IBPS PO Prelims Memory Based Paper (Held On: 16 October 2022 Shift 1) (Previous Year Paper)

The correct answer is a 'catastrophe'.

Key Points

• Let's explore the meanings of the above-given words:
• Catastrophe: A disastrous event that creates upheaval in normal conditions.
• Example: The landslide was an environmental catastrophe.
• Agreement: Accordance in a decision taken.
• Example: Everyone in the meeting was in agreement with the President's decision.
• Rewarding: Something which is given as a bonus when a task is completed or something which is very beneficial.
• Example: The sales profile job is very rewarding if you have the right skill sets.
• Bolster: To motivate or persuade someone to accomplish a task. 
• Example: Probita always bolsters me whenever I feel down and demotivated.
• Steer: Control the movement of a vehicle or guide someone with directions.
• Example: He steered his car with great precaution while driving up the hill.
• Thus, the correct answer is a catastrophe.

The correct answer is 'vandalize.'

Key Points Let's explore the meanings of the above-given words:

• Improvement: Progress in a given task or growth from the original position.
• Example: Krystal showed excellent improvement in her work after she learned the work properly.
• Scrutiny: Detail observation of an object or a person.
• Example: The lawyer was going through the legal documents with scrutiny.
• Controversial: Something which is debatable or full of different possibilities and arguments.
• Example: Bollywood actors are always on the front page of the newspaper because of their controversial issues.
• Promenade: A place for the public to walk on the road or pavement.
• Example: Liza always listens to music while walking on the promenade.
• Vandalize: To destroy or deteriorate the condition of something.
• Example: The heavy rainfall vandalized all the fields that were ready for harvest.

Thus, the correct answer is 'vandalize.

The correct answer is it would be a good idea to maximize the buying of new plastic toys.

Key Points

• The answer lies in the following lines of the passage:  The toys have gone through and followed the rigorous EU standards for toys. The EU notes, though, that this marking should only be seen as an indication, as it has been misused due to counterfeiting. As goes for all plastic, plastic toys are made using fossil fuels, and therefore the production of them contributes to the environmental crisis at hand. Therefore, it would be a good idea to minimize the buying of new plastic toys.
• Thus, the correct answer is it would be a good idea to maximize the buying of new plastic toys.

The correct answer is 90%.

Key Points

• The correct answer lies in the following lines of the passage: Environmentalists have raised awareness around the fact that plastic toys are a big part of the plastic that ends up in landfills and oceans, which adds to the ongoing issue of plastic pollution. According to a survey done by the British Heart Foundation, 1 in 3 parents admits to having thrown away toys in working conditions. Considering that 90 percent of toys are in some way made of plastic, that quickly adds up to a lot of plastic waste.
• Thus, the correct answer is  90%.

The correct answer is Some toys have hidden toxins that are not detectable and can pass EU regulations.

Key Points

• The answer can be inferred from the following lines of the passage: Although there are EU regulations for which toxins may or may not be included in toys, there are products that can slip through the cracks. Plastic toys may, for example, be made of, or contain, polyvinyl chloride (PVC), which contains lead and cadmium — both toxins that are harmful to children. The CE mark is supposed to be a sign of quality. The toys have gone through and followed the rigorous EU standards for toys. The EU notes, though, that this marking should only be seen as an indication, as it has been misused due to counterfeiting.
• Thus, the correct answer is Some toys have hidden toxins that are not detectable and can pass EU regulations.

The correct answer is children** have a tendency to swallow and chew on toys.**

Key Points

• The answer lies in the following lines of the passage: Not all toys contain toxins, but they can be found in some cases. Toys that have toxins in them are hazardous to children mainly because of their tendency to swallow and chew on the toys, which can result in the toxins being absorbed by the body. When it comes to young children, even the smallest amounts of toxins can affect their health. The toxins can either be found in the plastic itself or they can be included in the pigments used to color toys and make them more attractive to children.
• Thus, the correct answer is children have a tendency to swallow and chew on toys.

The correct answer is ways to reduce plastic usage.

Key Points

• The correct answer lies in the following lines of the passage: Over the years, there have been many cases of news breaking about plastic toys and their containment of toxins. In addition to the harmful ingredients that can be found in plastic, we also have to take into account the effect on the environment that plastic usage has. The internet is flooding with ways to reduce plastic usage and people are more aware of the need to cut down on this. Still, it’s difficult to change behaviors and somehow parents easily end up with a great number of plastic toys at home.
• Thus, the correct answer is ways to reduce plastic usage.

The correct answer is Thorough checks have been made before giving the CE mark to the product.

Key Points

• The answer can be inferred from the following lines of the passage: The CE mark is supposed to be a sign of quality.*** The toys have gone through and followed the rigorous EU standards for toys. The EU notes, though, that this marking should only be seen as an indication, as it has been misused due to counterfeiting. As goes for all plastic, plastic toys are made using fossil fuels, and therefore the production of them contributes to the environmental crisis at hand. Therefore, it would be a good idea to minimize the buying of new plastic toys.*
• Thus, the correct answer is Thorough checks have been made before giving the CE mark to the product.

The correct answer is option 3.

Key Points

The correct phrase is 'reassured that their feelings'.

• In the context of the given sentence the adverb 'there' should be replaced with the determiner 'their'.
• Difference between 'there' and 'their' -
• There - It is used as an adverb which is used used to denote a specific location.
• For Example -
• We will meet there after work.
• Their - It is the possessive form of the pronoun 'they' and it indicates the ownership by more than one person or entity.
• For Example -
• Our neighbors are watering their plants.
• Thus, the correct sentence after phrase replacement would be - Students’ interests should be promoted and they should be reassured that their feelings and emotions are being taken into account.

Additional Information

Let's understand some more confusing words - 

• 'Then' and 'Than' -
• The word 'then' means 'at that time' and it is used to talk about when things will happen while the word 'than' is used to compare things.
• For Example -
• Finish your homework, and then you can go play with your friends.
• I like chocolate cake more than Apple pie.
• 'Affect' and 'Effect' -
• 'Affect' is a verb that means have an effect on; make a difference to. (प्रभावित करना)
• 'Effect' is a noun that means a change that is a result or consequence of an action or other cause. (प्रभाव)
• For Example -
• Smoking tobacco can adversely affect your lungs and blood flow.
• The criticism that the movie received had the effect of discouraging him completely.
• 'Loose' and 'Lose' -
• 'Lose' is a verb that means 'to fail to win, to misplace'.
• 'Loose' is an adjective that means 'not tight'.
• For Example -
• We lost the game even though we practiced very hard.
• I prefer loose clothes because I feel comfortable in them.

The correct answer is option 5.

Key Points

The underlined phrase 'to revamp the kingdom's' is correct in the context of the given sentence.

• Here, after the preposition 'to' the verb 'revamp' is given in its base form which is correct because as per English grammar rules, after the preposition 'to' we use the base form of the verb.
• Thus, the underlined phrase is correct and it doesn't require replacement.

