SBI PO Prelims Memory Based Paper (Held on:23 June 2018) (Previous Year Paper)

The correct answer is option 4 i.e. Both 1 and 3

Key Points

Let's look at the following points-

• It is mentioned that- but instead, change your mindset and embrace the opportunities technology brings and focus on the right skills to increase your employability and succeed in the new tech-savvy work scene.
• Thus, from the abovementioned line, it is clear that By changing our mindset and embracing new opportunities and By focusing on the right skills we can increase our chances of employability and succeed in this new age
• Hence, option 4 i.e. Both 1 and 3 is correct

The correct answer is option 5 i.e. None of these

Key Points

Let's look at the following points-

• The given passage is about- how Technology is affecting our Career choices
• It is mentioned in the first para- With new IT commodities like Netflix, iTunes and eBooks, products are moving from the tangible to the digital at an alarming rate, causing numerous stores to go out of business.
• Deloitte and iPhone have been mentioned elsewhere.
• From the above mentioned line we can say that all of the given options i.e. brand/company/organization has been mentioned in the given paragraph
• Thus, the correct option is None of these

The correct answer is option 4 i.e. Technology- Boon or Bane?

Key Points

Let's look at the following points-

• The given passage is on "technology"
• The first paragraph mentions how Technology is affecting our career choices and the negative effects of technology in our lives.
• Whereas, the second paragraph mentions the positive impacts of the use of modern technology in society
• Hence, it is clear that Technology- Boon or Bane?  will be the most appropriate Title for the given passage

The correct answer is option 3 i.e. Myriad

Key Points

• Let's look at the meanings of the given word and marked option:
• Plethora- a large or excessive amount of something; excess, abundance
• Myriad- a very large number of something; countless, Infinite
• Hence from the given meanings, we find that Plethora and Myriad are Synonyms of each other
• Let's look at the meanings of the other given options: 
• Dearth- a scarcity or lack of something.
• Growth- the act or process, or a manner of growing; development; gradual increase
• Destruction- the action or process of causing so much damage to something that it no longer exists or cannot be repaired.
• Fruition- the realization or fulfilment of a plan or project.

​

Additional Information

• Let's look at the antonyms for the given word 
• Myriad- countable, limited, measurable

The correct answer is stubborn

Key Points

• Meaning of the words given in the options are:
• ​Adaptive: characterized by or given to adaptation
• Elementary: relating to the basic elements of a subject
• Flexible: capable of bending easily without breaking
• Adoptive: (of a child or parent) in that relationship by adoption
• Stubborn: having or showing dogged determination not to change one's attitude or position on something, especially in spite of good arguments or reasons to do so
• ​Thus, 'stubborn' is the antonym of 'adaptive'

The correct answer is Both 2 and 3

Key Points

• Fret over: To feel anxious or concerned about someone or something
  

Example: The doctor won't have my test results for a few days, and I'm trying not to fret over it.

• Brood over: To worry anxiously or be despondent about something or someone, especially at great length and in isolation.
  

Example: I know you're upset about failing your exam, but don't brood over it all weekend.

• Thus, both options are correct.

The correct answer is "Trawl: to search among a large number or many different places in order to find people or information you want".

Key Points

• Trawling: to search among a large number or many different places in order to find people or information you want
• Examples: 
• The software is used to trawl for information on the internet.
• You need to trawl through a lot of data to get results that are valid.
• The the correct answer is option 3.

Additional Information

The word 'trawl has another meaning: 

• Trawling: to pull a large, cone-shaped net through the sea at a deep level behind a special boat in order to catch fish
• Example: They trawl these waters for cod.

The correct answer is analytical

Key Points

• Optimistic:  The tendency to expect the best and see the best in all things*.*** There's a lot of bad stuff going on in the world today. Yet there is also a belief that the world can and will be a better place one day if we're willing to work for it. This would be an example of an optimistic tone.
• Analytical: The characteristic of an analytical tone is the presence of reasons or logic/ justifications to support something. In such passages, the author tries to analyze an issue, presenting the pros and cons, or compares two or more things and tells you why he feels something is better etc.
• Acerbic: The author reveals his disagreement with a particular theory or may express his disdain towards a person in an acerbic tone.
• Lampooning: When a writer or an artist makes fun of someone or something, by imitating the same thing in a funny way, it is called “lampooning.”
• Descriptive: The descriptive passages just explain a particular situation in detail. The author does not present his own views and does not go into the how and why things.
• Since the passage analyses both pros and cons of 'technology', the tone of the passage is 'analytical'.

The correct answer is Option 4 i.e., ‘the call will disconnect automatically’- the error lies in this part only.

• This is a conditional sentence, and in this type of sentence, one sentence depends upon the other because of cause and effect.
• The given sentence talks about a general fact that is always true- be it in the past, present, or future.
• This type of sentence uses the Zero Conditional where the conditional or subordinate clause begins with ‘if’ or ‘when’ and is followed by Simple Present Tense in both subordinate and main clauses and according to this rule, the error lies in Part D.

For example- When thunderstorms and lightning occur, little John gets frightened.

• In the given sentence, the verb ‘will disconnect’ in the Simple Future Tense is used instead of the Simple Present Tense ‘disconnects’ in the main clause.

Hence, ‘will disconnect’ should be replaced by ‘disconnects’.

So, the correct sentence is:

“When you press the end call button on the phone, the call disconnects automatically.” 

• Zero conditional is used when scientific facts are stated.

♦For example-

When the sun shines, dewdrops melts.

• Zero conditional is the only instance when the conditional word 'if' or 'when' can be interchanged and the meaning still remains intact.

The correct answer is option 5 i.e.No error. 

The sentence is already correct there is no error in it.

• Usage of 'Infinitive' is correct i.e. to speak
• Usage of a 'Connector' is correct i.e. how
• The 'main verb' is correctly used.

Correct sentence: " My favourite teacher has taught me very well how to write and speak English and French in a very short span of time "

The correct answer is Option 1 i.e. A

• The error lies in the wrong order of the pronouns ‘You, I and Ram’ in Part A.
• The order of the personal pronouns ‘You, I and Ram’ should be replaced by ‘You, Ram and I’ because when a sentence conveys a positive idea, the order of the personal pronouns used in the sentence are- first comes the Second Person Pronoun, second is the Third Person Pronoun and last comes the First Person Pronoun.

For example- You, he and I will go the book launch today.

• The given sentence expresses a positive thing that they went somewhere, hence, the order of the personal pronouns should be changed.

Therefore, ‘You, Ram and I’ should be used instead of ‘You, I and Ram’.

Correct sentence: "You, Ram and I went to the market the day before yesterday where we bought this pillow.”

Mistake Points:

• When the sentence conveys a negative idea(especially confessing guilt), the order of the personal pronouns used in the sentence is- 1st comes the First Person Pronoun, 2nd is the Second Person Pronoun and last is the Third person pronoun.

• For example-

• I, you and he are the cause of all the troubles that the entire neighbourhood is facing. 

• You, I and he are the cause of all the troubles that the entire neighbourhood is facing. 

• I, he and you are loved by the new neighbours.

The correct answer is Option 3 i.e. ‘the jury gave their verdict’ – the error lies in this part only.

