SBI PO Prelims Memory Based Paper (Held on: 22 Nov 2021 Shift 3) (Previous Year Paper)

‘Rural’ means related to village or country life. The appropriate antonym for ‘rural’ in the context of the passage is ‘urban’ which means ‘related to a city or city life’. The words ‘under-developed’, ‘agrarian’, ‘bucolic’, ‘rustic’ are all close in meaning to the word ‘rural’.  Hence ‘urban’ is the most suitable antonym for ‘rural’.

In a world of 7.3 billion people, 2.4 billion lack access to adequate sanitation which accounts for approximately 33% of people. Hence 33% of people lack access to sufficient sanitation.

The last two lines of the second paragraph states ‘In 1840, the “global sanitary revolution” transformed life in Europe and other parts of the developed world. In fact, it actually furthered the economic transformation, by making those societies cleaner and healthier. But many countries still await a sanitation revolution.’

The synonym for the word ‘adequate’ in the context in which it is used in the passage is, ‘sufficient’ which means ‘a quantity able to fulfil the need or demand’. The words ‘insufficient’, ‘unequal’, ‘deficient’, ‘lacking’ don’t fit here as they are antonyms for the word ‘adequate’. Therefore the appropriate synonym is ‘sufficient’.

‘Foster’ means to ‘nurture or contribute to the progress of something’. The synonym for the word ‘foster’ which suits the context is, ‘promote’ which means ‘contribute to the progress or growth of something’. The words ‘deprive’, ‘discourage’, ‘dispirit’, ‘dishearten’ are inappropriate in the context as they are antonyms for the word ‘foster’. Therefore the appropriate synonym is ‘promote’.

The author uses lines like

(1) “With so many solutions at hand, the continuing deprivation of so many is a shameful reflection of our society’s priorities.”

(2) “More than 72% of rural people relieve themselves behind bushes, in fields or by roadsides. The share is barely shrinking. Of the 1 billion people in the world who have no toilet, India accounts for nearly 600million.”

(3) “Public safety is one underappreciated problem, as young women have to leave their rural homes after dark.”

Clearly the author is being ‘critical’ of the problem of santitation in India.

The third paragraph clearly states “Because India’s population is huge, growing rapidly and densely settled, it is impossible even in rural areas to keep human faeces from crops, wells, food and children’s hands. They cause enteropathy, a chronic illness that prevents the body from absorbing calories and nutrients.”

The last paragraph states “in developing the 17 Sustainable Development Goals for the 2016-2030 period, UN Member States have recognized that good sanitation and hygiene (goal 6.2) have positive, knock-on effects for eight other goals.” Clearly the answer is ‘UN Member States.’

The first paragraph states “Millions lack menstrual hygiene and vital hand washing facilities.” It also states “Inadequate facilities also affect education and economic productivity and impact the dignity and personal safety of women and girls.” The passage also states “Underweight mothers produce stunted babies prone to sickness who may fail to develop to their full cognitive potential” which tells us that pregnancy is also affected by sanitation. The only one of the options among the given ones NOT being affected by the lack of sanitation for women is ‘marriage’.

The eighth line of the third paragraph states “Of the 1 billion people in the world who have no toilet, India accounts for nearly 600 million.” This accounts for about 60%.

The correct answer is option 1 i.e. CABED.

Explanation  

• First is C as it establishes the subject i.e. energy-efficiency models. C is the only opening segment that can lead to the formation of a meaningful and grammatically correct sentence.
• Next is A as it states the importance of these models.
• B follows A as it mentions one feature of these models.
• Next is E as it contextually follows B. 'Not only...but also' is a correlative conjunction.
• Last is D as it tells what will be saved.

Correct sentence- Energy-efficiency models hold the potential to not only improve operations for higher productivity, but also help save millions for any business.

The correct answer is option 5 i.e. CAEDB.

Explanation   

• First is C as it establishes the subject i.e. India. C is the only opening segment that can lead to the formation of a meaningful and grammatically correct sentence.
• Next is A as it contextually follows C.
• E follows A as it tells what the country faced. 'Severe' mentioned in A is an appropriate adjective for the noun 'food shortages.
• Next is D as it tells when the country faced these shortages i.e. after independence.
• Last is B as it states what India has become finally even though it faced severe food shortages.
  

Correct sentence- India has come a long way from facing severe food shortages after Independence to becoming a net exporter of food.

The correct answer is BEADC.

Key Points

• B is the part that establishes the subject of the matter i.e. 'People in unity'. Hence, it'll be the first part after rearrangement.
• Part E talks about people looking forward to work. Hence, E follows B.
• Part A is a continuation of part E as it says that people work towards a common thing. Hence, A follows E.
• Part D talks about the common thing towards which people work i.e. a common goal. So, D follows A.
• Part C tells us that people work towards a common goal keeping aside their own selfishness. Hence, C follows  D.
  

Correct rearrangement of segments is: People in unity look forward to work towards a common goal instead of satisfying their own selfish motives.

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 notions. So those options will be always at the end.

The correct answer is CDBEA.

Key Points

• C is the part that establishes the subject of the matter i.e. 'Recycling'. Hence, it'll be the first part after rearrangement.
• Part D talks about a procedure that is similar to the word methods used in C. Hence, D follows C.
• Part B talks about the collection which comes under the procedure which was mentioned in D. Hence, B follows D.
• Part E talks about breaking down garbage. This can be done only after garbage is collected. So, E follows B.
• Part A talks about the creation of new things which can be done only after breaking down old materials. Hence, A follows  E.
  

Correct rearrangement of segments is: Recycling is a method of procedure that includes the collection and breaking down of waste material to create something new out of it.

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 those options will be always at the end.

The correct answer is BDECA.

Key Points

• B is the part that establishes the subject of the matter i.e. 'countries'. Hence, it'll be the first part after rearrangement.
• In part D, which refers to countries mentioned in B. 'which' is also used to give more information about the thing it refers to. Hence, D follows C.
• Part E has a noun 'white population' whereas part E has the adjective 'considerable'.  'white population' will follow the adjective 'considerable'. Hence, C follows E and E follows D.
• Part A talks about the examples of white populations mentioned in C. Hence, A follows C. 
  

Correct rearrangement of segments is: The only countries in which there is a considerable white population are Algeria, Tunisia and New Caledonia. 

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 those options will be always at the end.

The correct answer is Convivial

Key Points

• Let's look at the meaning of the answer:
• Convivial: friendly, lively, and enjoyable
• The sentence talks about a cocktail party that was attended by a lot of respected people belonging to Hollywood circles.
• The sentence is talking about a party, and unless mentioned otherwise one can assume that a party is lively and that the people attending it are having fun.

Thus, the correct answer is Convivial

Additional Information

Let's look at the meaning of the other words: 

Confusion Points

• Based off the definition, 'vivid' seems like something that can be used to describe a party but is usually used to describe a memory of something or a piece of art.
• Even 'dramatic' seems like a apt descriptor for a party but has a negative connotation as it involves an element of surpise or even shock.

The correct answer is Catapulted

Key Points

• Let's look at the meaning of the answer:
• Catapulted: hurled or launched (something) in a specified direction
• The sentence talks about how something happened to Chris after having won an Olympic medal.
• When it comes to sport, winning an Olympic medal is one of the most honourable medals one can win on a global level (based on the sport one plays) and an achievement like this is likely to make a person very popular and famous as soon as they win the medal.
• This means they could be almost unknown one day and a national treasure the next.
• Hence, the verb in the blank needs to convey this sudden dive into fame that the person goes through.

Thus, the correct answer is Catapulted. 

Additional Information

Let's look at the meaning of the other words:

The correct answer is relegate.

Key Points

Let us look at the meaning of the correct word:

• Relegate- assign an inferior rank or position to; put down; lower
• The word relegate fits perfectly as it clearly depicts the paradigm shift where the individual is expected to lower/put down the position as he/she is expected to follow on the lines of Louise Childs that is to run home and rear child.
• Therefore, the only word that can make the sentence contextually and grammatically correct is relegate.​​

The sentence is: He expected that I would eventually relegate myself to running our home and rearing our children, much the way Louise Chil

Additional Information

Let us look at the meanings of the other options:

• Delegate: a person sent or authorized to represent others, in particular an elected representative sent to a conference
• Impede: delay or prevent (someone or something) by obstructing them; hinder
• Behest: a person's orders or command
• Delinquent: (typically of a young person) tending to commit a crime, particularly minor crime

The correct answer is displayed. 