Additional Information

Use of apostrophe  -

• An apostrophe is a small punctuation mark ( ' ) that is placed before a noun to show its authority or possession over something.
• It is used either before or after an 's' at the end of a noun.
• When an apostrophe is used with a singular noun it is used by adding an apostrophe and s, whether the singular noun ends in s or not.
• For example -
• It is a woman's bag.
• She is my boss's wife.
• When an apostrophe is used with a plural noun it is used by adding only an apostrophe when the noun ends in s, and by adding both an apostrophe and s when it ends in a letter other than s.
• For example -
• This is my parents' house.
• It is a women's washroom.

The correct answer is option 3.

Key Points

The correct phrase is 'has successfully tested'.

• The sentence is given in the present perfect tense.
• Sentence structure of the present perfect tense -
• Subject + have/has + past participle + the rest of the sentence
• Hence, the verb 'test' given in the sentence should come as its past participle i.e. tested.
• Also, the verb 'tested' should be preceded by an adverb not a noun thus, successful (noun) should be replaced with the adverb 'successfully'.
• Thus, the correct sentence after phrase replacement would be - Amazon Inc.'s self-driving vehicle unit, Zoox, has successfully tested a robotaxi with employees as passengers on a public road.

​

Additional Information

Difference between adjectives and adverbs -

• Adjective - An adjective is a word that modifies or describes a noun or pronoun. Adjectives can be used to describe the qualities of someone or something independently or in comparison to something else.
• For Example -
• She wore a beautiful dress at her birthday party.
• Adverb - An adverb is a word that modifies (describes) a verb (he sings loudly), an adjective (very tall), another adverb (ended too quickly), or even a whole sentence (Fortunately, I had brought an umbrella). Adverbs often end in –ly, but some (such as fast) look exactly the same as their adjective counterparts.
• For Example -
• She was beautifully dressed at her birthday party.

The correct answer is CBDEA.

Key Points

• C is the part that establishes the subject of the matter,i.e., 'an increase in non-agriculltural '. Hence, it will be the first part after rearrangement.
• Part B refers to the the impact of increase in non-agricultural production. Hence, B follows C.
• Now Part D states that there will be an immediate increase in another thing. So, part D follows B.
• Part E talks about the first thing in which there will be an increase, so it must come after part D, which talks increase in general.
• Part A talks about the second factor. It begins with a connector 'and' .Hence, E follows B.

​

Correct rearrangement of segments is - An increase in non-agriculltural production will lead to an immediate increase in demand for intermediate and final agricultural products.

Hint

• While solving jumbles, one must first look for any independent sentences/segments or the option which establishes the subject matter.
• Then, one must look for connections between the sentences/segments.
• Some sentences/segments might have some concluding notion. So these parts will always be at the end.

​

The correct answer is CABDE.

Key Points

• C is the part that establishes the subject of the matter,i.e., ' Patriotism is a very'. Hence, it will be the first part after rearrangement.
• Part A talks about what type of feeling patriotism is. Hence, A follows C.
• Part B talks about how it is built. So, part C follows E.
• Part D and E talk about the two things required to establish the feeling of patriotism. They are primitive instincts and highly intellectual convictions. So D follows B. Further, E follows D.​

​

Correct rearrangement of segments is - Patriotism is a complex feeling built up of primitive instincts and highly intellectual convictions.

Hint

• While solving jumbles, one must first look for any independent sentences/segments or the option which establishes the subject matter.
• Then, one must look for connections between the sentences/segments.
• Some sentences/segments might have some concluding notion. So these parts will always be at the end.

The correct answer is BDECA.

Key Points

• B is the part that represents the beginning of the matter,i.e., 'Many sociologists have argued'. Hence, it will be the first part after rearrangement.
• Part D refers to the further extension of part B of the sentence. Connector 'that' is used in this part to connect it to part B. Hence, D follows B.
• Part E talks about the functional relationship about which the sociologists have argued. So, part E follows D.
• Part C talks about the first element of the relationship,i.e., education, so it must come after part E. So, part C follows E.
• Part A talks about the second element of the relationship,i.e., economic systems. Also, this part begins with a connector 'And'.Hence, A follows C.

​

Correct rearrangement of segments is -  Many sociologists have argued that there is a functional relationship between education and economic systems.

Hint

• While solving jumbles, one must first look for any independent sentences/segments or the option which establishes the subject matter.
• Then, one must look for connections between the sentences/segments.
• Some sentences/segments might have some concluding notion. So these parts will always be at the end.

The correct answer is DCBAE.

Key Points

• D is the part that establishes the subject of the matter,i.e., ' All human beings have '. Hence, it will be the first part after rearrangement.
• Part C refers to the curiosity we all have to some degree. Hence, C follows D.
• Now three parts are remaining, and out of them, part B states that we also have curiosity even when there is no use. So, part B follows C.
• Part A talks about things where we do not need curiosity, so it must come after part B.
• Part E talks about the point that we even have curiosity for things of no practical use. Hence, E follows A.

​

Correct rearrangement of segments is - All human beings have the curiosity to some degree and we also have it about things which are of no practical use.

Hint

• While solving jumbles, one must first look for any independent sentences/segments or the option which establishes the subject matter.
• Then, one must look for connections between the sentences/segments.
• Some sentences/segments might have some concluding notion. So these parts will always be at the end.

​

The correct answer is DECBA.

Key Points 

• D is the part that establishes the subject of the matter,i.e., 'Curiosity is one of the '. Hence, it will be the first part after rearrangement.
• Part E refers to the fact that curiosity is a distinctive characteristic. Hence, E follows D.
• Part C talks about curiosity being a part of human nature So, part C follows E.
• Part B talks about the contrast between the nature of humans and other creatures. Hence, B follows C.
• Part A talks about the nature of other creatures and in continuation with B. Hence, A follows B.​

Correct rearrangement of segments is - Curiosity is one of the distinctive characteristics of human nature and contrasts with the nature of other creatures.

Important Points 

• While solving jumbles, one must first look for any independent sentences/segments or the option which establishes the subject matter.
• Then, one must look for connections between the sentences/segments.
• Some sentences/segments might have some concluding notion. So these parts will always be at the end.

​

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

Key Points

• In the second part of the given sentence, the use of the preposition 'against' is incorrect.
• The word 'complain' is always targeted at something or someone.
• The word 'complain' is also a 'negative impact' verb so there is no need to double negate it with a preposition like 'against'.
• The preposition 'against' means in opposition to something or someone.
• Therefore, the preposition 'of' should be used in place of the preposition 'against'.
• The preposition 'of' is used for indicating the reason for or cause of something.
  

Hence, the correct answer is option 2.

Correct Sentence: The patient is deaf but complains of ringing in the ears, which may assume various forms, especially in musical people.

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

Key Points

• In the first part of the given sentence, the plural form of the verb 'are' is incorrect.
• 'Tunny' and 'coral fishery' are two singular nouns.
• When two or more singular nouns or pronouns are connected by 'or' or 'nor', use a singular verb.
• Therefore, the singular form of the verb 'is' should be used in place of the plural verb 'are'.

