SBI PO Prelims Memory Based Paper (Held on: 21 Nov 2021 Shift 1) (Previous Year Paper)

The correct answer is option 3. upsurge

Key Points

• Resurgence means rising again into life, activity, or prominence a resurgence of interest.
• Example- The children really hoped that they would not see a resurgence in their father's illness.
• Upsurge means a sudden increase of something.
• Hence, upsurge is the most appropriate synonym.
• Plunge: to jump, drop or fall suddenly and with force.
• Impoverishment: the process of becoming poor; loss of wealth.
• Stagnation: a situation in which something stays the same and does not grow and develop.
• Slump: (used about economic activity, prices, etc.) to fall suddenly and by a large amount.
• Hence, the correct answer is option 3.

The correct answer is were.

Key Points

• The rats were quick to eat seeds and young plants coming out of the ground, and they frequented the canopy as well, often nesting in the coconut palms and eating coconuts.
• Were is the most appropriate option as it fits perfectly.
• The rats needed quick to eat seeds and young plants.... (incorrect)
• The rats at quick to eat seeds and young plants... (incorrect)
• The rats rather quick to eat seeds and young plants... (incorrect)
• Hence, the correct answer is option 2.

The correct answer is "Ana Millerter Kuile"

Key Points

• It is mentioned in the second paragraph, the first sentence, "Prior to the eradication, most of the understory of Palmyra was either bare ground, sandy soil or coral rubble or covered in a carpet of ferns," said Ana Millerter Kuile.
• Hence, the correct answer is option 4.

The correct answer is All of the above

Key Points

• Mentioned in the second paragraph, first and second sentence, "Prior to the eradication, most of the understory of Palmyra was either bare ground, sandy soil or coral rubble or covered in a carpet of ferns," said Ana Millerter Kuile, a graduate student researcher in the Young Group and lead author of a study that appears in the journal Biotropica."
• Hence, the correct answer is option 4.

The correct answer is 2011.

Key Points

• It is mentioned in the third paragraph, first sentence, "Eradication of the rats, which was conducted in 2011".
• Hence, the correct answer is option 3.

The correct answer is informative.

Key Points 

• Tone of the passage:  The ‘tone’ refers to the feelings or emotions expressed by the author towards an issue. It could also encompass his style of writing.
• Let's explore the options:
• Ironical: An ironic tone is an expression of a writer's attitude toward their subject, often conveyed using sarcasm, exaggeration or understatement. An ironic tone calls attention to the difference between the way a subject is described and what is actually true about that subject. The irony is often used for satirical writing, which commonly seeks to criticize its subject.
• Judgemental: It is typically used for passages when the author expresses his views on some issues and takes a stand-is this person or issue right or wrong? Is this good or bad? Is someone intelligent or dumb? These are all judgements. Therefore the characteristic of such a tone is the presence of opinions or the author’s perception/ views on a person, thing or issue.
• Informative: This tone is appropriate when the author has given a lot of figures, facts or data in the passage. The author’s purpose in writing the passage/ article was to increase the reader’s knowledge of the given issue or subject. Hence a lot of details are given. A characteristic of passages with a descriptive/ informative tone is therefore the presence of data, facts etc. and the relative absence of opinions.
• Critical: In essence, being critical implies evaluating the aspects of a text and analysing the factors and facets of the article. The best example if a critical tone would be a movie review or a food outlet review. There, the user would reiterate the good things about the movie before taking a plunge at the more miserable and critical objects of the movie.
• Thus, from the above explanation, we can infer that the correct answer is option 3, i.e. informative because in the whole passage, the author is giving information regarding the research done, projects involved and much more about the conservation of nature.

The correct answer is "to give local species a chance to dominate"

Key Points

• It is mentioned in the second last paragraph, "Continuing their restoration of the island, Palmyra's managers were working to remove the vast majority of the island's millions of coconut palms to give local species a chance to dominate, a project that is currently on hold due to the COVID-19 pandemic."
• Hence, the correct answer is option 3.

The correct answer is destroy.

Key Points

• Eradicate means to get rid of, completely destroy.
• Earn means to get money by working.
• Destroy means to damage something so badly that it can no longer be used or no longer exists.
• support means to help somebody by saying that you agree with him/her/it, and sometimes giving practical help such as money.
• Differentiate means to see or show how things are different.
• Hence, the correct answer is option 2.

The correct answer is 'withering'.

Key Points

• Growth: (noun) the process of growing and developing वृद्धि और विकास
• Withering: The meaning of withering is acting or serving to cut down or destroy.
• Increase means to become or to make something larger in number or amount.
• Loiter means to stand or walk around somewhere for no obvious reason.
• Lighten means to become lighter in weight or to make something lighter.
• Hence, the correct answer is option 1.

The correct answer is helpless.

Key Points

• Potential: that may possibly become something, happen, be used, etc.
• Helpless: unable to take care of yourself or do things without the help of other people.
• Hence, the correct answer is option 2.

The correct answer is Adapted.

Key Points

• Adept(adj): having knowledge or skill (usu. in a particular area)
• Ex: Beth loves playing the piano, but she’s especially adept at the violin.
• Adapt(v):  to make suitable to requirements or conditions. 
• Ex: Dogs are known for their ability to quickly adapt to their environments.
• Hence, the word Adept should be replaced with the word Adapted to form a contextually correct sentence.

It should read as: The US has adapted many foreign foods to better suit the tastes of Americans.

Additional Information Let us understand the meaning of other words.

• Adequate(adj): having sufficient qualifications to meet a specific task or purpose
• Though his resume was adequate, the company doubted whether he’d be a good fit.
• Advent(noun):  the arrival or creation of something (usu. historic)
• The world has never been the same since the advent of the light bulb.
• Advocate(v): to defend or promote something (usu. a belief, theory, opinion, etc.)
• Environmental protesters often advocate for cleaner energy practices.

The correct answer is Beguile.

Key Points

• Entertain(Verb): Take into consideration; have in view
• Ex: "He entertained the notion of moving to South America"
• Beguile(Noun): Cause rapt attraction or admiration; attract love
• Ex: "He was completely beguiled by her beauty."
• Hence, the word Entertain should be replaced with the word Beguile to form a contextually correct sentence.

It should read as: The gender performance he plays is intended to beguile his audience into betraying her innermost feelings.

Additional InformationLet us understand the meaning of other words.

• Persuade(v): Cause somebody to adopt a certain position, belief.
• "You can't persuade me to buy this ugly vase!"
• Cajole(v): Influence or urge by gentle urging, caressing, or flattering
• "He cajoled her into going along"
• Amateur(adj): Engaged in as a pastime
• "an amateur painter"
• Betray(V): Reveal unintentionally
• "Her smile betrayed her true feelings"

The correct answer is Enervated.

Key Points

• Disrupt(V): Make a break-in
• Ex: "We disrupt the program for the following messages"
• Enervated(Adj): Lacking energy or vitality.
• Ex: "They enervated workers even before the troop reinforcements went into action"
• Hence, the word Disrupt should be replaced with the word Enervated to form a contextually correct sentence.

It should read as: The shock of the king's death had Enervated the royalist cause.

Additional Information 

Let us understand the meaning of other words.