Key Points

• In the given sentence, we need a word close to the meaning of 'exhibited' to fill in the blank.
• Let us see the meanings of the given words:
• Suspended: to stop something from being active, either temporarily or permanently
• Spent: having been used and unable to be used again
• Displayed: to show something or a collection of things in an organized way for people to see
• Surrounded: to be everywhere around something
• Commanded: control over someone or something and responsibility for him, her, or it
• From the meanings of the words, we can say that 'displayed' is the most appropriate answer.
• Therefore, the correct answer is 'displayed.'

​The complete sentence: It was a strange fact, however, that talent and skill, if displayed for too long, cease to dazzle.

The correct answer is 'alleviating'.

Key Points

• The meaning of the word 'alleviating' is 'make (suffering, deficiency, or a problem) less severe; relieving.'
• For example, The medicines did nothing to alleviate her pain/suffering.
• The sentence means that the interviewers described some discussions as essential for developing a trustworthy relationship with the participant, as well as relieving their concerns/issues.
• So, the word 'alleviating' fits correctly in the given blank.
• Therefore, option 3 is the correct answer.

Additional Information

• Let's learn the meanings of the other words given in the options: 
• exacerbating: make (a problem, bad situation, or negative feeling) worse.
• hoodwink: deceive or trick.
• deferred: put off (an action or event) to a later time; postpone.
• squandering: waste (something, especially money or time) in a reckless and foolish manner.

The correct answer is B and C

Key Points

Sentence A has no grammatical or contextual errors. 

• Sentence B talks about how Pooja was very sad about the loss of her loving pet but at a certain point in time, she was able to move on from the death and adopt a new pet.
• The use of the verb 'was' in the past tense tells us that the incident has already happened.
• Pooja's pet has already passed away and it was only after that, that she adopted a new one.
• So all the verbs in the sentence should be in the past tense.

Thus, the verb 'manage' (present tense) needs to be replaced with 'managed' (past tense).

The correct answer is: 'Pooja was distraught after the loss of her beloved pet, but she managed to move on and adopt another puppy soon.'

• Sentence C talks about how Ali was not going to go on a trek but his friends pressured him into lying to his parents.
• The sentence mentions 'parent' in the singular, this means that any pronoun referring to the parent will be in the singular format.
• We've already established Ali's pronoun as 'he' so the 'they' in this case refers to a plural pronoun.

Thus, the plural 'they' pronoun needs to be replaced with the singular pronoun 'he/she'.

The correct sentence is: 'Ali wasn't going to go on the trek but his friends pressured him into lying to his parent until he/she agreed.'

The correct answer is Option 4)i.e. Neither 1 nor 2 have an error.

Key Points

• A participle is a word that is partly a verb and partly an adjective.
• Example: Hearing a loud noise, the boy woke up.
• Here the word 'hearing' qualifies the noun boy as an adjective does. It is formed from the verb hear and has an object 'noise'. The word 'hearing', therefore, has the properties of a verb and an adjective and is called a participle.
• Present participles end in -ing and represent an action as going on or incomplete or imperfect. Present participles formed from transitive verbs, take objects.
• Example: Knocking at the door, he demanded admission
• Here, knocking is a present participle and it represents the action of repeated knocks that are still going on at the current time.
• The past participle usually ends in -ed, -d, -t, -en or -n. It represents a completed action or state.
• ​Example: Driven by rain, we took shelter under a tree.
• Here, 'drive + en' is talking about an action (of driving ) that took place and was completed in the past.
• In sentence 1,'Having heard the news, he quickly sold his brother's record collection' The use of 'having heard' denotes the 'Having + past participle' for the past participle 'heard' it is correct.✔️
• Sentence 2, 'Having been promised a steak dinner, she looked less than impressed with her Happy Meal*'.*
• In sentence 2 'having been promised' denotes the 'Having + past participle'
• the past participle is 'promised', it can be seen the event took place in the past. It is correct.✔️

​

📌Correct sentence: Having heard the news, he quickly sold his brother's record collection.✔️

​📌Correct sentence: Having been promised a steak dinner, she looked less than impressed with her Happy Meal. ✔️

The correct answer is Option 1)i.e. 1 has an error.

Key Points

• The infinitive is the base form of a verb. In English, when we talk about the infinitive we are usually referring to the present infinitive, which is the most common.
• The to-infinitive is used in many sentence constructions, often expressing the purpose of something or someone's opinion about something. The to-infinitive is used following a large collection of different verbs as well.
• In some cases 'to' has the same meaning as 'in order to' or 'so as to'.
• Example: They came to collect their bonus cheques.
• This means that they were here ' in order to ' collect the bonus cheques.
• The sentence stated in 1, 'I managed reach the top of the hill before sunset on the beautiful mountain peak.' is incorrect.❌
• The sentence stated in 2, 'I hope to see you next week before the presentation commences.' is correct.✔️
• The word 'reach' means to arrive at a place.
• When you use an infinitive verb, the "to" is a part of the verb. It is not acting as a preposition in this case.
• In sentence 1, we should add 'to' before managed.✔️
• The form should be: to-infinitive = to + base verb
• The present infinitive base is the verb form you will find in a dictionary, it can be written as:

• So in the given sentence 1, we should write 'I managed to reach the top of the hill before sunset on the beautiful mountain peak.**'

​📌Correct sentence**:** I managed to reach the top of the hill before sunset on the beautiful mountain peak.✔️

​📌Correct sentence: I hope to see you next week before the presentation commences.✔️

The correct answer is "Neither 1 nor 2 has an error"

Key Points

• The gerund looks exactly the same as a present participle, but it is useful to understand the difference between the two. The gerund always has the same function as a noun (although it looks like a verb).
• Example: Hunting is a dangerous sport.
• The word 'hunting' is used as a noun in the sentence although Hunt + ing seems to be a verb in itself.
• Phrasal verbs are phrases that indicate actions. They are generally used in spoken English and informal texts.
• Examples of such verbs include: turn down, come across and run into.
• Phrasal verbs are composed of a verb + preposition or adverb.
• The gerund must be used when a verb comes after a preposition. This is also true of certain expressions ending in a preposition,
• For example the expressions 'in spite of' & 'there's no point in'.
• Example: His mother is his model. She is the person he looks up to.
• Here 'look up to' is the phrasal verb in the sentence.
• In the given sentences (1 and 2) while sentence 1 is correct 'Jenny rang earlier and asked after you, so I told her you were fine.', the phase verb in the given sentence asked after (Enquire about someone’s health, how life is going.)
• Sentence 2 is  also correct, 'The crowd backed away when the man pulled out a knife.'
• Here, 'backed away' means that the crowd steeped backward upon seeing the knife.

​

Correct sentence: Jenny rang earlier and asked after you, so I told her you were fine.

​Correct sentence: The crowd backed away when the man pulled a knife.

The correct answer is Option 1)i.e. 1 has an error. 

Key Points

• A participle is a word that is partly a verb and partly an adjective.
• Example: Hearing a loud noise, the boy woke up.
• Here the word 'hearing' qualifies the noun boy as an adjective does. It is formed from the verb hear and has an object 'noise'. The word 'hearing', therefore, has the properties of a verb and an adjective and is called a participle.
• Present participles end in -ing and represent an action as going on or incomplete or imperfect. Present participles formed from transitive verbs, take objects.
• Example: Knocking at the door, he demanded admission
• Here, knocking is a present participle and it represents the action of repeated knocks that are still going on at the current time.
• The past participle usually ends in -ed, -d, -t, -en or -n. It represents a completed action or state.
• ​Example: Driven by rain, we took shelter under a tree.
• Here, 'drive + en' is talking about an action (of driving ) that took place and was completed in the past.
• In sentence 1,'You should not waste your time staring at close doors. Try out something meaningful' The use of 'close' is incorrect.❌
• 'closed' should be the correct past participle that is used with 'doors' to indicate that options that do not exist should not be pursued. So it is correct.✔️
• Sentence 2, 'The risen sun blocked the moon completely for two years on the planet Minerav'.
• In sentence 2 'risen' denotes the past participle in which (the sun hid the moon) as it can be seen the event took place in the past. It is correct.✔️

​

📌Correct sentence: You should not waste your time staring at closed doors. Try out something meaningful.✔️

​📌Correct sentence: The risen sun blocked the moon completely for two years on the planet Minerav. ✔️

There is no doubt that this passage is related to technology, and the particular organisation in question is 'Google.' This is introduced to us in sentence R.