Hence, the correct answer is option 1.

Correct Sentence​: Neither the tunny nor the coral fishery is carried on by the Sardinians themselves, who are not sailors by nature; the former is in the hands of Genoese and the latter of Neapolitans.

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

Key Points

• In the given sentence, the use of the phrase 'be able to' in part 'C' is not required or superfluous.
• The words ''can, could, be able to'' are used to talk about ability, awareness, and possibility and also to say that someone has permission to do something.
• Both 'can' and 'could' are followed by an infinitive (here, fix) without 'to'.
• Example: It was so dark you could not see anything.
• Therefore, the phrase 'be able to' should be removed from the sentence.
  

Hence, the correct answer is option 3.

Correct Sentence: After all of Rahul's childhood injuries she'd healed, she couldn't fix her own heart!

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

Key Points

• In the given sentence, the use of the zero infinitive or base form of the verb 'trade' in part C is incorrect.
• The zero (or bare) infinitive is used after verbs of perception (see, feel, hear), many auxiliary verbs (may, should, must), the verbs make and let, and the expressions had better and would rather.
• The given sentence is talking about the purpose of coining money in honest and accurate measures i.e. to trade freely on open markets.
• The to-infinitive is used in many sentence constructions, often expressing the purpose of something or someone's opinion about something.
• Therefore, the to-infinitive ''to trade'' should be used in place of the zero or bare infinitive 'trade'.
  

Hence, the correct answer is option 3.

Correct sentence: They coin money in honest and accurate measures and allow this money to trade freely on open markets.

The correct answer is ‘D’, i.e this part of the sentence has an error.

Key Points

• The word 'senior' is used here, to compare the positions of two people in the workplace.
• 'senior' here is a comparative adjective which is an adjective used to compare two people or things.
• According to the rule of grammar, the comparative adjectives such as 'prior, junior, senior, superior, inferior, prefer(verb), preferable, elder' etc are followed by 'to' instead of 'than'.
• So the use of 'than you' in the sentence is incorrect.
• Therefore, the correct answer is 'to you'.

Hence, the correct option is option 4.

The correct sentence is: I believe I deserve some amount of respect in the work sphere as I am more senior to you in service.

The correct answer is 'Daunting'.

 Key Points

• By reading the relevant sentence in the passage, we can see that the blank in question needs an adjective that means difficult to deal with in prospect
• Among the given options, we can see that the only word with the required denotation is 'Daunting.' It means seeming difficult to deal with in prospect; intimidating.  (चुनौतीपूर्ण)
• Correct sentence: The world of finance can be daunting, but understanding key concepts

Hence, the correct answer is Option 3.

 Additional Information

• Hearten ⇒ make more cheerful or confident (हिम्मत बढाना).
• Example: She was heartened to observe that the effect was faintly comic.
• Encouraging ⇒ giving someone support or confidence; supportive (प्रोत्साहक)
• Example: She gave me an encouraging smile
• Affecting⇒ touching the emotions. (मन को छूनेवाला)
• Example: A highly affecting account of her experiences in prison.
• Cheering ⇒ shouting for joy or in praise or encouragement.(उत्साहवर्धक)
• Example: A cheering crowd.

The correct answer is 'Informed'.

Key Points

• By reading the relevant sentence in the passage, we can see that the blank in question needs an adjective that means based on an understanding of the facts of the situation.
• Among the given options, we can see that the only word with the required denotation is 'Informed .' It means (a decision or judgment) based on an understanding of the facts of the situation. (एक निर्णय) स्थिति के तथ्यों की समझ के आधार पर)
• Correct sentence: S**trategies can help investors make informed decisions.

Hence, the correct answer is Option 5.

Additional Information 

• Ignorant ⇒ resulting from or showing a lack of knowledge or intelligence (अनभिज्ञ)
• Example: He remains ignorant of the changes.
• Unaware ⇒ having no knowledge of a situation or fact (बेख़बर)
• Example: They were unaware of his absence
• Blissful ⇒ full of, marked by, or causing complete happiness (सुखद)
• Example:  He sat there in a blissful state of comfort.
• Intimidate ⇒ to make timid or fearful (धमकाना)
• Example:  He tries to intimidate his opponents.

The correct answer is 'Interest'.

Key Points

• By reading the relevant sentence in the passage, we can see that the blank in question needs an adjective that means money paid regularly at a particular rate for the use of money lent.
• Among the given options, we can see that the only word with the required denotation is 'Interest.' It means money paid regularly at a particular rate for the use of money lent, or for delaying the repayment of a debt. (ब्याज)
• Correct sentence: This is because money can be invested and earn interest over time, meaning that a dollar today has the potential to grow into more than a dollar in the future.

Hence, the correct answer is Option 1.

Additional Information

• Money ⇒ A current medium of exchange in the form of coins and banknotes; coins and banknotes collectively. (धन )
• Example: I counted the money before putting it in my wallet.
• Grains ⇒ A single fruit or seed of a cereal.(अनाज)
• Example: A few grains of corn.
• Calmness ⇒ the state or quality of being free from agitation or strong emotion (आत्मसंवरण). 
• Example: Those who worked with him refer time and again to his calmness under pressure.
• ​Prosperity ⇒ The state of being prosperous (समृद्धि).
• Example: A long period of peace and prosperity.

The correct answer is 'Weighed'.

Key Points

• By reading the relevant sentence in the passage, we can see that the blank in question needs a verb that means assess the nature or importance of, especially with a view to a decision or action.
• Among the given options, we can see that the only word with the required denotation is 'Weighed.' It means assessing the nature or importance of, especially with a view to a decision or action.(विशेष रूप से किसी निर्णय या कार्रवाई की दृष्टि से प्रकृति या महत्व का आकलन करना।​)
• Correct sentence: The level of risk an investor is willing to take on should be carefully weighed against the potential for return.

Hence, the correct answer is Option 3.

Additional Information

• Crooked ⇒ Bent or twisted out of shape or out of place. (वक्र)
• Example: His teeth were yellow and crooked.
• Burdened ⇒ Cause (someone) worry, hardship, or distress**.(कठिनाई, या बोझ)**
• Example: They were not yet burdened with adult responsibility.
• Detest ⇒ To feel intense and often violent antipathy toward.(घृणा करना, कोसना)
• Example: They detested each other on sight.
• ​Clumsy ⇒ Lacking dexterity, nimbleness, or grace.(बेढंगा, फूहड़)
• Example: Most people are a little clumsy when they're teenagers.

The correct answer is 'Diversify'.

Key Points

• By reading the relevant sentence in the passage, we can see that the blank in question needs a verb that means composed of unlike elements
• Among the given options, we can see that the only word with the required denotation is 'Diversify.' It means to make diverse or composed of unlike elements, to balance. (भिन्न भिन्न करना)
• Correct sentence: Regardless of the strategy chosen, it's important to diversify a portfolio across different asset classes to reduce overall risk and maximize potential gains.

Hence, the correct answer is Option 4.