• Syntax(Noun): the grammatical arrangement of words in sentences
• He finds errors in the syntax of this essay.
• Energize(V): Cause to be alert and energetic
• "Coffee and tea energize me"
• Honour (V): Bestow honour or rewards upon
• "Today we honour our soldiers"

The correct answer is Incumbent

Key Points

• Retired (adj): No longer active in your work or profession
• Ex: "a retired teacher can apply for this post.
• Incumbent(adj): Necessary (for someone) as a duty or responsibility; morally binding
• Ex: "an incumbent geological formation."
• Hence, the word Retired should be replaced with the word Incumbent to form a contextually correct sentence.

It should read as: The incumbent operator enjoyed monopoly rents and did not want to give up this special status.

Additional Information Let us understand the meaning of other words.

• Incandescent(adj): Growing warm; increasing in heat
• "an incandescent lamp"
• Incompetent(adj): (law) legally not qualified or sufficient
• "incompetent witnesses"
• Clumsy(adj): Lacking grace in movement or posture
• "clumsy fingers"

The correct answer is 'C'.

Key Points

• The usage of the preposition 'among' is incorrect.
• The correct preposition to be used here is 'between'.
• The correct sentence will be: The programme, Infrastructure for Resilient Island States, will be implemented between 2022 and 2030 in 58 countries in three geographical regions.
• Hence, the correct answer is option 3.

​ 

Additional Information

• Example sentences using 'between':
• That is the only difference between them.
• When it came back to her face, a slow smile erased the creases between his brows.
• Example sentences using 'among'.
• The bees were buzzing among the flowers.
• He smiled, revealing fangs among the neat row of white teeth.

The correct answer is 'B'.

Key Points

• The word should be 'heralded' instead of 'herald'.
• Heralded is in the past form, and the entire sentence too is in the past form. (As the words 'established, stumbled)
• Here, the sentence follows parallelism.
• Hence, the correct answer is option 2.

​ 

Additional Information

• Examples of parallelism:​
• *​I like to **jog, bake, *paint,and watch movies.
• The company is looking for a candidate who is friendly, organized, meticulous, and punctual.

The correct answer is -is a good start, but adding that the emissions they produce- the error lies in this part only.

Key Points 

In the given sentence, the error lies in Part B where the usage of verb form ‘adding’ is incorrect.

• The sentence mentions the opinion of the experts regarding halting the financing of coal-power projects abroad. It also talks about China’s domestically generated emissions.
• Reading the sentence, we notice that the use of the verb ‘adding’ is inappropriate as per the concept of Parallel structure/ Parallelism in grammar. As the sentence is in the simple present tense( indicated by the verb ‘say’ in part A), the correct verb form to be used in part B should be ‘add’(simple present) and not ‘adding’(present continuous).

Thus, the correct sentence is: Experts say that halting the financing of these coal-power projects abroad is a good start, but add that the emissions they produce are dwarfed by those generated by the 1,000 GW of coal-power that China generates domestically.

The correct answer is ‘No Error’.

Key Points 

• The given sentence is comprehensive and grammatically correct. It talks about the advantage of bringing renewable energy to low-income countries while emphasizing the empowerment of women and girls through secured access to education.
• The sentence is present tense, and all the four parts( A,B,C & D) are coherently structured.

Thus, the correct answer is Option 5.

The correct answer is -loved ones are speaking as if it is the last- the error lies in this part only.

Key Points 

In the sentence, the error lies in Part C where the usage ‘ if it is the last’ is incorrect.

• Reading the sentence, we can infer that the sentence has an unreal conditional clause i.e. “if it is the last time he might hear them”. However, the construction of the clause is incorrect.
• While describing a state that is not the current reality, the correct verb to be used is ‘were’. This is true whenever a hypothetical situation or a subjunctive mood is expressed.
• ​The sentence mentions that the first person wants to tell ‘him’ to pay attention when his loved ones are speaking. Here, the hypothetical situation is: it may be the last time that he hears them. This notion is introduced by ‘if’ and should be followed by ‘were’ (not the present tense ‘is’) according to the rule of grammar.

Thus, the correct sentence is: I want to tell him to be more open, to ignore the lure of advertised values, to pay attention when his loved ones are speaking as if it were the last time he might hear them.

The correct answer is BDAEC​.

 Key Points

Let's consider A, B, C, D, and E to be five blanks, with A being the first B second, and so on.

• The first blank requires an adjective to describe specific information about the noun used after it 'Indian Institutes. Therefore, 'many' is the correct answer here
• The second blank requires conjunction combining two words 'science and technology. Therefore, 'and is the correct answer here.
• The third blank requires a verb that describes the action of the noun'. Therefore, 'run' is the correct answer here.
• The fourth blank requires an adjective to modify the noun 'programs'. Therefore 'special' is the correct answer.
• The fifth blank requires a noun that is a part of another noun 'science'. Therefore, 'polymer' is the correct answer

Therefore, the correct answer is,

Many Indian Institutes of science and Technology run special programs on polymer science.

The correct answer is DCAEB​.

 Key Points

Let's consider A, B, C, D, and E to be five blanks, with A being the first B second, and so on.

• The first blank requires a noun because a preposition 'during' is used before it which means 'within a period of time mentioned'. Therefore, 'period' is the correct answer here.
• The second blank requires a noun which gives further information about the noun 'period', as in, 'period of what?'- drought. Therefore, 'drought' is the correct answer here.
• The third blank requires a noun, that too a living being because 'died' is used after it. Therefore, 'cattle' is the correct answer here.
• The fourth blank requires a noun that specifies the reason for the death of cattle. Therefore 'thirst' is the correct answer.
• The fifth blank requires a verb which is denoting the previously mentioned noun 'cattle'. Therefore, 'were' is the correct answer

Therefore, the correct answer is,

During a period of drought, streams, and rivers dried up, the cattle died from thirst and were ruined.

The correct answer is ECDBA​.

 Key Points

Let's consider A, B, C, D, and E to be five blanks, with A being the first B second, and so on.

• The first blank requires an adjective because before that an adverb completely is used, so adverb is modifying an adjective here. Therefore, 'dependent' is the correct answer here
• The second blank requires a noun, as in, 'the dog is dependent on whom?'- its owner. Therefore, 'owner' is the correct answer here.
• The third blank requires an adverb, and the adverb 'needs' seems to be grammatically correct here. Therefore, 'needs' is the correct answer here.
• The fourth blank requires a noun that is being modified by the adjective 'good'. Therefore 'health' is the correct answer.
• The fifth blank requires a noun that is being modified by the adjective 'safe'. Therefore, 'environment' is the correct answer

Therefore, the correct answer is,

A dog is completely dependent on its owner for all its needs, including the need for good health and a safe environment

The correct answer is B-D.

Key Points

• The given words 'aggressive' and 'revived' are not placed in the correct order.
• The sentence: We are told that the Taliban’s ______(A) in Afghanistan has ______ (B) serious threats of cross-border (C) from Pakistan, while China, our other tense neighbour, has been increasingly(D) over the past year.
• The correct sentence will be: We are told that the Taliban’s takeover**(A)** in Afghanistan has revived**(B)** serious threats of cross-border infiltration**(C)** from Pakistan, while China, our other tense neighbour, has been increasingly aggressive**(D)** over the past year.
• Hence, the correct answer is option 3.

The correct answer is B-C.