The next sentence must be P where it says that ‘the 20-year old mission’ is referring to the mission of making the search engine more intuitive. This tells us how they are going to achieve it.

The third sentence is T as this sentence starts with ‘to.’

The fourth sentence is Q. Since the paragraph has already introduced us to ‘Google’ now it is referring to it as ‘the search engine.’  This sentence tells us what they want to achieve and what their focus areas will be.

Finally, the fifth sentence will be S. 

Thus, the correct chronological order for the passage is RPTQS.

There is no doubt that this passage is related to technology, and the particular organisation in question is 'Google.' This is introduced to us in sentence R.

The next sentence must be P where it says that ‘the 20-year old mission’ is referring to the mission of making the search engine more intuitive. This tells us how they are going to achieve it.

The third sentence is T as this sentence starts with ‘to.’

The fourth sentence is Q. Since the paragraph has already introduced us to ‘Google’ now it is referring to it as ‘the search engine.’  This sentence tells us what they want to achieve and what their focus areas will be.

Finally, the fifth sentence will be S. 

Thus, the correct chronological order for the passage is RPTQS.

There is no doubt that this passage is related to technology, and the particular organisation in question is 'Google.' This is introduced to us in sentence R.

The next sentence must be P where it says that ‘the 20-year old mission’ is referring to the mission of making the search engine more intuitive. This tells us how they are going to achieve it.

The third sentence is T as this sentence starts with ‘to.’

The fourth sentence is Q. Since the paragraph has already introduced us to ‘Google’ now it is referring to it as ‘the search engine.’  This sentence tells us what they want to achieve and what their focus areas will be.

Finally, the fifth sentence will be S. 

Thus, the correct chronological order for the passage is RPTQS.

There is no doubt that this passage is related to technology, and the particular organisation in question is 'Google.' This is introduced to us in sentence R.

The next sentence must be P where it says that ‘the 20-year old mission’ is referring to the mission of making the search engine more intuitive. This tells us how they are going to achieve it.

The third sentence is T as this sentence starts with ‘to.’

The fourth sentence is Q. Since the paragraph has already introduced us to ‘Google’ now it is referring to it as ‘the search engine.’  This sentence tells us what they want to achieve and what their focus areas will be.

Finally, the fifth sentence will be S. 

Thus, the correct chronological order for the passage is RPTQS.

There is no doubt that this passage is related to technology, and the particular organisation in question is 'Google.' This is introduced to us in sentence R.

The next sentence must be P where it says that ‘the 20-year old mission’ is referring to the mission of making the search engine more intuitive. This tells us how they are going to achieve it.

The third sentence is T as this sentence starts with ‘to.’

The fourth sentence is Q. Since the paragraph has already introduced us to ‘Google’ now it is referring to it as ‘the search engine.’  This sentence tells us what they want to achieve and what their focus areas will be.

Finally, the fifth sentence will be S. 

Thus, the correct chronological order for the passage is RPTQS.

Calculation:

l. 2x² + 23x + 56 = 0

⇒ 2x² + 16x + 7x + 56 = 0

⇒ 2x(x + 8) + 7(x + 8) = 0

⇒ (2x + 7) (x + 8) = 0

⇒ x = -7/2, -8

ll. 12y² + 41y + 35 = 0

⇒ 12y² + 21y + 20y + 35 = 0

⇒ 3y(4y + 7) + 5(4y + 7) = 0

⇒ (3y + 5) (4y + 7) = 0

⇒ y = -5/3, -7/4

Comparison between x and y (via Tabulation):

∴ The result will be x < y.

I. 2x2 – 7x + 3 = 0

⇒ 2x² - 6x - x + 3 = 0

⇒ 2x (x - 3) - 1 (x - 3) = 0

⇒ (2x - 1) (x - 3) = 0

So, x = 1/2, x = 3

II. 2y2 – 9y + 4 = 0

⇒ 2y² - 8y - y + 4 = 0

⇒ 2y (y - 4) - 1 (y - 4) = 0

⇒ (y - 4) (2y - 1) = 0

So, y = 4, y = 1/2

Hence, the relation between x and y cannot be established

I. 2x² + 7x + 3 = 0

⇒ 2x² + x + 6x + 3 = 0

⇒ x(2x + 1) + 3(2x + 1) = 0

⇒ (x + 3)(2x + 1) = 0

Then, x = (-3) or x = (-1/2)

II. 4y² + 16y + 15 = 0

⇒ 4y² + 6y + 10y + 15 = 0

⇒ 2y(2y + 3) + 5(2y + 3) = 0

⇒ (2y + 5)(2y + 3) = 0

Then, y = (-5/2) or y = (-3/2)

So, when x = (-1/2), x > y for y = (-5/2) and x > y for y = (-3/2)

And when x = (-3), x < y for y = (-5/2) and x < y for y = (-3/2)

∴ So, the relationship can not be determined.

First we have to find the value of y

II. y² + 46y + 529 = 0

⇒ y² + 2 × 23y + 23² = 0

⇒ (y + 23)² = 0

⇒ y = -23

Now, we can find the value of x

I. x³ = y + 239

⇒ x³ = -23 + 239

⇒ x³ = 216

⇒ x = 6

∴ x > y

I. 16x² + 20x + 6 = 0

⇒ 16x² + 12x + 8x + 6 = 0

⇒ 4x(4x + 3) + 2(4x + 3) = 0

⇒ (4x + 2) (4x + 3) = 0

⇒ x = (-2/4) or x = (-3/4)

II. 10y² + 38y + 24 = 0

⇒ 10y² + 30y + 8y + 24 = 0

⇒ 10y(y + 3) + 8(y + 3) = 0

⇒ (10y + 8)(y + 3) = 0

⇒ y = (-8/10) or y = (-3)

So, when x = (-2/4), x > y for y = (-3) and x > y for y = (-8/10)

And when x = (-3/4), x > y for y = (-3) and x > y for y = (-8/10)

∴ x > y

Calculation:

The logic behind the given series is as follows:

300 + 45 = 345

345 + 90 = 435

435 + 135 = 570

570 + 180 = 750

750 + 225 = 975

975 + 270 = 1245

∴ The value of '?' is 435.

The series follows the following pattern:

15 + 2³ = 23

23 + 3² = 32

32 + 5³ = 157

157 + 7² = 206

206 + 11³ = 1537

The series follows the following pattern:

540 - 11² = 419

419 - 7² = 370

370 - 5² = 345

345 - 3² = 336

336 - 2² = 332

The series follows the following pattern:

0.5 × 0.5 = 0.25

1.5 × 1.5 = 2.25

2.5 × 2.5 = 6.25

3.5 × 3.5 = 12.25

4.5 × 4.5 = 20.25

5.5 × 5.5 = 30.25

The pattern followed by the series is

2 × 4 + 1 = 9

9 × 4 + 3 = 39

39 × 4 + 5 = 161

161 × 4 + 7 = 651

651 × 4 + 9 = 2613

Given 

 In 2015, Number of students studying Science, Music and Commerce = 720

 In 2015, Number of students studying Commerce = 120

Formula:

Difference of students in a year =( Music students – Commerce students)

Calculation

Number of students studying Science and Music together in 2015 = 720 – 120 = 600

According to question,

Difference of Science and Music student in 2015 = 100

Music students in 2015 = 500 / 2 = 250

And Science students in 2015 = 250 + 100 = 350

So, the required difference = 250 – 120 = 130

∴ Difference between Commerce and Music students in 2015 is  130.