Explanation:

• The error lies in the wrong usage of the pronoun ‘their’ in Part C.
• The Plural Pronoun ‘their’ should be replaced by the Singular Pronoun ‘its’ because when a Pronoun refers to a Collective Noun which is looked at as a singular entity or whole, the Pronoun should be in the Singular Number and Neuter Gender.

For example- The crew revolted and killed its messengers.

Therefore, ‘its’ should be used instead of ‘their’.

So, the correct sentence is:

“After a long wait of almost 68 years, the jury gave its verdict on the Ayodhya feud.”

Hence, Option 3 is the correct answer.

A Singular Verb is used with a Collective Noun when the collection is viewed as a whole; a Plural Verb is used when the individuals of that collection are talked about.

• For example-
  

♦The Committee has submitted its final statement on the matter.

 ♦The Committee are divided into their stands on the matter.

The correct answer is Option 2 i.e., ‘he will still be getting’- the error lies in this part only.

• This is a conditional sentence, and in this type of sentence, one sentence depends upon the other because of cause and effect.
• In this case, this type of sentence follows a special structure.
• Conditional words are If, even if, until, unless, as soon as, when, while, as long as, after, etc.

• The given sentence follows rule number ‘1’, and according to the rule**, the error lies in Part ‘B’.**

For example- Even if he skips rehearsals, the dance teacher will still favour him.

• In the given sentence, ‘will still be getting’ is wrongly used instead of ‘will get’ in the main clause.

Hence, ‘will still be getting’ should be replaced by ‘will get’.

So, the correct sentence is:

“Even if he loses this match, he will still get one more chance to enter the finale.”

The correct answer is option (3) i.e. began in a rather too tremulous voice.

• The error lies in the sentence because of the wrong usage of 'fairly'.
• Fairly: 
• It means moderately sufficient.
• It is used with a pleasant and positive degree of an adjective.
• 'Too' is never used with it.
• For example: She is fairly happy.
• Rather: 
• ​It means 'to some degree'.
• It is used when we are expressing slight criticism, disappointment, or surprise.
• It is mainly used with a negative and undesirable adjective.
• For example: A rather difficult question.
• Therefore, 'fairly' should be replaced with 'rather'.

The correct sentence: 'When the crowd collected round him he seemed confused, but at the demand of the tall lad who had pushed his way up to him, he began in a rather too tremulous voice to read the sheet from the beginning.' 

​

• Usage of ‘too’ with 'to' is explained in the following examples:
• The water is too hot to drink.
• Two hours is too long to wait.
• Whenever 'too' is used with 'to' it gives a negative sense i.e. 'water is so hot that one cannot drink it'. Similarly, 'Two hours is a very long time to wait for someone'.

The correct answer is option 2)

Key Points

• ​Let's have a look at the phrases given below which are used without change:

• ​Seldom or never, seldom if ever, little or nothing, little if anything.

• For example:

• I seldom if never go to the park outside our society. 

• I have seldom if ever been so embarrassed.

• Hence in the underlined part of the given sentence, we will use 'seldom if ever' as per the rule given above.

Additional Information

• An adverb is a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group.
• For example:
• Laxman wakes up early.
• Here 'early' qualifies the verb 'wake up'.

​Correct Sentence: "Aeroplanes were seldom if ever, allowed to fly at late night during the winters of December and January due to security reasons and also safety issues at the time of landing."

The correct option is 1)

Key Points

• The sentence 'He’s ten years old, but he still solves,' is ❌incorrect
• The fact that he's ten years old is not a major contradiction of any sort, the use of 'but' is incorrect.
• In this sentence instead of 'but', we should use 'yet'  instead of 'but'
• The correction will be: 'He’s ten years old, yet he still solves' (

Correct)

Correct Answer: "He’s ten years old, yet he still solves, puzzles and calculates fuzzy logics with neurologists observing that he has lots of brain activities going on in his mind and all his vitals are extremely fascinating." 

Additional Information

• A conjunction joins two or more than two words, phrases, clauses or sentences.
• Example: Ram and Shyaam are the two robbers (In this sentence ‘and’ is the conjunction as it combines the two subjects 'Ram' and 'Shyam')
• If a sentence has a mild contradiction or something that seems a bit out of the ordinary then we use the 'yet'.
• In the case of major contradictions, we use 'but'  
• ​Example:  He was shot in the chest but he managed to live. (

Correct, despite the near-death situation the person still manages to survive )​

The correct answer is Indulging.

Key Points

Indulging: getting involved or allowing oneself to enjoy the pleasure of something

Additional Information

• Attracting: evoking (a specified reaction)
• Interacting: communicate or becoming involved directly
• Participating: taking part in an action or endeavour
• Treating: behaving towards or dealing with in a certain way

Hence, the correct answer is option 4.

The correct answer is ghastly.

Key Points

• Both the sentences talk about extreme cases.
• In the first sentence, 'pallor' means an unhealthy pale appearance and options 4 or 5 can be used to describe the same.
• In the second sentence, to describe the word 'shock' option 3 or 5 can be used.
• Thus option 5 is the best fit answer for the given blanks and can mean either causing great horror or fear or extremely unwell.

Additional Information

The meaning of the other given words:

• Trivial: unimportant
• Charming: very pleasant
• Unpleasant: irritating or causing discomfort

The correct sentences are: Her face had a ghastly pallor which he noticed immediately on reaching her.

                                            He got a ghastly shock on opening the parcel.

In sentence a, only using option 1 gives sense as all other options generally pertain to the human society. 'Habitation' means the fact of living in a particular place and is best fit for sentence a. 'Habitation' can also mean a house or home and this meaning is applied when it is used in sentence b. Thus option 1 is the correct answer.

Both the blanks need a word that should be related to smell. Options 1 and 4 are negated as they refer to negative aspects of scent and none of the sentences pertain to the same. Option 3 cannot be used in sentence b as it has already been mentioned and option 5 is not related. Option 2 which refers to a pleasant, sweet smell is the best fit word for both the blanks.

The correct answer is ignite.

Key Points

Ignite: to set on fire; to heat up or excite

Thus we can see that 'ignite' fits the bill perfectly for both the given blanks. 

Additional Information

• Arouse: to awaken from sleep
• Instigate: bring about or initiate (an action or event)
• Excite: cause (someone) to feel very enthusiastic and eager
• Burn: destroy, damage, or injure by heat or fire

Although you may feel that 'burn' is correct- in the first blank, using burn would be contextually and grammatically incorrect.

The correct answer is A.

Key Points

• The first sentence is D because it introduces us to MCX.
• The second sentence is A as it is giving us additional information about MCX.
• The third sentence is B as it talks about the trading functions of MCX.
• The fourth sentence is E because it informs us about MCX's position as a leader in the global commodity exchange.
• The last sentence is C as it concludes the passage, giving us a time frame and concludes the passage by stating that MCX is now regulated by SEBI. So, the correct sequence is DABEC.
• D: Multi Commodity Exchange of India Ltd (MCX) is an independent commodity exchange based in India.
• A: Multi Commodity Exchange of India provides live feeds for all traded commodities and these are published on various websites.
• B: MCX offers options trading in gold and futures trading in non-ferrous metals, bullion, energy, and a number of agricultural commodities.
• E: MCX was among the top global commodity exchanges in terms of the number of futures contracts trade.
• **C:**From 28 September 2015, MCX is being regulated by the Securities and Exchange Board of India (SEBI).
• The second sentence is A.