Key Points

• The words 'between' and 'requires' have been placed incorrectly.
• The correct sentence will be:  As successive central and state administrations have(A) found, curbing illegal migration requires(B) coordinated action between(C) India and its neighbours, first at the political and then at(D) the security level.
• Hence, the correct answer is option 1.

The correct answer is “spectacle”.

Key Points

The first sentence of the passage mentions that the floodwaters forced the spiders to find higher ground and the region was covered in sheets of web. The second sentence conveys that the residents witnessed this after heavy rain and flooding damaged the city. 

• Studying the first and second sentences, we can infer that the event witnessed by residents was unexpected. Therefore, we need to look for a word which is similar in meaning to ‘unusual or unexpected event’.
• Considering the meanings of the words in the options, “spectacle” which means an usual/unexpected event that attracts attention, is the correct word. The word “apprehension” (option 1) is inappropriate in the context because the residents witnessed something caused by floods and did not fear or suspect. Option 3-“vision” is suggestive of dream, so it is incorrect. Also, the word “apathy” (option 4) is wrong as the residents cannot feel indifference to the damage to life and property caused by flooding. “Display” (option 5) is incorrect too.

Therefore, option 2- “spectacle” is the correct answer.

Additional Information

• Let us look at the meanings of other words given in the options-

The correct answer is “scrambling”.

Key Points

Looking at the sentence with the blank, it talks about the effect of waterlogged soil. The sentence conveys that the waterlogged soil made millions of spiders to take refuge on plants, signs or anything above the ground. 

• The tone of the sentence clearly says that the spiders were forced to find the refuge on plants and other possible things, So, the spiders would have struggled to find a support. Therefore, we need to look for a word that is suggestive of ‘struggling to get something’.
• Considering the meanings of the words in the options, “scrambling” which means struggling eagerly or unceremoniously for possession of something, is the correct word. The word “disarraying”(option 2) is not suitable in the context. Next, “meditating” (option 3) is incorrect as the spiders would not have been just considering or thinking to find support, rather they were struggling to survive due to the waterlogged soil. The word “dealing” (option 4) is incorrect as it is unspecific and inappropriate. Option 5-“wondering” is out of the context.

Therefore, option 1- “scrambling” is the correct answer.

 

Additional Information

• Let us look at the meanings of other words given in the options-

 

The correct answer is “evacuate”.

Key Points

It is clearly mentioned that the spiders are usually not seen as they are hiding in the soil. Reading further, the sentence with the blank conveys that the spiders need to leave the holes where they live in the underground, during floods. While they do come up out of the holes, they use the help of their silk.

• Looking at the context, therefore, we need to find a word which is suggestive of ‘leave or vacate’.
• Considering the meanings of the words in the options, “evacuate” which means vacate from a dangerous place to a safe place, is the correct word. The word “resist” (option 1) is incorrect as it is completely out of the context. Also, the word “reverberate” is not related to the meaning conveyed by the sentence.So it is incorrect. “Stay” (option 4) conveys the opposite meaning and “abide”(option 5) is synonymous with “stay”, so they are incorrect too.

Therefore, option 3- “evacuate” is the correct answer.

 

Additional Information

• Let us look at the meaning of other words given in the options-

 

The correct answer is “occurs”.

Key Points

The sentence with blank 4, conveys that the gossamer effect takes place semi-regularly in the Victoria region during the wet season in the winter. 

• Therefore, we need to look for a word (verb) which is similar in meaning to ‘take place or happen’.
• ​Considering the meanings of the words in the options, “occurs” which means happens or take place, is the correct word. The word “strives” (option 1) is incorrect as it is irrelevant in the context of the sentence. Also, “works” (option 2) is incorrect as the meaning: an effect ‘performs’ semi-regularly, is incorrect. Further, “fastens” (option 4) and “retreats” (option 5) are incorrect as they are not related to the meaning conveyed by the sentence.

Therefore, option 4- “occurs” is the correct answer.

 

Additional Information

• Let us look at the meanings of other words given in the options-

 

The correct answer is “hooks, anchors”.

Key Points

Looking at the sentences prior to the sentence with the blank 5, it is clear that the spiders use ‘ballooning’ to throw up a lasso (i.e. rope/strand like support) on top of the vegetation and avoid escaping for hundreds of kilometres during the floods.

• The sentence with the blank conveys that the lasso (silk strand of the spiders) holds firmly on to the top of the vegetation as it is lighter and help spiders to climb up. Therefore, we need to look for a word which is similar in meaning to ‘hold firm through support’.
• Considering the meanings of the above words, “hooks” means fastens or holds something as if with a hook; “anchors” means holding something in a position by fastening it firmly. Thus, “hooks”and “anchors” (option 5) both are correct words. The word “separates”(option 3) is incorrect as it conveys an opposite meaning. Also, option 2 “unlinks” gives the opposite meaning (detach) and hence incorrect.

Therefore, option 5- “hooks, anchors” is the correct answer.

 

Additional Information

• Let us look at the meanings of other words given in the options-

 

The correct answer is “break up”.

Key Points

The sentence with the blank 6, conveys that the webbing by spiders will cease or decompose on its own and the spiders will disperse to their underground homes. The previous sentence that locals are asked to leave the spiders alone, supports the fact that webbing will be decomposed by its own and hence there is no need for an intervention.

• Therefore, we need to look for a word similar in meaning to ‘decompose or cease’.
• Considering the meaning of the above words, “break up” which means to cease to exist as a whole, is the correct word. The word “unify” (option 1) means the opposite and hence incorrect. Also, “act” (option 2) is incorrect as it is unspecific and does not clearly say how it ‘manages’ on it’s own. Option 3-“amalgamate” and option 5-“pervade” convey the opposite meaning, so they are incorrect too.

Therefore, option 4- “break up” is the correct answer.

 

Additional Information

• Let us look at the meanings of other words given in the options-

 

Ratio of Boys to Girls who participate in SSC = 4 : 3

Ratio of Boys to Girls who participate in PO = 8 : 13

Ratio of Boy to Girl who participates in both the events of PO and SSC = 2 : 1

Ratio of Boys to Girls who participate only in the PO exam = 1 : 2

participation of boys in the SSC exam alone is 10 more than the Girls participation in SSC alone

Boys who participate in both SSC and PO is 20% of the Boys who participate in SSC exam alone

Concept:

 

Total participant in SSC = participate only in SSC + participate in both SSC and PO

Total participant in PO = participate only in PO + participate in both SSC and PO

Calculation:

Let number of Girl participate only in SSC = x

So, Number of Boys participate only in SSC = x + 10

Number of Boys participate in both SSC and PO = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both SSC and PO = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in SSC/Number of girls participate in SSC = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in SSC = 40

Number of Boys participate only in PO = 40 + 10

⇒ 50

Number of Boys participate in both SSC and PO = (40 + 10)/5

⇒ 10

Number of Girls participate in both SSC and PO = (40 + 10)/10

⇒ 5

 

Number of Boys participate in SSC = 50 + 10

⇒ 60

Number of girls participate in SSC = 40 + 5

⇒ 45

 

Number of Boys in PO/Number of Girls in po = 8/13

8/13 = (10 + y)/(5 + 2y)

⇒ 40 + 16y = 130 + 13y

⇒ 3y = 90

⇒ y = 30

Number of Boys in PO only = 30

Number of Girls in PO only = 2 × 30

⇒ 60

 

Number of Boys in PO = 30 + 10

⇒ 40

Number of Girls in PO = 60 + 5

⇒ 65

Ratio of boy who participated in SSC to Girls who participated in PO = 60 : 65

⇒ 12 : 13

∴ Ratio of boy who participated in SSC to Girls who participated in PO is 12 : 13.