Given 

In 2018, number of students in Science, Music and Commerce = 600

In 2018, number of students in Commerce = 240

Ratio of number of student in Science and Music = 5 ∶ 7

Formula

Required % =( student in Music / total number of students) × 100

Calculation

In 2018, number of students in Science and Music = 600 – 240 = 360

Ratio of Science and Music students = 5 ∶ 7

So, the number of Music students = 360 × 7 / 12 = 210

Required percent = 210 × 100 / 600 = 35%

∴ Number of students In Music is 35% of total students in year 2018.

Given

Number of students of Science, Music and Commerce in 2020 = 450

Number of students of Commerce in 2020 = 160

Science students in 2021 = 150

Formula

Required ratio = number of students in Science ∶ number of students in Commerce

Calculation

Number of students of Science and Music in 2020 together = 450 – 160 = 290

According to the question,

In 2021, Science students = 150, which is 60% of Music students in 2020

Music students in 2020 = 150 × 100 / 60 = 250

Science students in 2020 = 290 – 250 = 40

The ratio between science to commerce students in 2020 = 40 ∶ 160 ⇒ 1 ∶ 4

∴ Ratio of Science and Commerce students is 1 ∶ 4.

Given that:

Total students of Science, Music and Commerce in 2017 = 420

Commerce student in 2015 = 120

Total students of Science, music and Commerce in 2018 = 600

Commerce student in 2018 = 240

Formula:

Average = total students / number of years

Calculation:

Total students in 2014 = 130% of total students studying in 2017

⇒ 130 × 420/100 = 546

Now, Commerce students in 2014 = 120 × 4/5 = 96

So, the number of students of Science and Music in 2014 = 546 – 96 = 450

The number of students of Science and Music in 2018 = 600 – 240 = 360

Required average = (450 + 360)/2 = 810/2 = 405

∴ the average of total number of Science and Music student in 2014 and 2018 is 405.

Given 

Total students of Science, Music and Commerce in 2016 = 540

Students of Commerce in 2016 = 200

Total students of Science, Music and Commerce in 2018 = 600

Students of Commerce in 2018 = 240

Formula

Total student of Science and Music in 2016 and 2018 = number of student of Science and Music in 2016 + number of student of Science and Music in 2018

Calculation

Number of students of Science and Music in 2016 = 540 – 200 = 340

Number of students of Science and Music in 2018 = 600 – 240 = 360

So, the total  students of Music and Science students in 2016 and 2018 together = 340 + 360 = 700.

∴ The required sum is 700.

Shortcut Trick

Change in Total Expenditure = (25 × 50) − (15 × 70) = 1250 − 1050 = Rs. 200.

Variable Cost per guest = 200 ÷ (25 − 15) = 200 ÷ 10 = Rs. 20.

Fixed Cost = Total − Variable = 1050 − (15 × 20) = Rs. 750.

For 75 guests: Total = 750 + (75 × 20) = 750 + 1500 = Rs. 2250.

Average = 2250 ÷ 75 = Rs. 30.

∴ The correct answer is Rs. 30.

Alternate Method

Given: Average for 15 guests = Rs. 70 | Average for 25 guests = Rs. 50.

Formula Used: Total Expenditure = Fixed Cost + (Variable Cost × Number of Guests).

⇒ Total Exp₁ = 15 × 70 = Rs. 1050

⇒ Total Exp₂ = 25 × 50 = Rs. 1250

⇒ Variable Cost per guest (V) = (1250 − 1050) ÷ (25 − 15) = 200 ÷ 10 = Rs. 20

⇒ Fixed Cost (F) = 1050 − (15 × 20) = 1050 − 300 = Rs. 750

⇒ Total Exp for 75 guests = 750 + (75 × 20) = 750 + 1500 = Rs. 2250

⇒ Average Exp per guest = 2250 ÷ 75 = Rs. 30

∴ The correct answer is Rs. 30.

Additional Information

Fixed and Variable Expenses

Total Cost = Fixed Cost + (Variable Cost per unit × Number of units). Fixed cost remains constant regardless of production volume.

Average Expenditure Formula

Average Expenditure = Total Expenditure ÷ Total Number of Guests. As guests increase, the fixed component per guest decreases.

Shortcut Trick

Revenue = Rate × Sale

Use effective percentage change formula: a + b + (ab/100)

Rate change (a) = +12.5% | Sale change (b) = −25%

Change = 12.5 − 25 + [(12.5 × −25) ÷ 100] = −12.5 − 3.125 = −15.625%

∴ The correct answer is −15.625%.

Alternate Method

Given:

Increase in Rate = 12.5% = 1/8 (Fraction)

Decrease in Sale = 25% = 1/4 (Fraction)

Calculation:

⇒ Let initial Rate = 8 units and initial Sale = 4 units

⇒ Initial Revenue = 8 × 4 = 32 units

⇒ New Rate = 8 + 1 = 9 units

⇒ New Sale = 4 − 1 = 3 units

⇒ New Revenue = 9 × 3 = 27 units

⇒ Change in Revenue = 27 − 32 = −5 units

⇒ Percentage Change = (−5 ÷ 32) × 100

⇒ Percentage Change = −15.625%

∴ The correct answer is −15.625%.

Additional Information

Successive Percentage Formula

For two successive changes a% and b%, the net change is [a + b + (ab/100)]%.

Fraction Conversion

Converting percentages to fractions (like 12.5% = 1/8) simplifies calculations involving products of variables.

Revenue Relation

If Total = A × B, then any percentage change in A or B directly impacts the Total multiplicatively.

Shortcut Trick

Present sum of Father, Mother, and Son = (30 × 3) + (3 × 6) = 90 + 18 = 108 years.

Total present sum (including Daughter) = 29 × 4 = 116 years ⇒ Daughter age = 116 − 108 = 8 years.

Present sum of Father and Mother = 46 × 2 = 92 years.

Son present age = 108 − 92 = 16 years.

Difference = 16 − 8 = 8 years.

∴ The correct answer is 8 years.

Alternate Method

Given: Average age of Father, Mother, and Son 6 years ago = 30 years.

Formula: Total Age = Average Age × Number of Members

⇒ Sum of ages of Father (F), Mother (M) and Son (S) 6 years ago = 30 × 3 = 90 years.

⇒ Present sum of ages (F + M + S) = 90 + (3 × 6) = 108 years.

⇒ Present sum of all 4 members (F + M + S + Daughter) = 29 × 4 = 116 years.

⇒ Present age of Daughter (D) = 116 − 108 = 8 years.

⇒ Present sum of Father and Mother = 46 × 2 = 92 years.

⇒ Present age of Son (S) = (F + M + S) − (F + M) = 108 − 92 = 16 years.

⇒ Difference = Age of Son − Age of Daughter = 16 − 8 = 8 years.

∴ The correct answer is 8 years.

Additional Information

Average Age Shift

If the average age of n members is x years today, then n years ago it was (x − n) and n years later it will be (x + n).

Weighted Average

Combined Average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂) where n is the number of items and x is the average.

Shortcut Trick

Difference in Rate of Interest = 7% − 5% = 2% per annum.

Difference in Interest for 2 years = 2% × 2 = 4% of the sum.

Given, 4% of Sum = ₹80.

⇒ 1% of Sum = ₹20.

⇒ 100% (Sum) = ₹20 × 100 = ₹2000.

∴ The correct answer is ₹2000.

Alternate Method

Given: Rate for A (R₁) = 5%, Rate for B (R₂) = 7%, Time (T) = 2 years, Difference in Interest = ₹80.

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

⇒ Let the Sum be P.

⇒ Interest for B − Interest for A = 80

⇒ [(P × 7 × 2) ÷ 100] − [(P × 5 × 2) ÷ 100] = 80

⇒ (14P − 10P) ÷ 100 = 80

⇒ 4P ÷ 100 = 80

⇒ P = (80 × 100) ÷ 4

⇒ P = 20 × 100 = 2000

∴ The correct answer is ₹2000.

Additional Information

Simple Interest Principle

Simple interest is calculated only on the Principal amount. The formula is SI = (P×R×T)/100.

Amount in SI

The total amount (A) after T years is the sum of Principal and Interest: A = P + SI = P[1 + (RT/100)].

Direct Variation

Simple interest varies directly with Rate and Time if the Principal remains constant.

Shortcut Trick

Total target = 2000 pieces in 5 days → 400 pieces/day.

Current daily work: J = 100, I = 100 × (4/5) = 80, H = 80 × 1.5 = 120.