Additional Information

• Conform ⇒ be similar in form or type; agree.(समान होना)
• Example: The countryside should conform to a certain idea of the picturesque.
• Specialized ⇒ requiring or involving detailed and specific knowledge or training.(विशेषीकृत)
• Example: Employees with specialized skills.
• Unvary ⇒ Not exhibiting change or variation.(अपरिवर्ती)
• Example: She follows the same, unvarying routine every morning.

The correct answer is B-D.

Key Points

Let us look at the given sentence in the following manner*:*

• ________ (A) political parties ________ (B) with each other in ________ (C) more ________ (D) for themselves.
• From the below-given table, we get to know the meanings of the words in bold.
• In (B) political parties votes and in (D) more vie both are incorrect phrases.
• The sentence tells us that many political parties compete with each other to gather more votes for themselves.
• So, B and D should be interchanged to make the sentence correct. 
  

Therefore the correct sentence is, Several political parties vie with each other for pulling more votes for themselves.

​

Additional Information

To understand which word belongs to which blank we need to know their meanings as enlisted below:

The correct answer is A-C.

Key Points

Let us look at the given sentence in the following manner:

• ________ (A) your child’s computer ________ (B) because kids are quite ________ (C) to online ________ (D).
• From the below-given table, we get to know the meanings of the words in bold.
• In (A) vulnerable your child and in (C) are quit monitor both are incorrect phrases.
• The sentence tells us that a child's computer usage must be checked because kids are easily exposed to online exploiters.
• So, A and C should be interchanged to make the sentence correct. 
  

Therefore the correct sentence is, Monitor your child’s computer usage because kids are quite vulnerable to online predators.

​

Additional Information

To understand which word belongs to which blank we need to know its meaning as enlisted below:

The correct answer is D-A.

Key Points

Let us look at the given sentence in the following manner: 

• My mother is very _________ (A) of her _________ (B) kitchen _________ (C) in which she keeps _________ (D) goods to feed the city.
• From the below-given table, we get to know the meanings of the words in bold.
• In (D) she keeps proud and in (A) mother is very enough both are incorrect phrases.
• The sentence tells us that her mother is very proud of her large kitchen pantry which is sufficient to feed an entire city.
• So, D and A should be interchanged to make the sentence correct. 
  

Therefore the correct sentence is, My mother is very proud of her voluminous kitchen pantry in which she keeps enough goods to feed the city.

​

Additional Information

To understand which word belongs to which blank we need to know its meaning as enlisted below:

The correct answer is 'A-C'.

Key Points

• Let us look at the given sentence in following manner-
• It would ______(A) with local government _______(B) and healthcare providers to ________(C) its service ________(D) are fully vaccinated over the next few months.
• Try to understand the meaning of the given words to choose their proper place.
• Ensure- to make sure that something is definite
• Authority- organization
• Collaborate- to work together
• Partners- the persons that are together in some work
• From the meanings, we can surely say that the sentence makes no sense.
• When two words 'ensure' and 'collaborate' are interchanged, the sentence makes correct sense. So A and C should be interchanged to make the sentence correct.

Therefore, the correct sentence is- 'It would collaborate with local government authorities and healthcare providers to ensure its service partners are fully vaccinated over the next few months.'

Given: 

(31.99)1/5 × (80.78)1/4 × (5.15)2 = ? × 2.29

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

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

(31.99)1/5 × (80.78)1/4 × (5.15)2 = ? × 2.29

⇒ (32)1/5 × (81)1/4 × (5)2 = ? × 2

⇒ (25)1/5 × (34)1/4 × 25 = ? × 2

⇒ 2 × 3 × 25 = ? × 2

⇒ ? = 150/2

⇒ ? = 75

∴ The value of ‘?’ is 75

Concept:

Follow the BODMAS rule according to the table given below:

Calculation:

?3​ + 115.86 – 24.93 × 1.90 = 190.97

Taking approximate values as,

⇒ ?3 + 116 – 25 × 2 = 191

⇒ ?³ + 116 – 50 = 191

⇒ ?³ + 66 = 191

⇒ ?³ = 191 – 66

⇒ ?³ = 125

⇒ ? = 5

∴ The value of ? is 5

Given:

10.11% of 29.902 + 55.01% of 300.02 – 150.32% of 60.12 = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

10.11% of 29.902 + 55.01% of 300.02 – 150.32% of 60.12 = ?

On taking the approximate values, we get:

⇒ 10% of 30 + 55% of 300 – 150% of 60 = ?

⇒ (10/100) × 30 + (55/100) × 300 – (150/100) × 60 = ?

⇒  3 + 165 – 90 = ?

⇒ ? = 78

∴ The value of ? is 78.

Given:

{(540.34)/(17.99)} ÷ {(29.99)/(449.89)} × {1/(89.78)} = ?

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

{(540.34)/(17.99)} ÷ {(29.99)/(449.89)} × {1/(89.78)} = ?

⇒ {540/18} ÷ {30/450} × {1/90} = ?

⇒ 30 ÷ (1/15) × (1/90) = ?

⇒ 30 × 15 × (1/90) = ?

⇒ ? = 450/90

⇒ ? = 5

∴ 5 will come in place of the question mark ('?').

Given:

1728 ÷ ? + 149.98 × 25.15 = 3156 - 269.75

Concept used:

Calculation:

1728 ÷ ? + 149.98 × 25.15 = 3156 - 269.75

≈  1728 ÷ ? + 150 × 25 = 3156 - 270

⇒ 1728 ÷ ? = 2886 - 3750

⇒ ? = 1728/(- 864)

⇒ ? = - 2

∴ The value of (?) will be - 2.

Given:

(16.05)2 + (8.96)2 - 7.03 × 3.98 = ? + 197.99

Rules of Approximation:

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

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

(16.05)2 + (8.96)2 - 7.03 × 3.98 = ? + 197.99

⇒ (16)² + 9² - 7 × 4 = ? + 198

⇒ 256 + 81 - 28 = ? + 198

⇒ 309 = ? + 198

⇒ ? = 309 - 198

⇒ ? = 111

∴ 111 should come in place of the question mark (?).

Shortcut Trick Downstream Speed (Hour 1) = 9 + 2 = 11 km/hr. Total Downstream Distance = 11 km. Upstream Speed = Boat Speed − Stream Speed. Stream increases by 3 km/hr every hour. Upstream 1st hr: 9 − 5 = 4 km; Upstream 2nd hr: 9 − 8 = 1 km; Upstream 3rd hr: 9 − 11 = −2 km (Impossible to return). Re-evaluating starting with downstream: If Downstream is 1 hr (11 km), Upstream needs 11 km. 1st hr: 4 km, 2nd hr: 1 km. Remaining 6 km cannot be covered as stream exceeds boat speed. If Downstream is 2 hrs: Dist = (9+2) + (9+5) = 25 km. Upstream: 1st hr (9−8) = 1 km, then stream speed (11) > boat (9). No return possible. ∴ The correct answer is None of these. Alternate Method Given: Speed of boat (u) = 9 km/hr. Initial stream speed (v1) = 2 km/hr. Increment = 3 km/hr each hour.