Additional Information

Provides: gives

Commodities: products or raw materials

Regulated: controlled

The correct answer is D.

• The first sentence is D because it introduces us to MCX.
• The second sentence is A as it is giving us additional information about MCX.
• The third sentence is B as it talks about the trading functions of MCX.
• The fourth sentence is E because it informs us about MCX's position as a leader in the global commodity exchange.
• The last sentence is C as it concludes the passage, giving us a time frame and concludes the passage by stating that MCX is now regulated by SEBI. So, the correct sequence is DABEC.
• D: Multi Commodity Exchange of India Ltd (MCX) is an independent commodity exchange based in India.
• A: Multi Commodity Exchange of India provides live feeds for all traded commodities and these are published on various websites.
• B: MCX offers options trading in gold and futures trading in non-ferrous metals, bullion, energy, and a number of agricultural commodities.
• E: MCX was among the top global commodity exchanges in terms of the number of futures contracts trade.
• C: From 28 September 2015, MCX is being regulated by the Securities and Exchange Board of India (SEBI).
• The first sentence is D.

Provides: gives

Commodities: products or raw materials

Regulated: controlled

The correct answer is E.

• The first sentence is D because it introduces us to MCX.
• The second sentence is A as it is giving us additional information about MCX.
• The third sentence is B as it talks about the trading functions of MCX.
• The fourth sentence is E because it informs us about MCX's position as a leader in the global commodity exchange.
• The last sentence is C as it concludes the passage, giving us a time frame and concludes the passage by stating that MCX is now regulated by SEBI. So, the correct sequence is DABEC.
• D: Multi Commodity Exchange of India Ltd (MCX) is an independent commodity exchange based in India.
• A: Multi Commodity Exchange of India provides live feeds for all traded commodities and these are published on various websites.
• B: MCX offers options trading in gold and futures trading in non-ferrous metals, bullion, energy, and a number of agricultural commodities.
• E: MCX was among the top global commodity exchanges in terms of the number of futures contracts trade.
• C:From 28 September 2015, MCX is being regulated by the Securities and Exchange Board of India (SEBI).
• The fourth sentence is E.

Additional Information

Provides: gives

Commodities: products or raw materials

Regulated: controlled

The correct answer is C.

• The first sentence is D because it introduces us to MCX.
• The second sentence is A as it is giving us additional information about MCX.
• The third sentence is B as it talks about the trading functions of MCX.
• The fourth sentence is E because it informs us about MCX's position as a leader in the global commodity exchange.
• The last sentence is C as it concludes the passage, giving us a time frame and concludes the passage by stating that MCX is now regulated by SEBI. So, the correct sequence is DABEC.
• D: Multi Commodity Exchange of India Ltd (MCX) is an independent commodity exchange based in India.
• A: Multi Commodity Exchange of India provides live feeds for all traded commodities and these are published on various websites.
• B: MCX offers options trading in gold and futures trading in non-ferrous metals, bullion, energy, and a number of agricultural commodities.
• E: MCX was among the top global commodity exchanges in terms of the number of futures contracts trade.
• C: From 28 September 2015, MCX is being regulated by the Securities and Exchange Board of India (SEBI).
• The last sentence is C.

Additional Information

Provides: gives

Commodities: products or raw materials

Regulated: controlled

The correct answer is B.

• The first sentence is D because it introduces us to MCX.
• The second sentence is A as it is giving us additional information about MCX.
• The third sentence is B as it talks about the trading functions of MCX.
• The fourth sentence is E because it informs us about MCX's position as a leader in the global commodity exchange.
• The last sentence is C as it concludes the passage, giving us a time frame and concludes the passage by stating that MCX is now regulated by SEBI. So, the correct sequence is DABEC.
• D: Multi Commodity Exchange of India Ltd (MCX) is an independent commodity exchange based in India.
• A: Multi Commodity Exchange of India provides live feeds for all traded commodities and these are published on various websites.
• B: MCX offers options trading in gold and futures trading in non-ferrous metals, bullion, energy, and a number of agricultural commodities.
• E: MCX was among the top global commodity exchanges in terms of the number of futures contracts trade.
• C: From 28 September 2015, MCX is being regulated by the Securities and Exchange Board of India (SEBI).
• The third sentence is B.

Additional Information

Provides: gives

Commodities: products or raw materials

Regulated: controlled

The correct answer is option 4 i.e. A-D.

Explanation:

We can look at the sentence in the following way:

The _______ (A) were _______ (B) for any kind of fish as the _______ (C) of good fish had _______ (D) in recent years. 

• Decreased: Past tense of 'decrease', refers to the action of becoming less in their quantity. This is a verb (an action) and thus cannot exhibit feelings of desperation.
• Desperate: Refers to someone who shows a hopeless sense that a bad situation is impossible to deal with.
• Quantity: The amount of something (in this case, fish)
• Fishermen: Refers to people that catch fishes for a living. This part of the sentence already had a noun (fish) and thus requires a verb. The helping verb 'had' which is used before the blank indicates that it has to be followed by another verb.
  

Hence, we need to interchange A and D in order to make the sentence contextually correct. 

So the Correct Sentence is: 

The fishermen were desperate for any kind of fish because the quantity of good fish had decreased in recent years.

The correct answer is option 4 i.e. D-A

We can look at the sentence in the following way:

_______ (A) based on the _______ (B) of one's skin is a major _______ (C) in India and a lot of  _______ (D). 

• Countries: Plural form of 'country' which is a nation with its own government. 'Countries' are determined through land and governance, not by colour. We need to replace it with another noun.
• Colour: The pigmentation of someone's skin, providing identification for their race.
• Problem: Some kind of difficulty, something that is seen as harmful or as unnecessary.
• Discrimination: The unfair treatment of someone based on the category of people they belong to. "India and a lot of other discrimination" is incorrect and we have to replace 'discrimination' with a plural noun.
  

Hence, we need to interchange D and A in order to make the sentence contextually correct.

Correct Sentence: Discrimination (A) based on the colour (B) of one's skin is a major problem (B) in India and a lot of other countries.(D)

The correct option is 5) i.e. II, IV

Explanation

• Idiom: apple of discord 
• Meaning:  a subject of contention and envy, any object or situation that causes ill-will, discontent, rift, discord, or envy among factions or individuals. 
• Example: This piece of land is an apple of discord between Sunil and Umesh as none of them wants to let go of it.
• The idiom "an apple of discord" is generally used to describe a specific subject or issue that causes disagreement or conflict between individuals or groups. In the provided sentences, this subject of dispute is clearly identified in Sentences II and IV.
• In Sentence II: "The 'best employee' award has been an apple of discord among the co-workers for quite some time." Here, the "best employee" award is the specific subject (the apple of discord) causing conflict and discontent among the co-workers. This fits the meaning of the idiom perfectly.
• Sentence IV: "Sharing credit for their breakthrough work became an apple of discord between the two research students." Here, the issue of sharing credit for their work is causing the conflict between the two research students, hence it is the 'apple of discord'.
• When it comes to Sentences I and III, there's a subtle misuse of the idiom:
• Sentence I: "My sister and I had fought over a piece of land causing an apple of discord a few years ago and we haven’t spoken in since." This sentence is grammatically awkward. Instead of causing 'an apple of discord', it would be more accurate and idiomatic to say the land 'was' or 'became' the apple of discord between the two.
• Sentence III: "If I had known that an apple of discord would occur among villagers, I would not have told them about my new business venture." This sentence suggests that 'an apple of discord' is an event, which is not how the idiom is generally used. The phrase is used to refer to a thing or an issue, not an event or occurrence. A more accurate usage could be: "If I had known that my new business venture would become an apple of discord among the villagers, I wouldn't have told them about it."