Total daily pieces = 100 + 80 + 120 = 300 pieces in 9 hours.

To reach 400 pieces, time required = (400 ÷ 300) × 9 = 12 hours.

Extra hours = 12 − 9 = 3 hours.

∴ The correct answer is 3 hr.

Alternate Method

Given: Target = 2000 pieces in 5 days; Total time = 9 hours/day; J = 100 pieces/day.

Formula: Work = Efficiency × Time; Extra hours = Required time − Available time.

⇒ Efficiency of J = 100 pieces / 9 hours.

⇒ Ratio of I : J = 4 : 5 ∴ Efficiency of I = (4/5) × 100 = 80 pieces / 9 hours.

⇒ H is 50% more efficient than I ∴ Efficiency of H = 1.5 × 80 = 120 pieces / 9 hours.

⇒ Combined pieces per day = 100 + 80 + 120 = 300 pieces in 9 hours.

⇒ Target pieces per day = 2000 ÷ 5 = 400 pieces.

⇒ Total hours needed for 400 pieces = (400 ÷ 300) × 9 = 12 hours.

⇒ Extra hours = 12 − 9 = 3 hours.

∴ The correct answer is 3 hr.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to time taken for a fixed amount of work. If efficiency increases by 50% (ratio 3:2), the time taken decreases (ratio 2:3).

Work-Time Multiplier

The formula M₁D₁H₁ / W₁ = M₂D₂H₂ / W₂ is used when the number of men, days, or hours changes relative to the work volume.

Calculation:

Percentage of Bajaj bikes sold = 30%

Percentage of TVS bikes sold = 15%

Difference between % of Bajaj and TVS bikes sold = (30 - 15)%

⇒ Difference between % of Bajaj and TVS bikes sold = 15%

Difference in number of Bajaj and TVS bikes sold = 15% of 25000

⇒ (15 / 100) × 25000

⇒ 3750

∴ Difference in number of Bajaj and TVS bikes sold is 3750

Calculation:

Total number of bikes sold in 2019 = 25000

Percentage of Honda bikes sold = 25%

Number of Honda bikes sold = 25% × 25000

⇒ Number of Honda bikes sold = 6250

Percentage of Suzuki bikes sold = 10%

Number of Suzuki bikes sold = 10% × 25000

⇒ Number of Suzuki bikes sold = 2500

Now, Honda bikes sold is what % of the Suzuki bikes sold = (6250 / 2500) × 100

⇒ 250%

∴ Honda bikes sold is 250% of the Suzuki bike sold

Alternate solution:

(Percentage of Honda bikes / Percentage of Suzuki bikes) × 100

⇒ (25 / 10) × 100

⇒ 250%

Calculation:

Total number of bikes sold = 25000

Percentage of Hero bikes sold = 20%

Number of Hero bikes sold in 2019 = 20% × 25000

⇒ Number of Hero bikes sold = 5000

Now, Number of Hero bikes sold in 2018 = 80% of 5000

⇒ 4000

∴ Number of Hero bikes sold in 2018 is 4000

Alternate solution:

Total number of bikes sold in 2019 = 25000

Number of Hero bikes sold in 2018 = 20% of 80% × 25000

⇒ 4000

∴ Number of Hero bikes sold in 2018 is 4000

Calculation:

Total number of bikes sold in 2019 = 25000

Percentage of Bajaj bikes sold = 30%

Number of Bajaj bikes sold = 30% of 25000

⇒ Number of Bajaj bikes sold = 7500

∴ Number of Bajaj bikes sold in 2019 is 7500

Calculation:

Total number of bikes sold in 2019 = 25000

Percentage of Suzuki bikes sold = 10%

Number of Suzuki bikes sold = 10% × 25000

⇒ 2500

Percentage of Hero bikes sold = 20%

Number of Hero bikes sold = 20% × 25000

⇒ 5000

Number of Hero bikes - Number of Suzuki bikes = (5000 - 2500)

⇒ 2500

Less % = (2500 / 5000) × 100

⇒ 50%

The number of Suzuki bikes is 50% less than number of Hero bikes

Alternate solution:

Percentage of Suzuki bikes = 10%

Percentage of Hero bikes = 20%

Less % = (20 - 10) / 20 × 100

⇒ Less % = 50%

Number of Suzuki bikes is 50% less than number of Hero bikes in 2019

Shortcut Trick

Milk concentration in Container 1 = 3/7 and in Container 2 = 5/11.

Resultant Milk concentration = 4/9.

Using Alligation (Milk): |5/11 − 4/9| : |3/7 − 4/9| ⇒ 1/99 : 1/63 ⇒ 7 : 11.

Total ratio parts = 7 + 11 = 18 units = 18 L ∴ 1 unit = 1 L.

Quantity of 1st mixture = 7 L. Milk in it = 7 × (3/7) = 3 L.

∴ The correct answer is 3 L.

Alternate Method

Given: Ratio 1 = 3:4, Ratio 2 = 5:6, Final Ratio = 4:5, Total Volume = 18 L.

Formula: Quantity₁ × (C₁ − C_m) = Quantity₂ × (C_m − C₂)

⇒ Let Q₁ and Q₂ be the volumes of the two containers.

⇒ Milk fraction: Q₁(3/7) + Q₂(5/11) = (Q₁ + Q₂)(4/9)

⇒ Q₁(4/9 − 3/7) = Q₂(5/11 − 4/9)

⇒ Q₁(1/63) = Q₂(1/99) ⇒ Q₁/Q₂ = 63/99 = 7/11

⇒ Total units = 7 + 11 = 18 → 18 L ∴ Q₁ = 7 L

⇒ Milk in 1st container = 7 × (3 / (3 + 4)) = 7 × 3/7 = 3 L

∴ The correct answer is 3 L.

Additional Information

Alligation Rule

Used to find the ratio in which two ingredients at given prices/concentrations are mixed to produce a mixture of a mean price. Ratio = (Dearer − Mean) : (Mean − Cheaper).

Replacement Method

When a quantity is replaced repeatedly: Final Concentration = Initial Concentration × (1 − x/V)ⁿ, where x is replaced volume and V is total volume.

Multiple Mixtures

When mixing multiple containers, the total quantity of a component (milk) is the sum of quantities from each container: Σ(Ratio × Volume).

Shortcut Trick

Since time is constant, speed is directly proportional to distance (S ∝ D).

Ratio of lengths of platforms = 5 : 3.

Since the train length is negligible, ratio of speeds = ratio of distances = 5 : 3.

Percentage increase in speed = (Difference / Initial Speed) × 100.

Percentage increase = [(5 − 3) / 3] × 100 = (2 / 3) × 100 ≈ 66.66%.

∴ The correct answer is 67%.

Alternate Method

Given: Ratio of platform lengths L₁ : L₂ = 5 : 3. Time T is constant. Train length is negligible.

Formula Used: Speed (S) = Distance (D) / Time (T)

⇒ Let the length of the shorter platform be 3x and the longer platform be 5x.

⇒ Let the time taken in both cases be T.

⇒ Speed for longer platform S₁ = 5x / T.

⇒ Speed for shorter platform S₂ = 3x / T.

⇒ Percentage increase in speed = [(S₁ − S₂) / S₂] × 100.

⇒ [(5x/T − 3x/T) / (3x/T)] × 100 = (2 / 3) × 100 = 66.66%.

∴ The correct answer is 67%.

Additional Information

Relative Speed

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

Train crossing objects

When a train crosses a platform, total distance = Train Length + Platform Length. When it crosses a pole/point object, distance = Train Length.

Proportionality in Speed, Distance, Time

If Time is constant, D₁/D₂ = S₁/S₂. If Distance is constant, S₁/S₂ = T₂/T₁.

Shortcut Trick

Time taken Upstream (T_u) = 15 hours.

Time taken Downstream (T_d) = 15 − 6 = 9 hours.

Ratio of time (Upstream : Downstream) = 15 : 9 = 5 : 3.

Since distance is constant, Ratio of Speed (Upstream : Downstream) = 3 : 5.

Speed of rower (u) = (5 + 3)/2 = 4 units; Speed of stream (v) = (5 − 3)/2 = 1 unit.

