is false .

similarly S = V < T → V < T but in conclusion it is T < V so it is false 

Therefore Neither I nor II is true.

No. of people- 6- L, M, N, O, P, Q.

Different colours- Red, Yellow, White, Green, Blue, Black. 

1- M takes the vaccine on three persons before the one who wears Black . 

2- The one who takes the vaccine while wearing black does not take in the last. 

3- Q takes three persons before the one who takes immediately after P. 

4- Q takes on any 2nd date of any month. 

5- O takes two persons before the one who takes while wearing Yellow.