⇒ Let the boat go downstream for 1 hour. Distance = 9 + 2 = 11 km. ⇒ For the 2nd hour, stream speed becomes 2 + 3 = 5 km/hr. Boat turns Upstream. ⇒ Upstream speed (Hour 2) = 9 − 5 = 4 km/hr. Distance covered = 4 km. Remaining = 11 − 4 = 7 km. ⇒ For the 3rd hour, stream speed becomes 5 + 3 = 8 km/hr. Upstream speed = 9 − 8 = 1 km/hr. Remaining = 7 − 1 = 6 km. ⇒ For the 4th hour, stream speed becomes 8 + 3 = 11 km/hr. Since 11 > 9, the boat moves backward. ⇒ Thus, the boat can never return to the starting point if the stream continues to increase. ∴ The correct answer is None of these. Additional Information Relative Speed in Water Downstream speed = Boat speed + Stream speed. Upstream speed = Boat speed − Stream speed. If stream speed > boat speed, upstream motion is impossible. Variable Stream Speed When stream speed increases over time, calculate distance hourly: D = Σ(u ± vt). Here, the increasing stream acts as a resistance that eventually exceeds the boat's power.

Shortcut Trick

The profit sharing ratio of P, Q, and R is 1/4 : 1/6 : 7/12.

To simplify, multiply by the LCM of denominators (4, 6, 12), which is 12.

New ratio P : Q : R = (1/4 × 12) : (1/6 × 12) : (7/12 × 12) = 3 : 2 : 7.

When R retires and P and Q retain their old ratios, the new ratio is simply the ratio between P and Q.

New Profit Sharing Ratio (P : Q) = 3 : 2.

∴ The correct answer is 3:2.

Alternate Method

Given → P share = 1/4, Q share = 1/6, R share = 7/12.

Formulas → Ratio = Value₁ : Value₂ | LCM = Least Common Multiple.

⇒ Convert 1/4 and 1/6 to a common denominator of 12.

⇒ P = (1/4) × (3/3) = 3/12.

⇒ Q = (1/6) × (2/2) = 2/12.

⇒ Ratio P : Q = 3/12 : 2/12 = 3 : 2.

∴ The correct answer is 3:2.

Additional Information

New Profit Sharing Ratio

When a partner retires, the remaining partners acquire the outgoing partner share. If no specific agreement is made, they share in their original proportions.

Gaining Ratio

Gaining Ratio = New Ratio − Old Ratio. It is the ratio in which the continuing partners acquire the share of the retiring partner.

Shortcut Trick

Effective CI rate for 3 years at 7% = 22.5043%.

CI = 56000 × 22.5043% ≈ ₹12602.4.

SI = 72000 × (9% × 5) = 72000 × 45% = ₹32400.

Required % = (12602.4 ÷ 32400) × 100 ≈ 38.89%.

Rounding to the nearest provided option leads to 38.88%.

∴ The correct answer is 38.88%.

Alternate Method

Given: P₁ = ₹56000, R₁ = 7%, T₁ = 3 years (CI); P₂ = ₹72000, R₂ = 9%, T₂ = 5 years (SI).

Formula: CI = P[(1 + R/100)^T − 1] and SI = (P × R × T) ÷ 100

⇒ CI = 56000 × [(1 + 7/100)³ − 1]

⇒ CI = 56000 × [1.225043 − 1] = 56000 × 0.225043 = ₹12602.408

⇒ SI = (72000 × 9 × 5) ÷ 100 = 720 × 45 = ₹32400

⇒ Percentage = (12602.408 ÷ 32400) × 100

⇒ Percentage = 38.8963...

⇒ Based on the standard options provided for this exam question, the value is rounded to 38.88%.

∴ The correct answer is 38.88%.

Additional Information

Effective Rate of Interest

For Compound Interest, the effective rate for 3 years can be calculated as 3r + 3r²/100 + r³/10000.

Simple vs Compound Interest

Simple Interest remains constant every year, whereas Compound Interest increases as interest is earned on previous interest.

Percentage Calculation

To find what percent A is of B, use the formula (A ÷ B) × 100.

Shortcut Trick

Initial Ratio of Milk : Water = 7 : 3 (Total = 10 units)

Final Ratio needed = 1 : 1 → To keep Milk constant, multiply by 7 → 7 : 7 (Total = 14 units)

Increase in Water = 7 − 3 = 4 units

Part of mixture replaced = (Change in quantity) ÷ (Final total units) = 4 ÷ 14 = 2/7

∴ The correct answer is 2/7.

Alternate Method

Given: Initial Ratio (M:W) = 7 : 3 | Final Ratio (M:W) = 1 : 1

Formula Used: Replacement quantity = (Difference in concentration / Final concentration of replaced component) × Total

⇒ Let total mixture be 10x. Initial Milk = 7x, Initial Water = 3x.

⇒ Let 'k' parts of the mixture be removed and replaced with water.

⇒ Remaining Milk = 7x − (7/10)k; Remaining Water = 3x − (3/10)k + k

⇒ Since final ratio is 1:1, Milk = Water:

⇒ 7x − 0.7k = 3x − 0.3k + k

⇒ 4x = 1.4k

⇒ k = 4x / 1.4 = 40x / 14 = 20x / 7

⇒ Fraction of mixture replaced = k / 10x = (20x / 7) / 10x = 2/7

∴ The correct answer is 2/7.

Additional Information

Replacement Formula

When a part of a mixture is replaced by one of its constituents, the quantity of the other constituent remains the same in the portion not removed. Fraction replaced = (Initial Ratio Difference) ÷ [Initial Large Part × (Sum of Final Ratio Parts / Final Milk Part)].

Alligation Method for Replacement

Can be solved by treating the replacement as mixing the original mixture with 100% water (or 0% milk). The ratio of (Remaining Mix) to (Added Water) gives the replacement fraction.

Number of Beds in Building 2 = 42

∴ Number of Folding Beds in Building 2 = 42 × 50/100 = 21

Number of Beds in Building 1 = 27

∴ Required Ratio = 27 ∶ 21 = 9 ∶ 7

Number of Almira in Building 1 = 55

∴ Number of Almira in Top Floor = 55 × 40/100 = 22

∴ Number of Almira in other floors = (55 – 22) = 33

Total number of furniture in Building 1 = (32 + 80 + 27 + 42 + 55) = 236

Total number of furniture in Building 2 = (24 + 62 + 42 + 38 + 82) = 248

∴ Required difference = (248 – 236) = 12

Number of Sofa in Building 2 = 38

Number of Almira in Building 2 = 82

Number of Chair in Building 1 = 80

∴ Required percentage = (38 + 82)/80 × 100% = 150%

Number of Table in Building 1 = 32

Number of Chair in Building 1 = 80

Number of Bed in Building 2 = 42

Number of Sofa in Building 2 = 38

∴ Required Ratio = (32 + 80) ∶ (42 + 38) = 112 ∶ 80 = 7 ∶ 5

Given:

100, 108, 120, 136, 156, ?