Given v = 1 unit = 4 km/hr → u = 4 units = 16 km/hr.

∴ The correct answer is 16 km/hr.

Alternate Method

Given: Upstream time (T_u) = 15 hours; Downstream time (T_d) = 15 − 6 = 9 hours; Stream speed (v) = 4 km/hr.

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

⇒ (u − 4) × 15 = (u + 4) × 9

⇒ 15u − 60 = 9u + 36

⇒ 15u − 9u = 36 + 60

⇒ 6u = 96

⇒ u = 96 ÷ 6 = 16 km/hr.

∴ The correct answer is 16 km/hr.

Additional Information

Still Water Speed Formula

Speed of rower in still water (u) = (Downstream Speed + Upstream Speed) ÷ 2.

Stream Speed Formula

Speed of current/stream (v) = (Downstream Speed − Upstream Speed) ÷ 2.

Relative Speed in Boats

Downstream speed (D) is always greater than Upstream speed (U) because the current aids the rower.

Shortcut Trick

Ratio of Profit = Ratio of (Investment × Time).

Total Profit = 3600, C share = 1000 ⇒ (A+B) share = 2600.

A (7×400 + 5×700) + B (7×900 + 5×600) = 2800 + 3500 + 6300 + 3000 = 15600 units.

Since 2600 profit corresponds to 15600 units, 1000 profit corresponds to (15600 ÷ 2600) × 1000 = 6000 units.

Total Investment of C over 12 months = 6000 units.

∴ The correct answer is Rs. 6000.

Alternate Method

Given → Initial: A=400, B=900, C=400. Total Profit=3600, C profit=1000. Formulas: Profit Ratio = (I₁×T₁) : (I₂×T₂) : (I₃×T₃).

Steps: ⇒ Calculate equivalent investment for A: (400 × 7) + (700 × 5) = 2800 + 3500 = 6300 units. ⇒ Calculate equivalent investment for B: (900 × 7) + (600 × 5) = 6300 + 3000 = 9300 units. ⇒ Total units for A and B = 6300 + 9300 = 15600 units. ⇒ Profit share of (A+B) = Total Profit − C profit = 3600 − 1000 = 2600. ⇒ Ratio (A+B):C = 2600:1000 = 26:10 = 13:5. ⇒ 13 parts = 15600 ⇒ 1 part = 1200. ⇒ Total investment of C (for 12 months) = 5 parts × 1200 = 6000 units.

∴ The correct answer is Rs. 6000.

Additional Information

Partnership Ratios

In a partnership, the profit is divided based on the product of the Capital and the Time for which it was invested.

Active vs Passive Partner

An Active partner manages the business and may receive a salary or commission before the profit is split among all partners.

Shortcut Trick

Total items given = 10 + 1 = 11 shirts. Marked Price (MP) of 11 shirts = 11 × 310/9 = 3410/9.

Discount of 10% on 10 shirts bought: Total SP = (MP of 10 shirts) × 90/100 = (10 × 310/9) × 0.9 = 310.

Profit = SP − CP of 11 shirts ⇒ 200 = 310 − (11 × CP_unit).

11 × CP_unit = 310 − 200 = 110.

CP_unit = 110 ÷ 11 = 10.

∴ The correct answer is Rs. 10.

Alternate Method

Given → Marked Price (MP) of 1 shirt = Rs. 310/9, Free items = 1 per 10, Cash Discount = 10%, Total Profit = Rs. 200. Formulas: Total SP = (MP × Quantity Paid) × (100 − D%)/100 | Total CP = CP_unit × Total Quantity | Profit = Total SP − Total CP.

⇒ Total Selling Price (SP) for 10 shirts = 10 × (310/9) × (90/100) = 310. ⇒ Total Cost Price (CP) for 11 shirts = Total SP − Profit = 310 − 200 = 110. ⇒ CP of 1 shirt = Total CP ÷ Total Quantity = 110 ÷ 11 = 10.

∴ The correct answer is Rs. 10.

Additional Information

Free Item Calculation

When a shopkeeper gives 'x' items free on purchase of 'y' items, the effective discount is [x / (x + y)] × 100.

Profit and Loss on Total Transaction

Profit is always calculated on the total number of items that leave the shop (CP of all items) versus the total money received (SP of paid items).

Shortcut Trick

Let breadth of rectangle (and base of triangle) be B.

Area difference: (18 × B) − (1/2 × B × 20) = 96

⇒ 18B − 10B = 96 ⇒ 8B = 96 ⇒ B = 12 m.

Perimeter = 2(L + B) = 2(18 + 12) = 60 m.

∴ The correct answer is 60 m.

Alternate Method

Given:

Length (L) = 18 m, Height (H) = 20 m, Base (b) = Breadth (B).

Formula Used:

Area of Rectangle = L × B | Area of Triangle = 1/2 × b × H

Calculations:

⇒ Area of Rectangle − Area of Triangle = 96

⇒ (18 × B) − (1/2 × B × 20) = 96

⇒ 18B − 10B = 96

⇒ 8B = 96

⇒ B = 12 m

⇒ Perimeter = 2 × (18 + 12)

⇒ Perimeter = 2 × 30 = 60 m

∴ The correct answer is 60 m.

Additional Information

Perimeter and Area of Rectangle

Perimeter = 2(l + b) and Area = l × b. Diagonal d = √(l² + b²).

Triangle Area Properties

General Area = 1/2 × base × height. For an equilateral triangle, Area = (√3/4) × side².

Mensuration Conversion

Always ensure all dimensions (length, breadth, height) are in the same unit before calculation.

Shortcut Trick

Total ways to select 2 cards from 52 = ⁵²C₂ = (52 × 51) ÷ 2 = 26 × 51

Favorable ways (1 Spade and 1 Heart) = 13 × 13

Probability = (13 × 13) ÷ (26 × 51) = 13 ÷ (2 × 51) = 13/102

∴ The correct answer is 13/102.

Alternate Method

Given: Total cards = 52, Spades = 13, Hearts = 13.

Formula: P(E) = n(E) ÷ n(S)

⇒ Total outcomes n(S) = ⁵²C₂ = (52 × 51) ÷ (2 × 1) = 1326

⇒ Favorable outcomes n(E) = ¹³C₁ × ¹³C₁ = 13 × 13 = 169

⇒ Probability = 169 ÷ 1326

⇒ Dividing both by 13: 13 ÷ 102

∴ The correct answer is 13/102.

Additional Information

Combinations Formula

The number of ways to select r items from n is given by ⁿC_r = n! ÷ [r!(n−r)!].

Standard Deck Composition

A deck has 4 suits: Spades, Hearts, Diamonds, and Clubs, each containing 13 cards.

Probability of Success

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

Shortcut Trick

Total weight = 150 grams, Weight of third piece = 20 grams.

Remaining weight for first two pieces = 150 − 20 = 130 grams.

Ratio of 1^st : 2^nd = 8 : 5 → Total units = 13 units.

13 units = 130 grams ⇒ 1 unit = 10 grams.

Weight of first piece = 8 units = 8 × 10 = 80 grams.

∴ The correct answer is 80 g.

Alternate Method

Given:

Total weight = 150 grams

Weight of 3^rd piece = 20 grams

Ratio of 1^st : 2^nd piece = 8 : 5

Calculations:

⇒ Weight of (1^st + 2^nd) pieces = Total Weight − 3^rd Piece

⇒ Weight of (1^st + 2^nd) = 150 − 20 = 130 grams

⇒ Let the weights be 8x and 5x

⇒ 8x + 5x = 130

⇒ 13x = 130

⇒ x = 10

⇒ Weight of first piece = 8x = 8 × 10 = 80 grams

∴ The correct answer is 80 g.

Additional Information

Ratio and Proportion

To divide a quantity Q in ratio a:b, the parts are [a/(a+b)] × Q and [b/(a+b)] × Q.

Weight and Value Relationship

In advanced diamond problems, Value ∝ (Weight)². If a diamond breaks, the total weight remains conserved but total value decreases.

Unit Conversion

Always ensure units are consistent (e.g., all values in grams) before performing arithmetic operations.

Shortcut Trick

Total buckets filled by Ram and Shyam in 1 hour = 10 + 15 = 25 buckets.