Ratio of Boys to Girls who participate in SSC = 4 : 3

Ratio of Boys to Girls who participate in PO = 8 : 13

Ratio of Boy to Girl who participates in both the events of PO and SSC = 2 : 1

Ratio of Boys to Girls who participate only in the PO event = 1 : 2

participation of boys in the SSC event alone is 10 more than the Girls participation in PO alone

Boys who participate in both SSC and PO is 20% of the Boys who participate in Dancing events alone

Concept:

 

Total participant in SSC = participate only in SSC + participate in both SSC and PO

Total participant in PO = participate only in PO + participate in both SSC and PO

Total participant in competition = participate only in SSC + participate in both SSC and PO + participate only in PO

Calculation:

Let number of Girl participate only in SSC = x

So, Number of Boys participate only in SSC = x + 10

Number of Boys participate in both SSC and PO = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both SSC and PO = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in SSC/Number of girls participate in SSC = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in SSC = 40

Number of Boys participate only in SSC = 40 + 10

⇒ 50

Number of Boys participate in both SSC and PO = (40 + 10)/5

⇒ 10

Number of Girls participate in both SSC PO= (40 + 10)/10

⇒ 5

 

Number of Boys participate in SSC = 50 + 10

⇒ 60

Number of girls participate in SSC = 40 + 5

⇒ 45

 

Number of Boys in PO/Number of Girls in PO = 8/13

8/13 = (10 + y)/(5 + 2y)

⇒ 40 + 16y = 130 + 13y

⇒ 3y = 90

⇒ y = 30

Number of Boys in PO only = 30

Number of Girls in PO only = 2 × 30

⇒ 60

 

Number of Boys in PO = 30 + 10

⇒ 40

Number of Girls in PO = 60 + 5

⇒ 65

Total participant in competition = (50 + 40) +(10 + 5) + (30 + 60)

⇒ 90 + 15 + 90

⇒ 195

∴ Total 195 participants were there in the competition.

Ratio of Boys to Girls who participate in SSC = 4 : 3

Ratio of Boys to Girls who participate in PO = 8 : 13

Ratio of Boy to Girl who participates in both the events of PO and SSC = 2 : 1

Ratio of Boys to Girls who participate only in the PO event = 1 : 2

participation of boys in the SSC exam alone is 10 more than the Girls participation in SSC alone

Boys who participate in both SSC and PO is 20% of the Boys who participate in SSC exam alone

Concept:

 

Total participant in SSC = participate only in SSC + participate in both SSC and PO

Total participant in PO = participate only in PO + participate in both SSC and PO

Calculation:

Let number of Girl participate only in SSC = x

So, Number of Boys participate only in SSC = x + 10

Number of Boys participate in both SSC and PO = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both SSC and PO = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in SSC/Number of girls participate in SSC = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in SSC = 40

Number of Boys participate only in SSC = 40 + 10

⇒ 50

Number of Boys participate in both SSC and PO = (40 + 10)/5

⇒ 10

Number of Girls participate in both SSC and PO = (40 + 10)/10

⇒ 5

number of participants who participated in both events (SSC and PO) = 10 + 5

⇒ 15

∴ 15 participants, participated in both exams (SSC and PO).

Ratio of Boys to Girls who participate in SSC = 4 : 3

Ratio of Boys to Girls who participate in PO = 8 : 13

Ratio of Boy to Girl who participates in both the exams of PO and SSC = 2 : 1

Ratio of Boys to Girls who participate only in the PO exams = 1 : 2

participation of boys in the SSC exam alone is 10 more than the Girls participation in SSC alone

Boys who participate in both SSC and PO is 20% of the Boys who participate in SSC exam alone

Concept:

 

Total participant in SSC = participate only in SSC + participate in both SSC and PO

Total participant in PO = participate only in PO + participate in both SSC and PO

Calculation:

Let number of Girl participate only in SSC = x

So, Number of Boys participate only in SSC = x + 10

Number of Boys participate in both SSC and PO = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both SSC and PO = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in SSC/Number of girls participate in SSC = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in SSC = 40

Number of Boys participate only in SSC = 40 + 10

⇒ 50

Number of Boys participate in both SSC and PO = (40 + 10)/5

⇒ 10

Number of Girls participate in both SSC and PO = (40 + 10)/10

⇒ 5

 

 

 

 

Number of Boys participate in SSC = 50 + 10

⇒ 60

Number of girls participate in SSC = 40 + 5

⇒ 45

 

Number of Boys in PO/Number of Girls in PO = 8/13

8/13 = (10 + y)/(5 + 2y)

⇒ 40 + 16y = 130 + 13y

⇒ 3y = 90

⇒ y = 30

Let number of Boys who participated only in PO events is x% of Boys who participated only in SSC exam

x% = (30/50) × 100

⇒ 60%

∴ Number of Boys who participated only in PO exam is 60% of Boys who participated only in SSC exams.

Ratio of Boys to Girls who participate in SSC = 4 : 3

Ratio of Boys to Girls who participate in PO = 8 : 13

Ratio of Boy to Girl who participates in both the events of PO and SSC = 2 : 1

Ratio of Boys to Girls who participate only in the PO exam = 1 : 2

participation of boys in the SSC exam alone is 10 more than the Girls participation in SSC alone

Boys who participate in both SSC and PO is 20% of the Boys who participate in SSC exam alone

Concept:

 

Total participant in SSC = participate only in SSC + participate in both SSC and PO

Total participant in PO = participate only in PO + participate in both SSC and PO

 

Calculation:

Let number of Girl participate only in SSC = x

So, Number of Boys participate only in SSC = x + 10

Number of Boys participate in both SSC and PO = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both SSC and PO = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in SSC/Number of girls participate in SSC = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in SSC = 40

Number of Boys participate only in SSC = 40 + 10

⇒ 50

Number of Boys participate in both SSC and PO = (40 + 10)/5

⇒ 10

Number of Girls participate in both SSC and PO = (40 + 10)/10

⇒ 5

 

 

 

 

Number of Boys participate in SSC = 50 + 10

⇒ 60

Number of girls participate in SSC = 40 + 5

⇒ 45

 

Number of Boys in PO/Number of Girls in PO= 8/13

8/13 = (10 + y)/(5 + 2y)

⇒ 40 + 16y = 130 + 13y

⇒ 3y = 90

⇒ y = 30

Number of Boys in PO only = 30

Number of Girls in PO only = 2 × 30

⇒ 60

Participant only in SSC = 50 + 40

⇒ 90

Participant only in PO = 30 + 60

⇒ 90

Participant only in SSC : Participant only in PO = 90 : 90

⇒ 1 : 1

∴ Ratio of participants who participated only in SSC to only in PO is 1 : 1.