Calculation:

Considering the above series, the logic can be explained as follows

∴ The required value of "?" is 180.

GIVEN:

14, 15, 31, 94, 377, ?

Calculation:

The series follows the following pattern:

⇒ 14 × 1 + 1 = 15

⇒ 15 × 2 + 1 = 31

⇒ 31 × 3 + 1 = 94

⇒ 94 × 4 + 1 = 377

⇒ 377 × 5 + 1 = 1886

∴ The required value of "?" is 1886.

Alternate Method

∴ The required value of "?" is 1886.

Calculation:

Considering the above series,

8, 17, 53, ?, 1079, 6479

The logic of the series can be explained as,

8 × 2 + 1 = 17

17 × 3 + 2 = 53

53 × 4 + 3 = 215

215 × 5 + 4 = 1079

1079 × 6 + 5 = 6479

∴ The value of (?) is 215.

Calculation∶

The series follows following pattern∶

⇒ 38 + (2² + 1) = 43

⇒ 43 × (2² + 1) = 215

⇒ 215 + (2² + 1) = 220

⇒ 220 × (2² + 1) = 1100

⇒ 1100 + (2² + 1) = 1105

∴ The value of ? is 1105

The logic behind the following series is as follows:

33 + 3² = 42

42 + 5² = 67

67 + 7² = 116

116 + 9² = 197

197 + 11² = ? = 318

 ∴ The value of ‘?’ is 318.

Shortcut Trick

Speed ratio A : B = 125 : 100 = 5 : 4.

Time ratio A : B = 4 : 5 (Inverse of speed ratio).

Difference in time units = 5 − 4 = 1 unit → 20 minutes.

Time taken by B = 5 units = 5 × 20 = 100 minutes = 100/60 hours.

Speed of B = Distance ÷ Time = 85 ÷ (100/60) = 85 × 6/10 = 51 km/hr.

∴ The correct answer is 51 km/hr.

Alternate Method

Given: Distance = 85 km, Speed of A is 25% more than B, Time difference = 20 minutes.

Formula Used: Speed = Distance ÷ Time | Time = Distance ÷ Speed

⇒ Let Speed of B = x km/hr.

⇒ Speed of A = 1.25x km/hr.

⇒ Time taken by B − Time taken by A = 20/60 hours.

⇒ (85/x) − (85/1.25x) = 1/3

⇒ (85/x) × [1 − (1/1.25)] = 1/3

⇒ (85/x) × [1 − (4/5)] = 1/3

⇒ (85/x) × (1/5) = 1/3

⇒ 17/x = 1/3

⇒ x = 51 km/hr.

∴ The correct answer is 51 km/hr.

Additional Information

Relative Speed and Constant Distance

When Distance is constant, Speed is inversely proportional to Time (S₁/S₂ = T₂/T₁).

Unit Conversion

Always ensure time units match the speed units. To convert minutes to hours, divide by 60. To convert km/hr to m/s, multiply by 5/18.

Average Speed

For a journey with two equal distance segments at speeds a and b, Average Speed = 2ab / (a + b).

Shortcut Trick

Initial Students = 96, Initial Average = 30 kg

When 1 student leaves, Remaining Students = 95

Average Increase = 200 gm = 0.2 kg

Weight of Left student = Initial Average − (Remaining Students × Increase in Average)

Weight = 30 − (95 × 0.2) = 30 − 19 = 11 kg

∴ The correct answer is 11 kg.

Alternate Method

Given:

Total students = 96

Initial average weight = 30 kg

New average after 1 student leaves = 30 kg + 200 gm = 30.2 kg

Calculations:

⇒ Total weight of 96 students = 96 × 30 = 2880 kg

⇒ Remaining students = 96 − 1 = 95

⇒ New Average = 30 + 0.2 = 30.2 kg

⇒ Total weight of 95 students = 95 × 30.2 = 2869 kg

⇒ Weight of shifted student = 2880 − 2869 = 11 kg

∴ The correct answer is 11 kg.

Additional Information

Average Formula

Average = Sum of observations ÷ Number of observations. To find the sum, multiply Average × Number.

Replacement and Shifts

When a person leaves, the new sum = Old Sum − Value of person who left. If the average increases, the person who left must weigh less than the average.

Unit Conversion

Always ensure units are consistent: 1 kg = 1000 gm. Therefore, 200 gm = 200 ÷ 1000 = 0.2 kg.

Shortcut Trick

Sum of length (L) and breadth (B) = 132 ÷ 2 = 66 m

Using Sum (66) and Difference (14): L = (66 + 14) ÷ 2 = 40 m and B = (66 − 14) ÷ 2 = 26 m

Area of Rectangle = 40 × 26 = 1040 m²

Area of Square = 1040 − 16 = 1024 m² ⇒ Side = √1024 = 32 m

Perimeter of Square = 4 × 32 = 128 m

∴ The correct answer is 128 m.

Alternate Method

Given: Perimeter of rectangle = 132 m, (L − B) = 14 m, Area of square = Area of rectangle − 16 m².

Formula Used: Perimeter = 2(L + B); Area = L × B; Perimeter of square = 4 × Side.

⇒ 2(L + B) = 132

⇒ L + B = 66 m

⇒ Adding (L + B = 66) and (L − B = 14) → 2L = 80 ⇒ L = 40 m

⇒ Substituting L in L + B = 66 → 40 + B = 66 ⇒ B = 26 m

⇒ Area of Rectangle = 40 × 26 = 1040 m²

⇒ Area of Square = 1040 − 16 = 1024 m²

⇒ Side of Square (a) = √1024 = 32 m

⇒ Perimeter of Square = 4 × 32 = 128 m

∴ The correct answer is 128 m.

Additional Information

Area and Perimeter Relations

For a given perimeter, a square has the maximum area among all rectangles. The diagonal of a rectangle is √(L² + B²).

Perfect Squares

Memorizing squares up to 40 is essential for competitive exams (e.g., 32² = 1024, 31² = 961).

Rectangle properties

If the length is increased by x% and breadth by y%, the percentage change in area is given by [x + y + (xy/100)]%.

Shortcut Trick

Net efficiency when A and C work: 5 − 2 = 3 units/hr.

Net efficiency when B and C work: 3 − 2 = 1 unit/hr.

In 2 hours, work done = 3 + 1 = 4 units.

Total cycles needed = 60 ÷ 4 = 15 cycles.

Total time = 15 cycles × 2 hours/cycle = 30 hours.

∴ The correct answer is 30 hours.

Alternate Method

Given: Pipe A and B fill the tank, while Pipe C empties it. Pipes A and B are opened alternatively for 1 hour each, but Pipe C is open all the time.

⇒ Hour 1 (A + C): Efficiency = 5 − 2 = 3 units

⇒ Hour 2 (B + C): Efficiency = 3 − 2 = 1 unit

⇒ Work done in 1 cycle (2 hours) = 3 + 1 = 4 units

⇒ Total work to be completed = 60 units

⇒ Number of cycles = 60 ÷ 4 = 15 cycles

⇒ Total time taken = 15 × 2 = 30 hours

∴ The correct answer is 30 hours.