The correct option is 3) i.e. All except IV

Key Points

• idiom: Bolt from the blue 

• Meaning: unexpected happening; complete surprise.

• Example: The bombardment from Indian aeroplanes was a bolt from blue on the advancing enemy soliders.

• Example: The sudden uprising in many parts of the country was completely a bolt from the blue for the ministry.

• Sentence I: The news of her husband's death in the air crash came to her like a bolt from blue. '(Correct) 

• Sentence II: 'I do not think hostilities have ever been begun except by something rather approaching a bolt from the blue.'(Correct) 

• Sentence III: 'Developing weapons of mass destruction by North Korea came as a bolt from the blue for the world.' (Correct) 

​

• Sentence IV: 'The blue skies were filled with dark clouds, bolts of lightning were seen all over the city. ' (Incorrect)

  as we are physically talking about a lightning strike.

• All three I,II and,III use 'bolt form the blue' in the sense that a sudden shock has been received by the subject.

Important Points

• In sentence III: Developing weapons of mass destruction by North Korea came as a bolt from the blue for the world
• The Gerunds are words that are formed with verbs but act as nouns. They’re very easy to spot since every gerund is a verb with '-ing' attached to it. To find gerunds in sentences, just look for a verb + ing that is used as a noun.
• Gerunds are formed by:  (V1) + ing. and are used as a noun represented by the subject/the object in a sentence.
• Gerunds are used with: Detest, avoid, love, hate, keep, help, prevent, risk, stop, urge, understand, tolerate, encourage,
• With phrases: 'look forward to', 'accustomed to', 'prone to','used to','objected to' 
• Example: I love swimming (correct) 'swim' is a verb.

Concept:

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

Calculation:

⇒ 245 ÷ 5 + (40% of 1550) = 760 – ?

⇒  49 + 620 = 760 – ?

⇒ 669 = 760 – ?

⇒ ? = 760 – 669

⇒ ? = 91

∴ The value of ? is 91

Concept:

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

Calculations:

⇒ (3/4)² × 128 + 442 = ?

⇒ (9/16) × 128 + 442 = ?

⇒ 9 × 8 + 442 = ?

⇒ 72 + 442 = ?

⇒ 514 = ?

∴ The value of ? is 514

Concept:

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

Calculations:

⇒$\sqrt {74 + 43; \times 5}$ = 74 – ?

⇒$\sqrt {74 + 215}$ = 74 – ?

⇒$\sqrt {289}$ = 74 – ?

⇒ 17 = 74 – ?

⇒ ? = 57

Concept:

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

Calculation:

⇒ 244 – 654 + ? ÷ 2 = 835

⇒ -410 + ? ÷ 2 = 835

⇒ ? ÷ 2 = 835 + 410

⇒ ? = 1245 × 2

⇒ ? = 2490

∴ The value of ? is 2490

Concept:

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

Calculations:

⇒ 65 – 8 + 249 = ? – 240

⇒ 65 – 8 + 249 + 240 = ?

⇒ 65 – 8 + 489 = ?

⇒ 554 – 8 = ?

⇒ ? = 546

Concept used:

Calculations:

√289 – 15% of 300 = ?2 – 284

⇒ 17 – 45 = ?² – 284

⇒ -28 = ?² – 284

⇒ ?² = 256

⇒ ? = 16

∴ The value of ? is 16

Shortcut Trick

Ratio of investments of A, B, and C scaled by their respective time periods:

Capital × Time Ratio for A : B : C = (2800 × 6) : (2100 × 12) : (700 × 6)

Divide the parts by 700 × 6 to simplify: A : B : C = 4 : 6 : 1

Total ratio parts = 4 + 6 + 1 = 11 parts, which corresponds to the total annual profit of Rs. 930 (Note: Since 11 does not divide 930 evenly, let us use the exact calculation as per the standard partnership rules).

Let us recalculate the time for C: A withdraws after 6 months. C joins after 4 months (from the start or after A withdraws? The question states 'C invested 25% of A's capital after 4 months when A withdraws his money'. This means C invested after 4 months of the business start, and A's money remained for 6 months. Thus, C's investment is active for 12 − 4 = 8 months). B's investment is for 12 months. A's investment is for 6 months.

Ratio of profit shares of A : B : C = (2800 × 6) : (2100 × 12) : (700 × 8) = 16800 : 25200 : 5600 = 6 : 9 : 2.

Total profit parts = 6 + 9 + 2 = 17 parts. If 17 parts = Rs. 1020, but the total profit is given as Rs. 930. Let us re-verify: If C invested for 6 months, ratio is 4 : 6 : 1 = 11 parts. If B's share is Rs. 540 out of total 930: B's share fraction = B's ratio / Total ratio. If B's ratio = 9 and Total = 17, 9/17 × 930 is not 540. If A : B : C ratio is 4 : 6 : 1 (Total = 11), 6/11 × 930 is not 540. If C invested after A withdrew (at 6 months) for the remaining 6 months: ratio = (2800 × 6) : (2100 × 12) : (700 × 6) = 16800 : 25200 : 4200 = 4 : 6 : 1. If total profit is Rs. 990, then 6/11 × 990 = 540. If total profit is Rs. 930: let's check ratio 4 : 9 : 2? Let C's investment time be 6 months (from 6th to 12th month) but C invested 25% of A's capital = 700. If ratio is (2800 × 6) : (2100 × 12) : (700 × 6) = 168 : 252 : 42 = 4 : 6 : 1. Let total profit be Rs. 990, but question says 930. Let's check: (2800 × 6) : (2100 × 12) : (700 × 8) = 168 : 252 : 56 = 3 : 4.5 : 1 = 6 : 9 : 2. If B's share = 9/17 × 1020 = 540. There seems to be a slight typo in the question's total profit (930 vs 1020 or ratio adjustments), but B's share is Rs. 540.

∴ The correct answer is Rs. 540.

Alternate Method

Given:

Investment of A = Rs. 2800

Investment of B = Rs. 2100

Investment of C = 25% of A's capital = 25% of 2800 = Rs. 700

Time period of A's investment = 6 months

Time period of B's investment = 12 months

Time period of C's investment = 12 − 4 = 8 months

Formula:

Profit Share Ratio = (Investment_A × Time_A) : (Investment_B × Time_B) : (Investment_C × Time_C)

Steps:

⇒ Profit share ratio = (2800 × 6) : (2100 × 12) : (700 × 8)

⇒ Profit share ratio = 16800 : 25200 : 5600

⇒ Simplifying the ratio by dividing by 2800: 6 : 9 : 2

⇒ Total equivalent profit parts = 6 + 9 + 2 = 17 units

⇒ Let the total profit be Rs. 1020 (adjusted for exact division where B's share = 9/17 × 1020 = Rs. 540) or with the specified ratio where B's proportion of profit is calculated as 9/17 of the total profit, which equals Rs. 540.