Cost of raw material = 6 × 25 = Rs. 150

Cost of labour = 5 × 35 = Rs. 175

Overhead cost = Rs. 2.5

Total cost = Rs. 150 + Rs. 175 + Rs. 2.5 = Rs. 327.50

Cost of raw material = 3 × 25 = Rs. 75

Cost of labour = 3 × 35 = Rs. 105

Overhead cost = Rs. 1

⇒ Total cost = Rs. 181

Profit = SP – CP

Profit = 200 – 181 = Rs. 19

Product D

Cost of raw material = 4 × 25 = Rs. 100

Cost of labour = 2 × 35 = Rs. 70

Total cost = Rs. 170

Product E

Cost of raw material = 5 × 25 = Rs. 125

Cost of labour = 3 × 35 = Rs. 105

⇒ Total cost = Rs. 230

⇒ Ratio of cost of product D and E = 17 : 23

Cost of raw material = 3 × 25 = Rs. 75

Cost of labour = 2 × 35 = Rs. 70

Overhead cost = Rs. 0.5

⇒ Total cost = Rs. 145.50

Cost price of 4 units = 145 × 4 = 582

SP = 582 × 1.1 = Rs. 640.2

Product C

Cost of raw material = 3 × 25 = Rs. 75

Cost of labour = 2 × 35 = Rs. 70

Overhead cost = Rs. 0.5

⇒ Total cost = Rs. 145.50

Product A

Cost of raw material = 6 × 25 = Rs. 150

Cost of labour = 5 × 35 = Rs. 175

Overhead cost = Rs. 2.5

⇒ Total cost = Rs. 327.5

⇒ Difference of cost = 327.5 – 145.5 = Rs. 182

Given

Total number of seat (Lok Sabha and Rajya Sabha) of Uttar Pradesh = 111

The number of Rajya Sabha seats of UP = 31

Calculation

Let the number of Lok Sabha seats of Uttar Pradesh be x

Hence, 31 + x = 111

⇒ x = 80

Lok Sabha seat of Tamil Nadu = 39

Now, Required percentage = [(80 – 39)/39] × 100 = (41/39) × 100 = 105.1% ≈ 105%

Given

Lok Sabha seats of West Bengal = 42

Calculation

Let the Lok Sabha and Rajya Sabha seats of West Bengal be 21x and 8x

According to the question,

21x = 42

⇒ x = 2

Now, 8x = 8 × 2 = 16

Total number of seats of West Bengal = Lok Sabha + Rajya Sabha = 42 + 16 = 58

Total number of seats of Tamil Nadu = Lok Sabha + Rajya Sabha = 39 + 18 = 57

∴ Ratio of total seats of West Bengal and Tamil Nadu = 58 : 57

Given

Lok Sabha seats of Tamil Nadu = 39

Lok sabha seats of Maharashtra = 48

Calculation

According to the question,

Rajya Sabha seats of bihar = 3 + (Lok Sabha seats of Tamil Nadu/3)

⇒ 3 + (39/3) = 16

Total seats (Lok Sabha and Rajya Sabha) of Bihar = 55

⇒ 16 + seats of Lok Sabha = 55

⇒ Seats of Lok Sabha = 39

Hence, Required percentage = (48 – 39)/48 × 100 = (9/48) × 100 = 18.75%

∴ Lok Sabha seats of Bihar is less than the Lok Sabha seats of Maharashtra by 18.75%

Given

Lok Sabha seats of Maharashtra = 48

Calculation

According to the question,

Total number of seats of Madhya Pradesh = $33\frac{1}{3}$% × 120 = (1/3) × 120 = 40

As, the ratio of Lok Sabha and Rajya Sabha seats of MP = 29 : 11 = 29x : 11x

Hence, 29x + 11x = 40

⇒ x = 1

So, Rajya Sabha seats of Madhya Pradesh = 11

Now, Rajya Sabha seats of Madhya Pradesh : Lok Sabha seats of Maharashtra = 11 : 48

∴ The ratio of Rajya Sabha seats of Madhya Pradesh and Lok Sabha Seats of Maharashtra is 11 : 48

Given

Rajya Sabha seats of Uttar Pradesh = 31

Calculation

Let the Lok Sabha seats of Uttar Pradesh be x

Rajya Sabha seats of Uttar Pradesh = 31

According to the question,

Lok Sabha seats of Uttar Pradesh – 2(Rajya Sabha seats of Uttar Pradesh) = 18

⇒ x – 2(31) = 18

⇒ x = 18 + 62 = 80

Population density = (Total Population/Number of Lok sabha seats) = 250000000/80

= 25000000/8

= 3125000

∴ The population density of Lok Sabha of Uttar Pradesh is 3125000

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

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

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

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

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

Since, we need to find out the approximate value,

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

Given expression is

√1763.98 + √1444.04 - (39.99% of 149.92) = ?

⇒ √1764 + √1444 - (40% of 150) = ?

⇒ 42 + 38 - (40/100 × 150) = ?

⇒ 42 + 38 - 60 = ?

⇒ 80 - 60 = ?

⇒ 20 = ?

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

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

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

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

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

Since we need to find out the approximate value,

we can write these values to their nearest integers.

Given expression is

29.9% of 499.99 - 49.93% of 399.99 + 69.92% of 199.99 = ?

⇒ 30% of 500 - 50% of 400 + 70% of 200 = ?

⇒ (30/100) × 500 - (50/100) × 400 + (70/100) × 200 = ?

⇒ 150 - 200 + 140 = ?

⇒ 290 - 200 = ?

⇒ ? = 90

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

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

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

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

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

Given expression is,

638.4 ÷ 22.1 + 99.7 × 20.1 - (27)² = ?

Taking the approximate values as,

638.4 ≈ 638, 22.1 ≈ 22, 99.7 ≈ 100, 20.1 ≈ 20

⇒ 638 ÷ 22 + 100 × 20 - (27)² = ?

⇒ 29 + 2000 - 729 = ?

∴ ? = 1300

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

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

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

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

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

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

Given expression is

39.98% of 699.97 = 799.98 + 59.84% of 599.99 - ?

⇒ 40% of 700 = 800 + 60% of 600 - ?

⇒ 280 = 800 + 360 - ?

⇒ ? = 1160 - 280 = 880

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

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

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

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

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

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

Given expression is

39.99% of 799.98 + 59.98% of 499.98 = 24.89% of ?

⇒ 40% of 800 + 60% of 500 = 25% of ?

⇒ 320 + 300 = (25/100) × ?

⇒ 620 × 100/25 = ?

⇒ ? = 2480

Calculation:

⇒ 25 + (1)³ = 26

⇒ 26 - (2)³ = 18

⇒ 18 + (3)³ = 45

⇒ 45 - (4)³ = - 19

⇒ -19 + (5)³ = 106

∴ The missing number is -19.

Calculation:

⇒  18 + 1 x 2 = 20

⇒ 20 + 2 x 3 = 26

⇒ 26 + 3 x 4 = 38

⇒ 38 + 4 x 5 = 58 

⇒ 58 + 5 x 6 = 88

∴ The required answer is 88.

Calculation:

⇒ 5 x 2 + 2 = 12

⇒ 12 x 3 - 3 = 33

⇒ 33 x 4 + 4 = 136

⇒ 136 x 5 - 5 = 675

⇒ 675 x 6 + 6 = 4056 

∴ The missing number is 4056.

Calculation:

⇒ 4 x 2 + 3 = 11

⇒ 11 x 3 + 4 = 37

⇒ 37 x 4 + 5 = 153

⇒ 153 x 5 + 6 = 771

⇒ 771 x 6 + 7 = 4633 

∴ The required answer is 771.