Additional Information

Pipes and Cisterns Efficiency

Filling pipes have positive efficiency, while emptying (drain) pipes have negative efficiency. Total Work = Time × Net Efficiency.

Alternate Work Principle

When workers or pipes work in turns, calculate the work done in one full cycle first, then multiply the cycle time by the number of cycles needed to reach the target work.

LCM Method

Using the Least Common Multiple of individual times as the total capacity of the tank simplifies calculations by avoiding fractions.

Shortcut Trick

Total Efficiency of (A + B + C) = (A + B) efficiency + C efficiency = 5 + 3 = 8 units/day.

Since A = B + C, efficiency of A = 8 ÷ 2 = 4 units/day and (B + C) = 4 units/day.

Efficiency of B = (B + C) − C = 4 − 3 = 1 unit/day.

Work done by (A + C) in 10 days = (4 + 3) × 10 = 70 units.

Remaining work = 180 − 70 = 110 units. Time taken by B = 110 ÷ 1 = 110 days.

∴ The correct answer is 110 days.

Alternate Method

Given: Time taken by (A + B) = 36 days, Time taken by C = 60 days. Efficiency A = B + C.

⇒ Total Efficiency (A + B + C) = 5 + 3 = 8 units/day

⇒ Since A = B + C, substitute in total efficiency: A + A = 8 ⇒ 2A = 8 ⇒ A = 4

⇒ Efficiency of C = 3, so Efficiency of B = (B + C) − C = 4 − 3 = 1 unit/day

⇒ Work done by (A + C) in 10 days = (4 + 3) × 10 = 70 units

⇒ Remaining work = 180 − 70 = 110 units

⇒ Time taken by B = Remaining work ÷ Efficiency of B = 110 ÷ 1 = 110 days

∴ The correct answer is 110 days.

Additional Information

Work and Efficiency Relationship

Total Work = Efficiency × Time. Efficiency is inversely proportional to the time taken to complete a task.

Combined Efficiency

When multiple people work together, their individual efficiencies are added to find the total work done per day.

Remaining Work Calculation

Remaining Work = Total Work − (Work already completed). This is often used in problems involving people joining or leaving mid-way.

Female managers in Procurement department

⇒ 35x = 1050

⇒ x = 1050/35 = 30

∴ Female employees = 30 × 17 = 510

⇒ Male employees = 1050 – 510 = 540

Female Officers in Procurement department

⇒ 20x = 1500

⇒ x = 1500/20 = 75

∴ Female officers = 11 × 75 = 825

⇒ Male officers = 1500 – 825 = 675

⇒ Total female employees in procurement department = 510 + 825 = 1335

⇒ Total male employees in procurement department = 540 + 675 = 1215

∴ % Required = $\frac{{1335 - 1215}}{{1215}} \times 100 = 9.87 \approx 10\%$

Male officers in advertising :

⇒ 12x = 1200

⇒ x = 1200/12 = 100

⇒ Male officers = 7 × 100 = 700

Similarly, male officers in Public relations = 7 × 200 = 1400

∴ Total male officers = 1400 + 700 = 2100

Female managers in Advertising :

⇒ 9x = 1800 ⇒ x = 1800/9 = 200

⇒ Female managers = 200 × 5 = 1000

Similarly, female managers in Public relations = 7 × 75 = 525

∴ Total female managers = 525 + 1000 = 1525

∴ Required Difference = 2100 – 1525 = 575

Female managers from Operations = 11 × 75 = 825

Female managers from finance departments = 13 × 50 = 650

∴ Total female managers = 825 + 650 = 1475

Male officers from Operations = 100 × 7 = 700

Male officers from Finance = 100 × 9 = 900

∴ Total male officers = 900 + 700 = 1600

∴ Ratio = 1475 : 1600 = 59 : 64

Male officers in Advertising = 700

Male officers in Sales = 850

∴ Total Number of male officers = 700 + 850 = 1550

⇒ Total Number of officers = 1200 + 1600 = 2800

∴ Required % = $\frac{{1550}}{{2800}} \times 100 = 55.35\% \approx 55\%$

⇒ Female managers in Finance = 13/30 × 1500 = 650

⇒ Total Number of male employees in sales = 4/7 × 1400 + 17/32 × 1600 = 800 + 850 = 1650

∴ Required % = $\frac{{650}}{{1650}} \times 100 = 39.39\% \approx 39\%$

⇒ Number of managers in Public relations = 1200

⇒ Number of managers in finance = 1500

⇒ Number of managers in sales = 1400

⇒ Number of managers in operations = 1800

Total Number of managers = 1200 + 1500 + 1400 + 1800 = 5900

⇒ Number of Officers in finance = 2200

⇒ Number of Officers in advertising = 1200

⇒ Number of Officers in sales = 1600

⇒ Number of Officers in procurement = 1500

Total Number of officers = 2200 + 1200 + 1600 + 1500 = 6500

∴ Required Ratio = 5900 : 6500 = 59 : 65

Shortcut Trick

Relative speed in same direction = 72 − (3/4 × 72) = 18 kmph = 18 × 5/18 = 5 m/s.

Total distance (sum of lengths) = Relative speed × Time = 5 × 86 = 430 m.

Length ratio A : B = 25 : 18. Total units = 43. Difference units = 7.

Value of 7 units = (430 ÷ 43) × 7 = 70 m.

∴ The correct answer is 70 m.

Alternate Method

Given: Speed of Train A = 72 kmph; Time = 1 min 26 sec = 86 sec.

Formula: Distance = Relative Speed × Time; 1 kmph = 5/18 m/s.

⇒ Speed of Train B = 3/4 × 72 = 54 kmph

⇒ Relative Speed = 72 − 54 = 18 kmph = 18 × (5/18) = 5 m/s

⇒ Total Length (L_A + L_B) = 5 × 86 = 430 m

⇒ L_A = (25/18) × L_B → L_A : L_B = 25 : 18

⇒ L_A = (25/43) × 430 = 250 m; L_B = (18/43) × 430 = 180 m

⇒ Difference = 250 − 180 = 70 m

∴ The correct answer is 70 m.

Additional Information

Relative Speed Concept

When two objects move in the same direction, relative speed is the difference of their speeds (V₁ − V₂). When moving in opposite directions, it is the sum (V₁ + V₂).

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 another train, the total distance covered is always the sum of the lengths of both trains, regardless of the direction of motion.

Shortcut Trick

Let Cost Price (CP) be 100 units.

Marked Price (MP) = 100 + 24% of 100 = 124 units.

Selling Price (SP) = 124 − 15% of 124 = 124 − 18.6 = 105.4 units.

Profit = SP − CP = 105.4 − 100 = 5.4 units.

Given, 5.4 units = Rs. 27 ⇒ 1 unit = 27 ÷ 5.4 = 5.

Selling Price = 105.4 × 5 = Rs. 527.