Total buckets to fill the cistern = 25 buckets/hour × 8 hours = 200 buckets.

Total capacity of the cistern = 200 buckets × 50 liters/bucket = 10,000 liters.

Total buckets drawn by Anil in 50 hours = 2 buckets/hour × 50 hours = 100 buckets.

Since 100 buckets empty the whole 10,000 liters cistern, Capacity of 1 bucket = 10,000 ÷ 100 = 100 liters.

∴ The correct answer is 100 liters.

Alternate Method

Given: Capacity of Ram/Shyam's bucket = 50 liters. Ram's rate = 10 buckets/hr. Shyam's rate = 15 buckets/hr. Total time = 8 hrs. Anil's emptying time = 50 hrs. Anil's rate = 2 buckets/hr.

Formula Used: Total Capacity = Rate × Bucket Volume × Time

⇒ Total buckets filled by both per hour = 10 + 15 = 25 buckets

⇒ Volume of water filled in 1 hour = 25 × 50 = 1250 liters

⇒ Total capacity of cistern = 1250 × 8 = 10,000 liters

⇒ Total buckets used by Anil to empty it = 2 buckets/hr × 50 hr = 100 buckets

⇒ Capacity of Anil's bucket = 10,000 / 100 = 100 liters

∴ The correct answer is 100 liters.

Additional Information

Pipes and Cisterns Logic

Total Capacity = Efficiency × Time. For emptying pipes, the work done is considered negative in net flow calculations.

Unitary Method for Capacity

If N buckets of volume V fill a tank, then Capacity = N × V. If the tank is constant, N₁V₁ = N₂V₂.

Shortcut Trick

Total Pass % = (Pass in Math + Pass in Stats) − Pass in Both

Total Pass % = (68% + 62%) − 40% = 130% − 40% = 90%

Fail % in both = 100% − 90% = 10%

10% of Total Candidates = 30 ⇒ Total = 300

∴ The correct answer is 300 candidates.

Alternate Method

Given:

Passed in Mathematics n(M) = 68%

Passed in Statistics n(S) = 62%

Passed in both subjects n(M ∩ S) = 40%

Number of candidates failed in both = 30

Formula Used:

n(M ∪ S) = n(M) + n(S) − n(M ∩ S)

Calculations:

⇒ Total Pass % = 68% + 62% − 40%

⇒ Total Pass % = 90%

⇒ Total Fail % = 100% − 90% = 10%

⇒ Let total candidates be X

⇒ 10% of X = 30

⇒ (10/100) × X = 30

⇒ X = 30 × 10 = 300

∴ The correct answer is 300 candidates.

Additional Information

Venn Diagram Concept

The union of two sets A and B is given by n(A ∪ B) = n(A) + n(B) − n(A ∩ B). This represents individuals belonging to at least one category.

Percentage Base

Total candidates in such problems are always considered as 100%. Failed candidates in both = 100% − (Passed in at least one subject).

The information given can be represented as follows,

Thus, ‘we’ is coded as ‘ac’.

The information given can be represented as follows,

Hence, ‘strict’ is coded by either 'ea' or 'ae’.

The information given can be represented as follows,

The code ‘cc’ is for ‘the’.

The information given can be represented as follows,

From the given options, 'bb ee' is the codes of ‘for efforts’.

The information given can be represented as follows,

 'ca ac cc' is the code for ‘we are the’.

Given statements,

S = U ≤ K < W, X < Q < S

On combining, we get:

X < Q < S = U ≤ K < W

Conclusions**:**

I. U < X → False (X < Q < S = U → X < U i.e. U > X).

II. W > Q → True (Q < S = U ≤ K < W → Q < W i.e. W > Q).

Hence, the correct answer is only conclusion II follows.

Given:

 Statements: H < Y < U ≥ Q = N > R; S = T ≥ G = V < H 

S = T ≥ G = V < H < Y < U ≥ Q = N > R

Conclusions: 

I. U > V - True (U > Y > H > V)

II. S ≥ Y - False (S = T ≥ G = V < H < Y, no relation between S and Y)

Hence, the answer is Only I follows.

Let us check each option:

1. E > F > M < X; S > M > K; K > Y < B → E > K; relation between S and B can’t be determined.

2. E > F = M < X; S > M > K; K > Y < B → E > K; relation between S and B can’t be determined.

3. E > F > M < X; S > M > K; K > Y > B → E > K; S > B as required.

4. E > F < M < X; S > M < K; K > Y ≥ B → relation between E and K can’t be determined; relation between S and B can’t be determined.

5. E > F < M < X; S > M > K; K > Y = B → relation between E and K can’t be determined; S > B.  

Hence, >, >, > are to be placed so that both E > K and S > B hold definitely true.

Putting all the signs step by step in place of & and @ we get:

R ≥ P > T ≥ S > K = L; W ≥ B < S - (R ≥ P > T ≥ S > B ≤ W) - R > W is False

R ≥ P > T < S > K = L; W > B < S - (R ≥ P > T < S > B < W) - R > W is False

R ≥ P > T = S > K = L; W < B < S -  (R ≥ P > T = S > B > W) - R > W is True

R ≥ P > T ≤ S > K = L; W > B < S -  **(**R ≥ P > T ≤ S > B < W) - R > W is False

R ≥ P > T ≤ S > K = L; W ≤ B < S -  **(**R ≥ P > T ≤ S > B ≥ W) - R > W is False

Hence, the correct answer is '=, <'.

Given: Ten students are sitting on two parallel benches, student sitting on bench 1 are facing south and students sitting on bench 2 are facing north.

Bench 1: A, B, H, E and J

Bench 2: D, I, C, G and F

1) A is sitting at one of the extreme ends.

2) One student is sitting between A and H.

3. I is sitting to the left to the one who is sitting opposite to H.

4) There is 1 person between I and the one one whose roll number is 7.

5. G and C are immediate neighbours.

6) C is sitting left to the G but do not have roll number 7.

7) Roll number of E is 9.

8) Roll number of F is 5 and is sitting to the right of one who is sitting opposite to E.

9) Sum of roll numbers of A and E is 13.

Roll number of E is 9

→ Roll number of  A is 4

10) Sum of roll numbers of A and B is equals to 10. 

→ Roll number of B is 6

11. D is sitting opposite to the one whose roll number is 4.

Here, possibility 2 will be cancelled as place opposite to A is already occupied.

12. B is facing the one whose roll number is 3.

13) J has the last roll number. 

14)  Difference between roll numbers of the people sitting in extreme ends of bench 2 is 3.

Now, we have two possibilities to satisfy this condition:

i) Roll number of D is 2, or

ii) Roll number of D is 8

15)  The one with lesser roll number among these two is sitting at the left end of the bench. 

Now, we can conclude that, roll number of D must be 2.

16) Sum of roll numbers of the students sitting at bench one is 19 more than the sum of roll numbers of students sitting at bench 2.

So, the above shown arrangement is our final arrangement.

Hence, the roll number of B is 6.

Given: Ten students are sitting on two parallel benches, student sitting on bench 1 are facing south and students sitting on bench 2 are facing north.

Bench 1: A, B, H, E and J

Bench 2: D, I, C, G and F

1) A is sitting at one of the extreme ends.

2) One student is sitting between A and H.

3. I is sitting to the left to the one who is sitting opposite to H.

4) There is 1 person between I and the one whose roll number is 7.

5. G and C are immediate neighbours.

6) C is sitting left to the G but do not have roll number 7.

7) Roll number of E is 9.

8) Roll number of F is 5 and is sitting to the right of one who is sitting opposite to E.

9) Sum of roll numbers of A and E is 13.

Roll number of E is 9

→ Roll number of  A is 4

10) Sum of roll numbers of A and B is equals to 10. 

→ Roll number of B is 6

11. D is sitting opposite to the one whose roll number is 4.

Here, possibility 2 will be cancelled as place opposite to A is already occupied.

12. B is facing the one whose roll number is 3.

13) J has the last roll number. 

14)  Difference between roll numbers of the people sitting in extreme ends of bench 2 is 3.

Now, we have two possibilities to satisfy this condition:

i) Roll number of D is 2, or

ii) Roll number of D is 8

15)  The one with lesser roll number among these two is sitting at the left end of the bench. 