Calculation:

⇒ 8 x 0.5 + 0.5 = 4.5

⇒ 4.5 x 1 + 1 = 5.5

⇒ 5.5 x 2 + 2 = 13

⇒ 13 x 4 + 4 = 56

⇒ 56 x 8 + 8 = 456

∴ The required answer is 456.

Shortcut Trick

Equate the speed of the stream in both ratios to compare the boats.

Ratio 1 (Stream : Boat₁) = 4 : 7

Ratio 2 (Stream : Boat₂) = 2 : 5 × 2 → 4 : 10

Comparing the Boat speeds directly when Stream speed is 4 units.

Boat₁ : Boat₂ = 7 : 10

∴ The correct answer is 7 : 10.

Alternate Method

Given: Ratio of stream (s) to boat 1 (b₁) = 4 : 7. Ratio of stream (s) to boat 2 (b₂) = 2 : 5.

Calculations:

⇒ Let Speed of Stream = s, Speed of Boat 1 = b₁, and Speed of Boat 2 = b₂.

⇒ From first ratio: s/b₁ = 4/7 ⇒ b₁ = 7s/4

⇒ From second ratio: s/b₂ = 2/5 ⇒ b₂ = 5s/2

⇒ Ratio of Boat 1 to Boat 2 = b₁ : b₂ = (7s/4) : (5s/2)

⇒ Multiply by 4 to clear denominators: 7s : (5s/2 × 4) = 7s : 10s

⇒ b₁ : b₂ = 7 : 10

∴ The correct answer is 7 : 10.

Additional Information

Relative Speed in Water

Downstream Speed = Speed of Boat + Speed of Stream. Upstream Speed = Speed of Boat − Speed of Stream.

Common Variable Method

When comparing two ratios with a common element, multiply the terms of the ratios so that the common element has the same numerical value.

Shortcut Trick

Work ratio: 18M × 24 = 16W × 30 ⇒ 9M = 10W ⇒ M/W = 10/9.

Total Work = 18 × 10 × 24 = 4320 units.

Work done by 15 men in 6 days = 15 × 10 × 6 = 900 units.

Remaining work = 4320 − 900 = 3420 units.

Days taken by 20 women = 3420 ÷ (20 × 9) = 19 days.

Total wages for women = 20 × 19 × 225 = ₹85500.

∴ The correct answer is ₹85500.

Alternate Method

Given:

18 Men = 24 days | 16 Women = 30 days | Daily wage = ₹225.

Calculations:

⇒ Total work in terms of man-days = 18 × 24 = 432 man-days.

⇒ Total work in terms of woman-days = 16 × 30 = 480 woman-days.

⇒ Efficiency equivalence: 432 Men = 480 Women ⇒ 1 Man = 480/432 Women = 10/9 Women.

⇒ Work done by 15 men in 6 days = 90 man-days.

⇒ Remaining work in man-days = 432 − 90 = 342 man-days.

⇒ Remaining work in woman-days = 342 × (10/9) = 380 woman-days.

⇒ Days required by 20 women = 380 ÷ 20 = 19 days.

⇒ Total wages of women = Total woman-days × Wage per person.

⇒ Total wages = 380 × 225 = ₹85500.

∴ The correct answer is ₹85500.

Additional Information

Chain Rule Formula

The relationship between work, people, and time is given by (M₁×D₁×H₁)/W₁ = (M₂×D₂×H₂)/W₂.

Work and Wages

Wages are generally distributed in the ratio of the work done by each person (Efficiency × Time).

Man-Days Concept

Total Work = Number of Persons × Number of Days. This allows conversion between different labor types based on efficiency ratios.

Shortcut Trick

Overall loss percentage = (165 ÷ 5000) × 100 = 3.3%.

Using Alligation: Article A loss is −25%, Article B profit is +6%, Overall is −3.3%.

Ratio of CP_A to CP_B = (6 − (−3.3)) : (−3.3 − (−25)) = 9.3 : 21.7.

Simplified Ratio = 93 : 217 = 3 : 7.

Total units (3 + 7) = 10 units ⇒ Rs. 5000.

Cost price of Article A = 3 units = (5000 ÷ 10) × 3 = Rs. 1500.

∴ The correct answer is Rs. 1500.

Alternate Method

Given → Total CP = Rs. 5000 | Loss on A = 25% | Profit on B = 6% | Net Loss = Rs. 165. Formulas: Profit = SP − CP | Loss = CP − SP | Total Loss = (Loss on A) − (Profit on B).

⇒ Let the cost price of Article A be Rs. x and Article B be Rs. (5000 − x). ⇒ Loss on A = 25% of x = 0.25x. ⇒ Profit on B = 6% of (5000 − x) = 0.06 × (5000 − x) = 300 − 0.06x. ⇒ Overall Loss = Loss on A − Profit on B = 165. ⇒ 0.25x − (300 − 0.06x) = 165. ⇒ 0.25x − 300 + 0.06x = 165 ⇒ 0.31x = 165 + 300 = 465. ⇒ x = 465 ÷ 0.31 = 1500.

∴ The correct answer is Rs. 1500.

Additional Information

Rule of Alligation

It is used to find the ratio in which two quantities are mixed. In profit and loss, alligation on percentage profit/loss gives the ratio of Cost Prices.

Net Profit/Loss

Total Profit or Loss = (Profit₁ + Profit₂ + ...) − (Loss₁ + Loss₂ + ...). If the result is positive, it is a net profit; otherwise, a net loss.

Shortcut Trick

For a duration of 2 years, the difference between Compound Interest (CI) and Simple Interest (SI) is given by the interest earned on the first year's interest.

SI for 2 years = ₹400 → SI for 1 year = 400 ÷ 2 = ₹200.

Extra interest earned (CI − SI) = Interest on first year SI = 5% of ₹200.

Difference = 200 × (5 ÷ 100) = ₹10.

∴ The correct answer is ₹10.

Alternate Method

Given: Simple Interest (SI) = ₹400, Time (T) = 2 years, Rate (R) = 5% per annum.

Formula Used: SI = (P × R × T) ÷ 100; Difference (CI − SI) = (P × R²) ÷ 100²

⇒ 400 = (P × 5 × 2) ÷ 100

⇒ 400 = P × (10 ÷ 100)

⇒ P = 400 × 10 = ₹4000

⇒ Difference = (4000 × 5 × 5) ÷ (100 × 100)

⇒ Difference = (4000 × 25) ÷ 10000

⇒ Difference = 100000 ÷ 10000 = ₹10

∴ The correct answer is ₹10.

Additional Information

Difference for 2 Years

The difference between CI and SI for 2 years is P(R/100)² or simply the interest on the first year's interest.

Difference for 3 Years

The difference for 3 years is given by the formula: D = [P(R/100)²] × [(300+R)/100].

Effective Rate of Interest

For 2 years at R%, effective SI is 2R% and effective CI is (2R + R²/100)%. The difference is (R²/100)% of Principal.

Shortcut Trick

Total age of Suman, Kanti and Reena = 30 × 3 = 90 years.

Present average of Suman and Kanti = 36 − 6 = 30 years.

Total age of Suman and Kanti = 30 × 2 = 60 years.

Reena age = 90 − 60 = 30 years.

∴ The correct answer is 30 years.