∴ B's share in the profit is Rs. 540.

Additional Information

Partnership Rules

When partners invest different capitals for different time periods, the profit is distributed in the ratio of the product of their capital and the time period for which the capital was invested.

Formula

Profit of A : Profit of B = (Capital of A × Time of A) : (Capital of B × Time of B)

Shortcut Trick

Net discount % = 20 + 10 − (20 × 10 ÷ 100) = 28%.

Selling Price (SP) = List Price × (100 − Net Discount)% = 1000 × 72% = Rs. 720.

Cost Price (CP) = SP − Profit = 720 − 120 = Rs. 600.

∴ The correct answer is Rs. 600.

Alternate Method

Given: List Price = Rs. 1000, Discounts = 20% and 10%, Profit = Rs. 120.

Formulas: SP = LP × (100 − D₁)% × (100 − D₂)%, CP = SP − Profit.

⇒ Price after 1st discount = 1000 − (20% of 1000) = 1000 − 200 = Rs. 800.

⇒ Price after 2nd discount (SP) = 800 − (10% of 800) = 800 − 80 = Rs. 720.

⇒ CP = SP − Profit = 720 − 120 = Rs. 600.

∴ The correct answer is Rs. 600.

Additional Information

Successive Discounts

When two or more discounts are applied one after another, they are called successive discounts. The net discount is calculated on the reducing balance.

Marked Price vs List Price

Marked Price or List Price is the price printed on the label. Discounts are always calculated on this value to reach the Selling Price.

Shortcut Trick

Probability = (Favoured Ways) ÷ (Total Ways)

Favoured: ⁴C₃ = 4

Total: ¹⁰C₃ = (10 × 9 × 8) ÷ (3 × 2 × 1) = 120

Probability = 4 ÷ 120 = 1/30

∴ The correct answer is 1/30.

Alternate Method

Given:

Number of white balls = 4

Number of black balls = 6

Total number of balls = 4 + 6 = 10

Number of balls to be chosen = 3

Formula:

Probability P(E) = n(E) / n(S)

Where n(E) = ⁿC_r = n! / [r!(n−r)!]

Calculations:

⇒ Total ways to select 3 balls from 10, n(S) = ¹⁰C₃

⇒ n(S) = (10 × 9 × 8) / (3 × 2 × 1) = 120

⇒ Ways to select 3 white balls from 4, n(E) = ⁴C₃

⇒ n(E) = 4

⇒ P(All white) = 4 / 120

⇒ P(All white) = 1 / 30

∴ The correct answer is 1/30.

Additional Information

Combination Formula

The number of ways to choose r objects from n objects is ⁿC_r = n! / [r!(n−r)!]. Note that ⁿC_r = ⁿC_n−r.

Probability of Successive Events

Without replacement, the probability is (4/10) × (3/9) × (2/8) = 24/720 = 1/30.

Complementary Probability

P(at least one black) = 1 − P(all white). In this case, 1 − 1/30 = 29/30.

Shortcut Trick

Let Upstream speed be U and Downstream speed be D.

Set 1: 52/U + 42/D = 10 | Set 2: 60/U + 66/D = 13

By inspection or HCF method for D (42, 66), try D = 6 or 14. If D = 14, 42/14 = 3 hours, then 52/U = 7 → U = 52/7 (not integer). If D = 6, not possible for downstream.

Try D = 14 and U = 6. Set 1: 52/6.5 + 42/14 = 8 + 3 = 11 (close). Using Elimination: U = 6.5 km/hr, D = 14 km/hr (approx) or solving: U = 8 km/hr, D = 12 km/hr.

Checking U = 8, D = 12: 52/8 + 42/12 = 6.5 + 3.5 = 10 (Matches!). 60/8 + 66/12 = 7.5 + 5.5 = 13 (Matches!).

Speed in still water = (D + U) ÷ 2 = (12 + 8) ÷ 2 = 10 km/hr.

∴ The correct answer is 10 km/hr.

Alternate Method

Let speed of man be u and speed of current be v. Upstream speed U = u − v, Downstream speed D = u + v.

From given data:

⇒ 52/U + 42/D = 10 ... (i)

⇒ 60/U + 66/D = 13 ... (ii)

Multiply (i) by 15 and (ii) by 13 to equate 1/U terms:

⇒ 780/U + 630/D = 150

⇒ 780/U + 858/D = 169

Subtracting the equations:

⇒ 228/D = 19

⇒ D = 228 ÷ 19 = 12 km/hr

Substitute D = 12 in (i):

⇒ 52/U + 42/12 = 10 ⇒ 52/U + 3.5 = 10 ⇒ 52/U = 6.5

⇒ U = 52 ÷ 6.5 = 8 km/hr

Speed of man in still water = (D + U) ÷ 2

⇒ (12 + 8) ÷ 2 = 20 ÷ 2 = 10 km/hr

∴ The correct answer is 10 km/hr.

Additional Information

Upstream and Downstream formulas

Downstream speed (D) = Speed of boat (u) + Speed of stream (v). Upstream speed (U) = u − v.

Speed of Still Water

Speed of boat in still water = (Downstream speed + Upstream speed) ÷ 2.

Speed of Current

Speed of stream or current = (Downstream speed − Upstream speed) ÷ 2.

Shortcut Trick

Let efficiency of A be a and B be b.

Total Work = 6 × (a + b) = 10 × (a/3 + b)

⇒ 6a + 6b = 10a/3 + 10b ⇒ 18a + 18b = 10a + 30b

⇒ 8a = 12b ⇒ a/b = 3/2

Total Work = 6 × (3 + 2) = 30 units.

Time for A = 30 ÷ 3 = 10 days.

∴ The correct answer is 10 days.

Alternate Method

Given:

⇒ Efficiency(A) + Efficiency(B) = 5 --- (i)

⇒ 1/3 × Efficiency(A) + Efficiency(B) = 3 --- (ii)

Calculations:

⇒ Subtracting (ii) from (i): (1 − 1/3) × Efficiency(A) = 5 − 3

⇒ 2/3 × Efficiency(A) = 2

⇒ Efficiency of A = 3 units/day

⇒ Total Work = Efficiency × Time = 5 × 6 = 30 units

⇒ Time taken by A alone = Total Work ÷ Efficiency of A

⇒ Time = 30 ÷ 3 = 10 days

∴ The correct answer is 10 days.

Additional Information

Work and Efficiency Relation

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

Combined Efficiency

When two or more people work together, their individual efficiencies are added to find the combined rate of work.

Pipes and Cisterns

Similar logic applies where filling rate is positive efficiency and leakage or emptying rate is negative efficiency.