Now, we can conclude that, roll number of D must be 2.

16) Sum of roll numbers of the students sitting at bench one is 19 more than the sum of roll numbers of students sitting at bench 2.

So, the above shown arrangement is our final arrangement.

Hence, D is sitting at the left corner of the bench 2.

Given: Ten students are sitting on two parallel benches, student sitting on bench 1 are facing south and students sitting on bench 2 are facing north.

Bench 1: A, B, H, E and J

Bench 2: D, I, C, G and F

1) A is sitting at one of the extreme ends.

2) One student is sitting between A and H.

3. I is sitting to the left to the one who is sitting opposite to H.

4) There is 1 person between I and the one whose roll number is 7.

5. G and C are immediate neighbours.

6) C is sitting left to the G but do not have roll number 7.

7) Roll number of E is 9.

8) Roll number of F is 5 and is sitting to the right of one who is sitting opposite to E.

9) Sum of roll numbers of A and E is 13.

Roll number of E is 9

→ Roll number of  A is 4

10) Sum of roll numbers of A and B is equals to 10. 

→ Roll number of B is 6

11. D is sitting opposite to the one whose roll number is 4.

Here, possibility 2 will be cancelled as place opposite to A is already occupied.

12. B is facing the one whose roll number is 3.

13) J has the last roll number. 

14)  Difference between roll numbers of the people sitting in extreme ends of bench 2 is 3.

Now, we have two possibilities to satisfy this condition:

i) Roll number of D is 2, or

ii) Roll number of D is 8

15)  The one with lesser roll number among these two is sitting at the left end of the bench. 

Now, we can conclude that, roll number of D must be 2.

16) Sum of roll numbers of the students sitting at bench one is 19 more than the sum of roll numbers of students sitting at bench 2.

So, the above shown arrangement is our final arrangement.

Hence, A is sitting opposite to the one who is sitting left to I.

Given: Ten students are sitting on two parallel benches, student sitting on bench 1 are facing south and students sitting on bench 2 are facing north.

Bench 1: A, B, H, E and J

Bench 2: D, I, C, G and F

1) A is sitting at one of the extreme ends.

2) One student is sitting between A and H.

3. I is sitting to the left to the one who is sitting opposite to H.

4) There is 1 person between I and the one whose roll number is 7.

5. G and C are immediate neighbours.

6) C is sitting left to the G but do not have roll number 7.

7) Roll number of E is 9.

8) Roll number of F is 5 and is sitting to the right of one who is sitting opposite to E.

9) Sum of roll numbers of A and E is 13.

Roll number of E is 9

→ Roll number of  A is 4

10) Sum of roll numbers of A and B is equals to 10. 

→ Roll number of B is 6

11. D is sitting opposite to the one whose roll number is 4.

Here, possibility 2 will be cancelled as place opposite to A is already occupied.

12. B is facing the one whose roll number is 3.

13) J has the last roll number. 

14)  Difference between roll numbers of the people sitting in extreme ends of bench 2 is 3.

Now, we have two possibilities to satisfy this condition:

i) Roll number of D is 2, or

ii) Roll number of D is 8

15)  The one with lesser roll number among these two is sitting at the left end of the bench. 

Now, we can conclude that, roll number of D must be 2.

16) Sum of roll numbers of the students sitting at bench one is 19 more than the sum of roll numbers of students sitting at bench 2.

So, the above shown arrangement is our final arrangement.

Hence, 2 people are sitting between B and J.

Given: Ten students are sitting on two parallel benches, student sitting on bench 1 are facing south and students sitting on bench 2 are facing north.

Bench 1: A, B, H, E and J

Bench 2: D, I, C, G and F

1) A is sitting at one of the extreme ends.

2) One student is sitting between A and H.

3. I is sitting to the left to the one who is sitting opposite to H.

4) There is 1 person between I and the one whose roll number is 7.

5. G and C are immediate neighbours.

6) C is sitting left to the G but do not have roll number 7.

7) Roll number of E is 9.

8) Roll number of F is 5 and is sitting to the right of one who is sitting opposite to E.

9) Sum of roll numbers of A and E is 13.

Roll number of E is 9

→ Roll number of  A is 4

10) Sum of roll numbers of A and B is equals to 10. 

→ Roll number of B is 6

11. D is sitting opposite to the one whose roll number is 4.

Here, possibility 2 will be cancelled as place opposite to A is already occupied.

12. B is facing the one whose roll number is 3.

13) J has the last roll number. 

14)  Difference between roll numbers of the people sitting in extreme ends of bench 2 is 3.

Now, we have two possibilities to satisfy this condition:

i) Roll number of D is 2, or

ii) Roll number of D is 8

15)  The one with lesser roll number among these two is sitting at the left end of the bench. 

Now, we can conclude that, roll number of D must be 2.

16) Sum of roll numbers of the students sitting at bench one is 19 more than the sum of roll numbers of students sitting at bench 2.

So, the above shown arrangement is our final arrangement.

Let's check each option one by one.

1) B is sitting next to the right of A.:  False( B is sitting left to A.)

2) G is sitting at the centre of the bench facing north direction. : False(G is sitting in the right half of the table, not at the centre)

3) H whose roll number is 8 is sitting next to the one having roll number 9. : True

Hence, Option 3 is the correct one.

Preparing the family tree using the following symbols:

Hence, C is the sister of D.

Preparing the family tree using the following symbols:

Hence, C is the aunt of H.

Preparing the family tree using the following symbols:

Hence, H is the grandson of B.

A certain number of persons are sitting in a row facing south direction.

1)Two persons sit between A and D. A is in the right of D.

2. One person sits between B and A.

3. B is the fourth person from the right end. 

4. H sits second to the left of D, who sits exactly between E and B.

5. Neither A nor H sits at any extreme ends. 

6. G sits immediate left of E. Hence Case 1 gets canceled.

7. Number of persons to the left of G is equal to the number of persons to the right of B.

8. F sits at extreme end, which is closest to B.

Therefore, the final arrangement is, 

Hence, 18 persons sit in the row.

A certain number of persons are sitting in a row facing south direction.

1)Two persons sit between A and D. A is in the right of D.

2. One person sits between B and A.

3. B is the fourth person from the right end. 

4. H sits second to the left of D, who sits exactly between E and B.

5. Neither A nor H sits at any extreme ends. 

6. G sits immediate left of E. Hence Case 1 gets canceled.

7. Number of persons to the left of G is equal to the number of persons to the right of B.

8. F sits at extreme end, which is closest to B.

Therefore, the final arrangement is, 

Hence, The one who sits second to the left of B sits third to the right of D.

A certain number of persons are sitting in a row facing south direction.

1)Two persons sit between A and D. A is in the right of D.

2. One person sits between B and A.

3. B is the fourth person from the right end. 

4. H sits second to the left of D, who sits exactly between E and B.

5. Neither A nor H sits at any extreme ends. 

6. G sits immediate left of E. Hence Case 1 gets canceled.

7. Number of persons to the left of G is equal to the number of persons to the right of B.

8. F sits at extreme end, which is closest to B.

Therefore, the final arrangement is, 

Hence, Three persons sit to the left of G.

A certain number of persons are sitting in a row facing south direction.

1)Two persons sit between A and D. A is in the right of D.

2. One person sits between B and A.

3. B is the fourth person from the right end. 

4. H sits second to the left of D, who sits exactly between E and B.

5. Neither A nor H sits at any extreme ends. 

6. G sits immediate left of E. Hence Case 1 gets canceled.

7. Number of persons to the left of G is equal to the number of persons to the right of B.

8. F sits at extreme end, which is closest to B.

Therefore, the final arrangement is, 

Hence, Eight persons sit to the right of D.

A certain number of persons are sitting in a row facing south direction.

1)Two persons sit between A and D. A is in the right of D.

2. One person sits between B and A.

3. B is the fourth person from the right end. 

4. H sits second to the left of D, who sits exactly between E and B.

5. Neither A nor H sits at any extreme ends. 

6. G sits immediate left of E. Hence Case 1 gets canceled.

7. Number of persons to the left of G is equal to the number of persons to the right of B.

8. F sits at extreme end, which is closest to B.

Therefore, the final arrangement is, 

Hence, E sits third to the left of H.