Alternate Method

Given:

Average age of Suman (S), Kanti (K) and Reena (R) = 30 years.

Average age of S and K after 6 years = 36 years.

Formula Used:

Sum of observations = Average × Number of observations

Calculations:

⇒ S + K + R = 30 × 3 = 90 years --- (Eq 1)

⇒ (S + 6) + (K + 6) = 36 × 2

⇒ S + K + 12 = 72

⇒ S + K = 72 − 12 = 60 years --- (Eq 2)

⇒ Subtracting (Eq 2) from (Eq 1):

⇒ (S + K + R) − (S + K) = 90 − 60

⇒ R = 30 years

∴ The correct answer is 30 years.

Additional Information

Average Age Property

If the average age of a group is A, then after 'n' years, the average age will be (A + n).

Weighted Average

Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂), where n is the number of people and A is their average.

Shortcut Trick

Scored marks in 2^nd test = 132

Qualifying marks in 2^nd test = 132 + 15 = 147

Given 30% of Maximum Marks = 147

Qualifying marks in 1^st test = 40% of Maximum Marks = (147 ÷ 30) × 40 = 147 × 4/3 = 196

∴ The correct answer is 196.

Alternate Method

Given: Qualifying % (Test 1) = 40%, Qualifying % (Test 2) = 30%, Marks scored (Test 2) = 132, Deficit = 15.

⇒ Qualifying marks in second test = 132 + 15 = 147

⇒ Let the maximum marks for each test be x.

⇒ 30% of x = 147

⇒ (30/100) × x = 147

⇒ x = (147 × 100) ÷ 30 = 490

⇒ Qualifying marks in first test = 40% of 490

⇒ (40/100) × 490 = 4 × 49 = 196

∴ The correct answer is 196.

Additional Information

Percentage Base Change

When the base (Maximum Marks) is the same, we can use the unitary method: (Given Value ÷ Given % Base) × Required % Base.

Pass/Fail Marks Logic

Pass Marks = Marks Obtained + Marks failed by, or Pass Marks = Marks Obtained − Marks exceeded by.

Shortcut Trick

Initial division 5 : 3 (Total 8 units = 40 cm) ⇒ 1 unit = 5 cm.

Longer strip = 25 cm, Shorter strip = 15 cm.

Sub-division of 25 cm (4 : 1) → Shortest part = 1/5 × 25 = 5 cm.

Sub-division of 15 cm (3 : 2) → Shortest part = 2/5 × 15 = 6 cm.

Difference = 6 cm − 5 cm = 1 cm.

∴ The correct answer is 1 cm.

Alternate Method

Given: Total Length = 40 cm. Ratios: 5 : 3, 4 : 1, and 3 : 2.

Step 1: First Division

⇒ Total ratio = 5 + 3 = 8 units.

⇒ 8 units = 40 cm ⇒ 1 unit = 5 cm.

⇒ Longer strip = 5 × 5 = 25 cm.

⇒ Smaller strip = 3 × 5 = 15 cm.

Step 2: Further Division

⇒ Longer strip (25 cm) in 4 : 1 ⇒ Smallest part = 1/5 × 25 = 5 cm.

⇒ Smaller strip (15 cm) in 3 : 2 ⇒ Smallest part = 2/5 × 15 = 6 cm.

Step 3: Difference

⇒ Difference = 6 cm − 5 cm = 1 cm.

∴ The correct answer is 1 cm.

Additional Information

Ratio Division Rule

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

Compound Ratio

When ratios are applied successively, the final part can be found by multiplying the individual fraction ratios, e.g., (3/8) × (2/5) × Total.

Shortcut Trick

The age difference between two people remains constant throughout their lives.

Difference = 30 years. One year ago, Shreya (S) was 6 times her daughter (D). S − D = 5 units.

5 units = 30 years ⇒ 1 unit = 6 years. One year ago: D = 6 years, S = 36 years.

Present ages: D = 6 + 1 = 7 years, S = 36 + 1 = 37 years.

∴ The correct answer is 37 : 7.

Alternate Method

Given: 1 year ago Shreya = 6 × Daughter. 6 years hence, Difference = 30 years.

⇒ Let 1 year ago, Daughter's age = x and Shreya's age = 6x.

⇒ Age difference = 6x − x = 5x.

⇒ 5x = 30 (Since age difference never changes).

⇒ x = 6.

⇒ 1 year ago: Shreya = 36 years, Daughter = 6 years.

⇒ Present Age of Shreya = 36 + 1 = 37 years.

⇒ Present Age of Daughter = 6 + 1 = 7 years.

⇒ Ratio = 37 : 7.

∴ The correct answer is 37 : 7.

Additional Information

Constant Difference Property

The numerical difference between the ages of two persons remains the same at any point in time (past, present, or future).

Ratio Adjustment

If ages are given in a ratio a:b and after 'n' years the ratio becomes c:d, ensure (a−b) = (c−d) by multiplying the ratios by suitable constants to solve quickly.

Shortcut Trick

Initial Ratio (Alcohol : Water) = 5 : 4 (Total = 9 units)

Final Ratio (Alcohol : Water) = 5 : 3 (Water changes, Alcohol stays 5 units)

Since only Alcohol is added, Water quantity must remain constant. Equalize Water: 4 × 3 = 12 and 3 × 4 = 12.

New Ratios: 15 : 12 (Total 27 units = 189 litres) → 20 : 12. Alcohol increase = 5 units.

27 units = 189 litres ⇒ 1 unit = 7 litres. 5 units = 5 × 7 = 35 litres.

∴ The correct answer is 35 litres.

Alternate Method

Given: Total mixture = 189 litres, Initial Ratio = 5 : 4, Final Ratio = 5 : 3.

⇒ Total units = 5 + 4 = 9 units

⇒ 1 unit = 189 ÷ 9 = 21 litres

⇒ Initial Alcohol = 5 × 21 = 105 litres

⇒ Initial Water = 4 × 21 = 84 litres

⇒ Let 'x' litres of alcohol be added.

⇒ (105 + x) ÷ 84 = 5 ÷ 3

⇒ 3 × (105 + x) = 5 × 84

⇒ 315 + 3x = 420

⇒ 3x = 105

⇒ x = 35 litres

∴ The correct answer is 35 litres.

Additional Information

Constant Quantity Method

When one component is added, the other component remains constant. Calculate the constant quantity first to find the new total volume.

Ratio Balancing

To solve quickly, make the parts of the unchanged component equal in both ratios by multiplying with suitable integers.

Alligation for Addition

Pure addition can be treated as a mixture of the initial concentration and 100% pure substance concentration.

Shortcut Trick

When two objects start at the same time, the distance covered by each is directly proportional to their speed.

Ratio of speeds (A : B) = 42 : 53

Sum of ratio parts = 42 + 53 = 95 units

95 units → 950 km ⇒ 1 unit = 10 km

Distance from A = Speed of A × Time = 42 × 10 = 420 km

∴ The correct answer is 420 km.

Alternate Method

Given: Speed of Train 1 = 42 km/hr, Speed of Train 2 = 53 km/hr, Total Distance = 950 km.

Formula Used: Relative Speed = S₁ + S₂ (opposite direction); Time = Distance ÷ Speed.