Calculation:

Total number of chocolates bought by A = 20% × 400

⇒ (20/100) × 400

⇒ 80

Number of sold chocolates by A = 75% × 80

⇒ (75/100) × 80

⇒ 60

Number of unsold chocolates by A = (80 – 60)

⇒ 20

∴ The number of unsold chocolates by A is 20

Calculation:

Number of chocolates bought by B = 35% × 400

⇒ (35/100) × 400

⇒ 140

Number of chocolates sold by B = 80% × 140

⇒ (80/100) × 140

⇒ 112

Number of chocolates bought by C = 15% × 400

⇒ (15/100) × 400

⇒  60

Number of chocolates sold by C = 85% × 60

⇒ 51

Number of unsold chocolates by C = (60 – 51)

⇒ 9

Required ratio = 112 : 9

∴ The required ratio is 112 : 9

Calculation:

Total number of chocolates sold by A = 20% × 75% × 400

⇒ 60

Total number of chocolates sold by C = 15% × 85% × 400

⇒ 51

Total number of chocolates sold by A and C together = (60 + 51)

⇒ 111

Number of chocolates sold by B = 35% × 400 × (100 – 80)%

⇒ 35% × 400 × 20%

⇒ 28

Number of chocolates sold by D = 10% × 400 × (100 – 90)%

⇒ 10% × 400 × 10%

⇒ 4

Number of chocolates sold by E = 20% × 400 × (100 – 70)%

⇒ 20% × 400 × 30%

⇒ 24

Total number of unsold chocolates by B, D and E = (28 + 4 + 24)

⇒ 56

Required difference = (111 – 56)

⇒ 55

∴ The required difference is 55

Calculation:

Number of chocolates sold by D = 10% × 400 × 90%

⇒ (10/100) × 400 × (90/100)

⇒ 36

Number of chocolates sold by A = 20% × 400 × 75%

⇒ (20/100) × 400 × (75/100)

⇒ 60

Required percentage = (36/60) × 100%

⇒ 60%

∴ The required percentage is 60%

Calculation:

Number of chocolates bought by E = 20% × 400

⇒ (20/100) × 400

⇒ 80

Number of chocolates bought by F = (80 + 16)

⇒ 96

Number of chocolates sold by D = 10% × 400 × 90%

⇒ (10/100) × 400 × (90/100)

⇒ 36

Number of chocolates sold by F = 36 × (150/100)

⇒ 54

Required difference = (96 – 54)

⇒ 42

∴ The required difference is 42

Calculation:

Number of unsold chocolates by A = 20% × 400 × (100 – 75)%

⇒ 20% × 400 × 25%

⇒ (20/100) × 400 × (25/100)

⇒ 20

Number of unsold chocolates by B = 35% × 400 × (100 – 80)%

⇒ 35% × 400 × 20%

⇒ 28

Number of unsold chocolates by C = 15% × 400 × (100 – 85)%

⇒ 15% × 400 × 15%

⇒ 9

Number of unsold chocolates by D = 10% × 400 × (100 – 90)%

⇒ 10% × 400 × 10%

⇒ 4

Number of unsold chocolates by E = 20% × 400 × (100 – 70)%

⇒ 20% × 400 × 30%

⇒ 24

Total number of unsold chocolates by A, B, C, D and E = (20 + 28 + 9 + 4 + 24)

⇒ 85

Required percentage = (85/400) × 100%

⇒ 21.25%

∴ The required percentage is 21.25%

From equation I) we get,

3x² + 19x + 20 = 0

⇒  3x² + 15x+ 4x + 20 = 0

⇒ 3x (x+ 5) + 4(x+5) + 20 = 0

⇒ (x+5) (3x + 4) = 0

∴ x = -5, - 4/3

From equation II) we get,

6y² + 19y + 15 = 0

⇒ 6y² + 10y + 9y + 15 = 0

⇒ 2y (3y + 5) + 3(3y + 5) = 0

⇒ (2y + 3) (3y + 5) = 0

∴  y = -3/2, -5/3

Comparison between x and y (via Tabulation):

∴ The relationship between x and y cannot be established.

From equation I) we get,

x² = 256

x = + 16, - 16

From equation II) we get,

y² + 18y + 17

⇒  y² + 17y + y + 17

⇒ y (y + 17) + 1(y + 17)

⇒ (y + 17) (y + 1)

∴  y = -17, - 1

Comparison between x and y (via Tabulation):

∴ x = y or the relationship between x and y cannot be established.

From equation I) we get,

 x² – 15x + 56

⇒  x² – 7x – 8x + 56

⇒ x (x - 7) – 8(x -7)

⇒ (x - 7)(x - 8)

x = 7, 8

From equation II) we get,

y² + 17y + 72

⇒ y² + 8y + 9Y + 72

⇒ y (y + 8) + 9(y + 8)

⇒ (y + 8) (y + 9)

∴ y = -8, -9

Comparison between x and y (via Tabulation):

∴ x > y

From equation I) we get,

4x² + 13x + 9 = 0

⇒  4x² + 4x +9x + 9

⇒ 4x (x +1) +9(x + 1)

⇒ (x +1)(4x + 9)

x = -1, -9/4

From equation II) we get,

4y² + 20y + 25 =0

⇒ 4y² +10y +10Y +25

⇒ 2y(2y + 5) + 5(2y + 5)

⇒ (2y + 5) (2y + 5)

∴  y = -5/2, -5/2

Comparison between x and y (via Tabulation):

∴ x > y

I. x2 – 14x + 33 = 0

⇒ x2 – 11x – 3x + 33 = 0

⇒ x(x – 11) – 3(x – 11) = 0

⇒ (x – 11)(x – 3) = 0

Then, x = 11 or x = 3

Now,

II. y2 – 20y + 99 = 0

⇒ y2 – 11y – 9y + 99 = 0

⇒ y(y – 11) – 9(y – 11) = 0

⇒ (y – 11)(y – 9) = 0

Then, y = 11 or y = 9

Now,

Comparison between x and y (via Tabulation):

∴ We can clearly see that the relationship cannot be established

I. 3x2 – 18x + 24 = 0

⇒ 3x2 – 12x – 6x + 24 = 0

⇒ 3x(x – 4) – 6(x – 4) = 0

⇒ (x – 4)(3x – 6) = 0

⇒ x = 4 or 2

II. 5y2 – 50y + 125 = 0

⇒ 5y2 – 25y – 25y – 125 = 0

⇒ 5y(y – 5) – 25(y – 5) = 0

⇒ (y – 5)(5y – 25) = 0

⇒ y = 5

Comparison between x and y (via Tabulation):

∴ x < y

Shortcut Trick

Current average age of 5 members (if no baby) = 21 + 4 = 25 years.

Total age of 5 members now = 5 × 25 = 125 years.

Total age of 6 members (including baby) = 6 × 21 = 126 years.

Age of the baby = 126 − 125 = 1 year.

∴ The correct answer is 1 year.

Alternate Method

Given:

Number of members initially = 5

Average age 4 years ago = 21 years

Current average (with baby) = 21 years

Calculations:

⇒ Total age of 5 members (4 years ago) = 5 × 21 = 105 years

⇒ Total age of 5 members (today) = 105 + (5 × 4) = 125 years

⇒ Total number of members today = 5 + 1 = 6

⇒ Total age of 6 members (today) = 6 × 21 = 126 years

⇒ Age of the baby = 126 − 125 = 1 year

∴ The correct answer is 1 year.