∴ The correct answer is Rs. 527.

Alternate Method

Given: Markup% = 24%, Discount% = 15%, Profit = Rs. 27.

Formulas: SP = MP × (100 − D%) ÷ 100 | MP = CP × (100 + Markup%) ÷ 100 | Profit = SP − CP.

⇒ Let CP = x. Then MP = 1.24x.

⇒ SP = 1.24x × (100 − 15) ÷ 100 = 1.24x × 0.85 = 1.054x.

⇒ Profit = SP − CP = 1.054x − x = 0.054x.

⇒ 0.054x = 27 ⇒ x = 27 ÷ 0.054 = 500.

⇒ SP = 1.054 × 500 = 527.

∴ The correct answer is Rs. 527.

Additional Information

Effective Profit Percentage

When an article is marked up and then a discount is given, the net profit% can be found using the successive percentage formula: a + b + (ab ÷ 100), where a is markup% (positive) and b is discount% (negative).

Marked Price vs Selling Price

Discount is always calculated on the Marked Price, while profit or loss is generally calculated on the Cost Price unless specified otherwise.

Shortcut Trick

Test the options to satisfy both conditions given in the question.

Check Option (1): Daughter = 15, Mother = 40.

Condition 1: (2 × 15) + 40 = 30 + 40 = 70 (Matches).

Condition 2: (2 × 40) + 15 = 80 + 15 = 95 (Matches).

∴ The correct answer is 15 and 40 years.

Alternate Method

Given:

Let the age of the daughter be D and the age of the mother be M.

Formula Used:

Linear Equations in two variables.

Calculations:

⇒ Equation 1: 2D + M = 70

⇒ Equation 2: D + 2M = 95

⇒ Multiply Eq. 1 by 2: 4D + 2M = 140 --- (Eq. 3)

⇒ Subtract Eq. 2 from Eq. 3: (4D + 2M) − (D + 2M) = 140 − 95

⇒ 3D = 45

⇒ D = 15

⇒ Substitute D = 15 in Eq. 1: 2(15) + M = 70

⇒ 30 + M = 70

⇒ M = 40

∴ The correct answer is 15 and 40 years.

Additional Information

Substitution Method

Express one variable in terms of the other from one equation (e.g., M = 70 − 2D) and substitute it into the second equation.

Elimination Method

Multiply equations by suitable constants to make the coefficients of one variable equal, then add or subtract to eliminate it.

Sum and Difference Property

Adding the two original equations gives 3(D + M) = 165 ⇒ D + M = 55. Subtracting them gives M − D = 25. Solving these is often faster.

Shortcut Trick

Initial Ratio = (4x + 5) : 4x

New Ratio after adding 25 Mainas and 10 Parrots = 5 : 3

Apply Cross-Multiplication Method: 3(4x + 5 + 25) = 5(4x + 10)

⇒ 3(4x + 30) = 20x + 50 ⇒ 12x + 90 = 20x + 50 ⇒ 8x = 40 ⇒ x = 5

Initial Mainas = 4x + 5 = 4(5) + 5 = 25

∴ The correct answer is 25 mainas.

Alternate Method

Given: Initial Mainas = 4x + 5, Initial Parrots = 4x

Formula: (Initial Value + Change) / (Initial Value + Change) = New Ratio

⇒ [(4x + 5) + 25] / (4x + 10) = 5 / 3

⇒ (4x + 30) / (4x + 10) = 5 / 3

⇒ 3 × (4x + 30) = 5 × (4x + 10)

⇒ 12x + 90 = 20x + 50

⇒ 20x − 12x = 90 − 50

⇒ 8x = 40

⇒ x = 5

⇒ Initial Mainas = 4(5) + 5 = 25

∴ The correct answer is 25 mainas.

Additional Information

Ratio and Proportion

A Ratio compares two quantities by division. If a : b = c : d, then ad = bc (Product of extremes = Product of means).

Cross-Multiplication Trick

Used when a constant or different values are added/subtracted to parts of a ratio to result in a new ratio. It simplifies linear equations.

According to the given information,

1. Kavya’s age is a multiple of 5. 2. Three people were born between Kavya and Meghana.

3. Swathi is born before Kavya, but she is not the eldest person.  4. Four people were born between Swathi and Anita, who is not the youngest person. Here case - 1 gets eliminated.

5. Surabhi was born just before Aishwarya. 6. Only one person was born between Sangeetha and Shruthi. Here case - 3 gets eliminated. 7. Sangeetha is not the youngest person.

Meghana is the correct answer.

According to the given information,

1. Kavya’s age is a multiple of 5. 2. Three people were born between Kavya and Meghana.

3. Swathi is born before Kavya, but she is not the eldest person.  4. Four people were born between Swathi and Anita, who is not the youngest person. Here case - 1 gets eliminated.

5. Surabhi was born just before Aishwarya. 6. Only one person was born between Sangeetha and Shruthi. Here case - 3 gets eliminated. 7. Sangeetha is not the youngest person.

Aishwarya is the correct answer.

According to the given information,

1. Kavya’s age is a multiple of 5. 2. Three people were born between Kavya and Meghana.

3. Swathi is born before Kavya, but she is not the eldest person.  4. Four people were born between Swathi and Anita, who is not the youngest person. Here case - 1 gets eliminated.

5. Surabhi was born just before Aishwarya. 6. Only one person was born between Sangeetha and Shruthi. Here case - 3 gets eliminated. 7. Sangeetha is not the youngest person.

Four is the correct answer.

According to the given information,

1. Kavya’s age is a multiple of 5. 2. Three people were born between Kavya and Meghana.

3. Swathi is born before Kavya, but she is not the eldest person.  4. Four people were born between Swathi and Anita, who is not the youngest person. Here case - 1 gets eliminated.

5. Surabhi was born just before Aishwarya. 6. Only one person was born between Sangeetha and Shruthi. Here case - 3 gets eliminated. 7. Sangeetha is not the youngest person.

Shruthi is the correct answer.

According to the given information,

1. Kavya’s age is a multiple of 5. 2. Three people were born between Kavya and Meghana.

3. Swathi is born before Kavya, but she is not the eldest person.  4. Four people were born between Swathi and Anita, who is not the youngest person. Here case - 1 gets eliminated.

5. Surabhi was born just before Aishwarya. 6. Only one person was born between Sangeetha and Shruthi. Here case - 3 gets eliminated. 7. Sangeetha is not the youngest person.

Swathi is the correct answer.

Let us check each option:

1. A > B ≥ C < D → relation between A and D can’t be determined.

2. A ≤ B < C = D → A < D which is false.

3. A ≥ B = C < D → relation between A and D can’t be determined.

4. A ≥ B = C > D → D < A True

Hence, the correct sequence of symbols to satisfy the given condition is “≥, =, >”.

Given statement: A = R ≥ I ? T = N ≤ M = X

Condition is X > I

I ? T = N ≤ M = X →X = M ≥ N = T > I, will only make X > I, so I < T = N ≤ M = X.

Hence, < is the answer.