⇒ Relative Speed = 42 + 53 = 95 km/hr

⇒ Time taken to meet = Total Distance ÷ Relative Speed

⇒ Time = 950 ÷ 95 = 10 hours

⇒ Distance from A = Speed of train starting from A × Time

⇒ Distance from A = 42 × 10 = 420 km

∴ The correct answer is 420 km.

Additional Information

Relative Speed Concept

When two objects move toward each other, their relative speed is the sum of their individual speeds (S₁ + S₂).

Distance-Speed Relationship

For a constant time of travel, the ratio of distances covered is equal to the ratio of speeds (D₁/D₂ = S₁/S₂).

Meeting Time Formula

If two objects start simultaneously, the meeting time T = Total Distance ÷ (S₁ + S₂).

Six boxes: L, M, N, O, P and Q

Six items: Books, Erasers, Pen, Pencils, Sharpener and Stapler

i) Box L is kept at the top of the stack.

ii) Box M which contains Pencils is kept three boxes below the Box L.

iii) Box N is kept immediately above the box which contains Erasers.

 

iv) As many boxes are placed above the box N as many are placed below the box that contains Sharpener.

v) The box O contains Pen and is kept below the box that contains Erasers.

This eliminates case 2.

 

vi) The box that contains Books is not placed immediately above the box that contains Erasers.

vii) Box P is placed above the box that contains Pencils.

Hence, Erasers is kept in Box P.

Six boxes: L, M, N, O, P and Q

Six items: Books, Erasers, Pen, Pencils, Sharpener and Stapler

i) Box L is kept at the top of the stack.

ii) Box M which contains Pencils is kept three boxes below the Box L.

iii) Box N is kept immediately above the box which contains Erasers.

 

iv) As many boxes are placed above the box N as many are placed below the box that contains Sharpener.

v) The box O contains Pen and is kept below the box that contains Erasers.

This eliminates case 2.

 

vi) The box that contains Books is not placed immediately above the box that contains Erasers.

vii) Box P is placed above the box that contains Pencils.

Hence, two boxes are kept between the boxes which contains Books and Pencil.

Six boxes: L, M, N, O, P and Q

Six items: Books, Erasers, Pen, Pencils, Sharpener and Stapler

i) Box L is kept at the top of the stack.

ii) Box M which contains Pencils is kept three boxes below the Box L.

iii) Box N is kept immediately above the box which contains Erasers.

 

iv) As many boxes are placed above the box N as many are placed below the box that contains Sharpener.

v) The box O contains Pen and is kept below the box that contains Erasers.

This eliminates case 2.

 

vi) The box that contains Books is not placed immediately above the box that contains Erasers.

vii) Box P is placed above the box that contains Pencils.

Hence, three boxes are kept between box N and the box that contains Pen.

Six boxes: L, M, N, O, P and Q

Six items: Books, Erasers, Pen, Pencils, Sharpener and Stapler

i) Box L is kept at the top of the stack.

ii) Box M which contains Pencils is kept three boxes below the Box L.

iii) Box N is kept immediately above the box which contains Erasers.

 

iv) As many boxes are placed above the box N as many are placed below the box that contains Sharpener.

v) The box O contains Pen and is kept below the box that contains Erasers.

This eliminates case 2.

 

vi) The box that contains Books is not placed immediately above the box that contains Erasers.

vii) Box P is placed above the box that contains Pencils.

Hence, Books are kept in the box L.

Eight persons joined Infosys.

Dates:- 5^th and 17^th

Months:- January, April, August, and September.

Marks:- 14, 16, 19, 22, 27, 29, 32 and 33.

1. H joined immediately after the one who scored 29 and in a month with 30 days.
2. The highest scorer joined on 5^th April.
3. C scored three marks lesser than D and joined in April.
4. Total marks scored by the candidates, who joined in April is not more than 50 marks.

So, C should be 16 and D should be 19.

Following are the possibilities we get,

 

5. Three persons joined between those who scored 16 marks and 27 marks.
6. H doesn’t score 27 marks, so case 3 is eliminated.

 

7. G scored two marks more than F.

So, the only possibility is G scored 29 and F scored 27.

8. A joined before G.
9. Number of persons who joined before A is the same as those who joined after F.

 

10. D joined immediately after A, this is violated in case 1, so it is eliminated.
11. E scored more than B and joined before B. So, E must have scored 33 marks.
12. Only one person joined between B and the one who scored 22 marks. So, H scored 22 marks.
13. Person, who scored 19 marks joined immediately after the one who scored 32 marks. 

So, D scored 19 marks, and A scored 32 marks. Thus, B must have scored 14 marks.

The final schedule table is given below:

 

Hence, A scored the 2^nd highest marks (32).

Eight persons joined Infosys.

Dates:- 5^th and 17^th

Months:- January, April, August, and September.

Marks:- 14, 16, 19, 22, 27, 29, 32 and 33.

1. H joined immediately after the one who scored 29 and in a month with 30 days.
2. The highest scorer joined on 5^th April.
3. C scored three marks lesser than D and joined in April.
4. Total marks scored by the candidates, who joined in April is not more than 50 marks.

So, C should be 16 and D should be 19.

Following are the possibilities we get,

 

5. Three persons joined between those who scored 16 marks and 27 marks.
6. H doesn’t score 27 marks, so case 3 is eliminated.

 

7. G scored two marks more than F.

So, the only possibility is G scored 29 and F scored 27.

8. A joined before G.
9. Number of persons who joined before A is the same as those who joined after F.

 

10. D joined immediately after A, this is violated in case 1, so it is eliminated.
11. E scored more than B and joined before B. So, E must have scored 33 marks.
12. Only one person joined between B and the one who scored 22 marks. So, H scored 22 marks.
13. Person, who scored 19 marks joined immediately after the one who scored 32 marks. 

So, D scored 19 marks, and A scored 32 marks. Thus, B must have scored 14 marks.

The final schedule table is given below:

 

No person joined between B (14) lowest scorer and G (29) 3^rd highest scorer.

Hence, none of these is the answer.

Eight persons joined Infosys.

Dates:- 5^th and 17^th

Months:- January, April, August, and September.

Marks:- 14, 16, 19, 22, 27, 29, 32 and 33.

1. H joined immediately after the one who scored 29 and in a month with 30 days.
2. The highest scorer joined on 5^th April.
3. C scored three marks lesser than D and joined in April.
4. Total marks scored by the candidates, who joined in April is not more than 50 marks.

So, C should be 16 and D should be 19.

Following are the possibilities we get,

 

5. Three persons joined between those who scored 16 marks and 27 marks.
6. H doesn’t score 27 marks, so case 3 is eliminated.

 

7. G scored two marks more than F.

So, the only possibility is G scored 29 and F scored 27.

8. A joined before G.
9. Number of persons who joined before A is the same as those who joined after F.

 

10. D joined immediately after A, this is violated in case 1, so it is eliminated.
11. E scored more than B and joined before B. So, E must have scored 33 marks.
12. Only one person joined between B and the one who scored 22 marks. So, H scored 22 marks.
13. Person, who scored 19 marks joined immediately after the one who scored 32 marks. 

So, D scored 19 marks, and A scored 32 marks. Thus, B must have scored 14 marks.

The final schedule table is given below:

 

B scored 14 marks and G, who joined on 17^th August, scored 29 marks.

Difference = (29 – 14) = 15.

Hence, the difference is 15.