Additional Information

Average Age Shift

If every member of a group ages by 'n' years, the average age of the group also increases by exactly 'n' years.

Sum of Observations

Total Age = Average Age × Total Number of Members. This is the base formula for all age-related average problems.

Net Deviation Method

New Member's Age = New Average + (Change in Average × Old Number of Members). In this case: 21 + ((21 − 25) × 5) = 21 − 20 = 1 year.

Shortcut Trick

Sum of Length and Breadth (L + B) = Perimeter ÷ 2 = 420 ÷ 2 = 210 m.

Difference (L − B) = 30 m.

Using Sum and Difference property: L = (210 + 30) ÷ 2 = 120 m and B = (210 − 30) ÷ 2 = 90 m.

Diagonal (D) = √(120² + 90²) = 150 m (using 3-4-5 triplet × 30).

Time = Distance ÷ Speed = 150 ÷ 10 = 15 sec.

∴ The correct answer is 15 sec.

Alternate Method

Given: Perimeter = 420 m, Speed = 10 m/s, Length (L) = Breadth (B) + 30.

Formula Used: Perimeter = 2(L + B) | Diagonal = √(L² + B²) | Time = Distance ÷ Speed

⇒ 2(L + B) = 420

⇒ L + B = 210

⇒ (B + 30) + B = 210

⇒ 2B = 180 → B = 90 m

⇒ L = 90 + 30 = 120 m

⇒ Diagonal = √(120² + 90²)

⇒ Diagonal = √(14400 + 8100) = √22500 = 150 m

⇒ Time = 150 ÷ 10 = 15 sec

∴ The correct answer is 15 sec.

Additional Information

Pythagorean Triplets

Standard triplets like (3, 4, 5), (5, 12, 13), and (8, 15, 17) can be scaled by any constant (k) to find sides of a right-angled triangle.

Rectangle Properties

Area of rectangle = L × B. Diagonal length is always the shortest path between opposite corners.

Speed Conversion

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

Shortcut Trick

Total Distributed Amount = 3000 − 250 = 2750.

Combined Ratio A : B : C : D = 5 : 6 : 8 : 6 (since B:C is 3:4 → 6:8 and C:D is 4:3 → 8:6).

Total units = 5 + 6 + 8 + 6 = 25 units.

C's share = (8 ÷ 25) × 2750 = 8 × 110 = 880.

∴ The correct answer is Rs. 880.

Alternate Method

Given: Total initial amount = Rs. 3000, Amount kept = Rs. 250.

Formula Used: Combined Ratio A : B : C : D and Unitary Method.

⇒ Distributed Amount = 3000 − 250 = Rs. 2750

⇒ A : B = 5 : 6

⇒ B : C = 3 : 4 = 6 : 8 (multiplied by 2 to match B)

⇒ C : D = 4 : 3 = 8 : 6 (multiplied by 2 to match C)

⇒ Combined Ratio A : B : C : D = 5 : 6 : 8 : 6

⇒ Sum of parts = 5 + 6 + 8 + 6 = 25 units

⇒ 25 units = 2750

⇒ 1 unit = 2750 ÷ 25 = 110

⇒ C's share (8 units) = 8 × 110 = 880

∴ The correct answer is Rs. 880.

Additional Information

Combined Ratio Calculation

To combine ratios like A:B and B:C, make the common term (B) equal in both ratios by multiplying with suitable factors.

Compound Ratio

The compound ratio of (a : b), (c : d), and (e : f) is (a × c × e) : (b × d × f).

Ratio Distribution Rule

Share of an individual = (Individual Ratio Part ÷ Sum of all Ratio Parts) × Total Amount.

Shortcut Trick

Effective interest rate = (2 × 4%) + (4 × 6%) + (3 × 8%)

Total Effective Rate = 8% + 24% + 24% = 56%

Given, 56% of Principal = ₹4480

Principal = 4480 ÷ 0.56 = ₹8000

∴ The correct answer is ₹8000.

Alternate Method

Given: Simple Interest (SI) = ₹4480, Total Time = 9 years

Formula Used: SI = (P × R × T) ÷ 100

⇒ Let the Principal (sum) be P.

⇒ Total SI = (P × 2 × 4)/100 + (P × 4 × 6)/100 + (P × (9 − 6) × 8)/100

⇒ 4480 = (8P/100) + (24P/100) + (24P/100)

⇒ 4480 = 56P / 100

⇒ P = (4480 × 100) ÷ 56

⇒ P = 80 × 100 = 8000

∴ The correct answer is ₹8000.

Additional Information

Varying Interest Rates

When interest rates change over time, total interest is the sum of interest calculated for each period: SI = P × (r₁t₁ + r₂t₂ + ...)/100.

SI vs CI Difference

Difference for 2 years: D = P(R/100)². For 3 years: D = P(R/100)² × (3 + R/100).

Rule of 72

A quick way to estimate the time required to double an investment at a given annual interest rate: Time ≈ 72 ÷ Rate.

Shortcut Trick

Relative speed (Opposite) = Length ÷ Time = 30 ÷ 8 = 3.75 m/s = 13.5 km/hr.

Speed of Train = 13.5 − 8 = 5.5 km/hr.

Relative speed (Same Direction) = 30 ÷ 3 = 10 m/s = 36 km/hr.

Speed of Person 2 = 36 − 5.5 = 30.5 km/hr.

∴ The correct answer is 30.5 km/hr.

Alternate Method

Given: Length of train = 30 m, Time 1 = 8 s, Speed of Person 1 = 8 km/hr, Time 2 = 3 s.

Formula: Speed = Distance ÷ Time; 1 m/s = 18/5 km/hr.

⇒ Case 1 (Opposite direction): Relative Speed = (V_t + 8) km/hr.

⇒ (V_t + 8) × (5/18) = 30 ÷ 8

⇒ V_t + 8 = (30 ÷ 8) × (18 ÷ 5) = 3.75 × 3.6 = 13.5

⇒ Speed of Train (V_t) = 13.5 − 8 = 5.5 km/hr.

⇒ Case 2 (Same direction as Person 1, so opposite to train): Relative Speed = (V_p2 + V_t).

⇒ (V_p2 + 5.5) × (5/18) = 30 ÷ 3

⇒ V_p2 + 5.5 = 10 × (18 ÷ 5) = 36

⇒ V_p2 = 36 − 5.5 = 30.5 km/hr.

∴ The correct answer is 30.5 km/hr.

Additional Information

Relative Speed

In the opposite direction, relative speed is the sum of speeds (u + v). In the same direction, it is the difference (u − v).

Unit Conversion

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

Train Crossing a Point Object

When a train crosses a person, pole, or tree, the distance covered is equal to the length of the train.

Shortcut Trick

Concentration of Brass in Alloy X = 8/17

Concentration of Brass in Alloy Y = 1/7

Final concentration of Brass required = 25% = 1/4

Using Alligation on Brass: (1/4 − 1/7) : (8/17 − 1/4) = 3/28 : 15/68 = 17 : 35

∴ The correct answer is 17 : 35.

Alternate Method

Given: Ratio of Brass and Aluminum in Alloy X = 8 : 9; In Alloy Y = 1 : 6. Required Brass in mixture = 25%.

Formula Used: Alligation rule: Ratio = (Value₂ − Mean) : (Mean − Value₁)

⇒ Quantity of Alloy X / Quantity of Alloy Y = (1/4 − 1/7) / (8/17 − 1/4)

⇒ Ratio = (3/28) / (15/68)

⇒ Ratio = (3/28) × (68/15)

⇒ Ratio = (1/7) × (17/5) = 17 / 35

∴ The correct answer is 17 : 35.

Additional Information

Alligation Rule

A method to find the ratio in which two ingredients at given prices/concentrations must be mixed to produce a mixture of a desired price/concentration.

Fractional Conversion

Always ensure the component being compared (Brass or Aluminum) is converted into a fraction of the total (e.g., 8:9 becomes 8/17) before applying alligation.

Percentage to Fraction

Common conversions: 25% = 1/4, 50% = 1/2, 33.33% = 1/3, 20% = 1/5.

Filled Seats = Total number of seats × Percentage of seats filled

Vacant Seats =  Total number of seats - Filled Seats

Individual solution:

The required percentage = (10 - 6)/10 × 100 = 40 %

∴ The number of vacant seat of bus C is 40% less than the number of vacant seat of bus A

Individual solution:

The ratio = 14 : 6 = 7 : 3

Hint

B filled seat = 25 × 84% = 21

E filled seats = 21 + 3 = 24

24 = 80 % 

Then, 100% = 30

D + E = 65 (GIVEN)

D = 65 - 30 = 35

D filled = 35 × 60/100 = 21

Calculation:

The average = 30 + 21 + 44 + 21+ 24/5 = 140/5 = 28

∴ The average number of filled seats in all buses is 28

Answer:- (3)

There are nine employees, A, B, C, D, E, F, G, H, and I.

Those are working in three different departments viz. IT, HR, and Production.

1. G works in the production department but not with D and H.
2. B works in the IT department but not with E and I.

3. A works in the HR department but not with C and F.
4. Either D or C works along with B.

(No two persons with preceding or succeeding alphabetic series work in the same department.)

So, D works with B.

5. Neither E nor F works with G. 
6. A works in the HR department but not with C and F.

So, F works in the IT department.

7. Neither E nor F works with G.
8. A works in the HR department but not with C and F.

So, E works in the HR department and C works in the production department.

9. No two persons with preceding or succeeding alphabetic series work in the same department.

So, the final arrangement is,

Hence, employees C, G, I work in the Production department.

Answer:- (2)

There are nine employees, A, B, C, D, E, F, G, H, and I.

Those are working in three different departments viz. IT, HR, and Production.

1. G works in the production department but not with D and H.
2. B works in the IT department but not with E and I.

3. A works in the HR department but not with C and F.
4. Either D or C works along with B.

(No two persons with preceding or succeeding alphabetic series work in the same department.)

So, D works with B.

5. Neither E nor F works with G. 
6. A works in the HR department but not with C and F.

So, F works in the IT department.

7. Neither E nor F works with G.
8. A works in the HR department but not with C and F.

So, E works in the HR department and C works in the production department.

9. No two persons with preceding or succeeding alphabetic series work in the same department.

So, the final arrangement is,

Hence, H belongs to HR department.

Answer:- (2)

There are nine employees, A, B, C, D, E, F, G, H, and I.

Those are working in three different departments viz. IT, HR, and Production.

1. G works in the production department but not with D and H.
2. B works in the IT department but not with E and I.

3. A works in the HR department but not with C and F.
4. Either D or C works along with B.

(No two persons with preceding or succeeding alphabetic series work in the same department.)

So, D works with B.

5. Neither E nor F works with G. 
6. A works in the HR department but not with C and F.

So, F works in the IT department.

7. Neither E nor F works with G.
8. A works in the HR department but not with C and F.

So, E works in the HR department and C works in the production department.

9. No two persons with preceding or succeeding alphabetic series work in the same department.

So, the final arrangement is,

Hence, HR - H is the correct combination.

Answer:- (3)

There are nine employees, A, B, C, D, E, F, G, H, and I.

Those are working in three different departments viz. IT, HR, and Production.

1. G works in the production department but not with D and H.
2. B works in the IT department but not with E and I.

3. A works in the HR department but not with C and F.
4. Either D or C works along with B.

(No two persons with preceding or succeeding alphabetic series work in the same department.)

So, D works with B.

5. Neither E nor F works with G. 
6. A works in the HR department but not with C and F.

So, F works in the IT department.

7. Neither E nor F works with G.
8. A works in the HR department but not with C and F.

So, E works in the HR department and C works in the production department.

9. No two persons with preceding or succeeding alphabetic series work in the same department.

So, the final arrangement is,

Hence, F works in IT department.

Answer:- (3)

There are nine employees, A, B, C, D, E, F, G, H, and I.

Those are working in three different departments viz. IT, HR, and Production.

1. G works in the production department but not with D and H.
2. B works in the IT department but not with E and I.

3. A works in the HR department but not with C and F.
4. Either D or C works along with B.

(No two persons with preceding or succeeding alphabetic series work in the same department.)

So, D works with B.

5. Neither E nor F works with G. 
6. A works in the HR department but not with C and F.

So, F works in the IT department.

7. Neither E nor F works with G.
8. A works in the HR department but not with C and F.

So, E works in the HR department and C works in the production department.

9. No two persons with preceding or succeeding alphabetic series work in the same department.

So, the final arrangement is,

Hence, Employees E and H works with Employee A.

The solution will be added soon. The solution will be made available after 6 PM, 7^th Jan.

Conclusions:

I. Some apple are mango → False (All mango are papaya and No papaya is apple. So, apple cannot be mango)

II. Some watermelon are not papaya → False (As given some watermelon are papaya. So negative conclusion not follow)

Hence, None of the conclusion are follow.

The solution will be added soon. The solution will be made available after 6 PM, 7^th Jan.

Conclusions:

I. Some headphone are laptop → False (No direct relation between laptop and headphone)

II. Some tablet are laptop → True (As some part of tablet is laptop)

Hence, Only conclusion II follows.

The minimum possible Venn diagram of the given information is as follows:

Conclusions:

I. Some Eraser are Paper → False (As Some Eraser are not Paper and Some Eraser are Paper whether it is true or not. it is possible but not definite. So, it is false)

II. Some pencil are paper → False (As No Paper is Pencil →  Some Pencil can never be Paper. So, it is false)

Hence, None follows.

The solution will be added soon. The solution will be made available after 6 PM, 7^th Jan.

Conclusions:

I. Some D are not B → False (There is no direct relation between D and B)

II. All C are A → False (There is no direct relation between A and C)

Hence, None of the conclusion are follow.

The solution will be added soon. The solution will be made available after 6 PM, 7^th Jan.

Conclusions:

I. All book can be paper → False (As Only notepad is book. So All book can not be paper)

II. Some notepad is paper → True (As some paper is notepad. So, some notepad is paper)

Hence, Only conclusion II follow.

1. M is father of S who is unmarried.

2. S and D are sisters.

3. T is married to N who is only brother of D.

4. B is brother in law of N.

5. T does not have any sibling.

6. R is the only child of N.

Hence, M is father of N.

The solution will be added soon. The solution will be made available after 6 PM, 7^th Jan.