SBI PO Prelims Memory Based Paper (Held On: 18 Dec 2022 Shift 1) (Previous Year Paper)

The correct answer is Option 2. 

Key Points

• Concur means to agree or have the same opinion, which is similar to conceding. This option is a possible synonym for concede.

Additional Information

• Refute: Refute means to prove something to be false or incorrect, which is the opposite of conceding. Therefore, refute is not a synonym for concede.
• Deny: Deny means to refuse to accept or acknowledge something, which is opposite to conceding. Therefore, deny is not a synonym for concede.
• Oppose: Oppose means to be against or resist something, which is contrary to conceding. Therefore, oppose is not a synonym for concede.
• Challenge: Challenge means to question or dispute something, which is not synonymous with conceding. Therefore, challenge is not a synonym for concede.

The correct answer is Option 1. 

Key Points

• Disagree means to have a different opinion or to be in conflict with someone, which is the opposite of agreeing. This option is a possible antonym for agree.

Additional Information

• Consent: Consent means to give permission or to agree to something, which is synonymous with agreeing. Therefore, consent is not an antonym for agree.
• Concur: Concur means to agree or have the same opinion, which is synonymous with agreeing. Therefore, concur is not an antonym for agree.
• Harmonize: Harmonize means to blend or reconcile different elements, which does not represent the opposite of agreeing. Therefore, harmonize is not an antonym for agree.
• Support: Support means to endorse or assist, which can be done both when agreeing and disagreeing. Therefore, support is not an antonym for agree.

The correct answer is Option 3. 

 Key Points

• To ensure passenger safety by addressing concerns and providing evidence
  
• The passage states that extensive research and stringent testing protocols should be implemented to alleviate concerns and provide unequivocal evidence.
• This suggests that the purpose of these measures is to address any potential safety concerns related to cellular signals in airplanes. By conducting thorough research and testing, stakeholders aim to gather evidence that supports the notion that cellular signals do not pose a threat to the aircraft's avionics.
• The ultimate goal is to ensure passenger safety by addressing concerns and providing concrete evidence to support the implementation of a robust 5G network.

The correct answer is Option 3. 

Key Points

• The passage mentions several aspects that must be addressed to ensure the efficacy and reliability of 5G within an airplane, including the need for stakeholders to collaborate to address technical obstacles and guarantee passenger safety.
• Among these obstacles, the challenge of cellular signals potentially interfering with the aircraft's operations is explicitly stated.
• Hence, the "signal interference" (option 3) is a correct answer as one of the challenges in ensuring the efficacy and reliability of 5G within an airplane.

The correct answer is Option 4.

Key Points

• The third paragraph of the passage discusses what these agreements should focus on: "These agreements should focus on optimizing network coverage, minimizing signal interference, and maximizing bandwidth capacity."
• 'Signal interference' (Option 3) is the key element when securing agreements for in-flight 5G infrastructure according to this passage, as minimizing it is essential to providing a reliable and efficient network for passengers.
• Therefore, Option 3 'Signal interference' is the correct answer. The telecom providers are pivotal in this process, but the question specifically asks for a key element within the agreements, not a key party involved.

The correct answer is Option 2.

Key Points

• This option accurately reflects the meaning of "hammering out" in the given passage. It refers to the team's determined efforts to engage in discussions and negotiations to reach a viable solution.
• Passage context: "The team of experts gathered in the conference room, diligently discussing the details of the project. They were determined to reach a consensus and overcome any differences. Hours went by, and finally, after intense negotiations, they started hammering out a viable solution.

Additional Information

• Physically using a hammer to construct something: The passage context does not suggest any physical construction work. "Hammering out" is not related to physical hammer usage in this context.
• Hammering a point repeatedly to emphasize its importance: While this option contains the word "hammering," it does not capture the meaning of "hammering out" in the context of the passage. The phrase does not refer to emphasizing a point through repetitive hammering.
• Engaging in a physical activity to relieve stress after negotiations: The passage does not mention any stress or physical activities after negotiations. This option does not align with the meaning of "hammering out" in the given context.
• Demonstrating determination and perseverance through the use of a hammer: While determination and perseverance are implied in the passage, "hammering out" does not involve the literal use of a hammer. This option does not accurately represent the meaning in the given context.

The correct answer is Option 4. 

Key Points

• Optimizing network coverage, minimizing signal interference, and maximizing bandwidth capacity
• The passage mentions that securing agreements with telecom companies is a vital element in establishing reliable 5G infrastructure for passenger mobile usage in airplanes. These agreements should focus on three main aspects: optimizing network coverage, minimizing signal interference, and maximizing bandwidth capacity. By emphasizing these factors, stakeholders aim to ensure a reliable and seamless 5G network for in-flight usage. This will help provide consistent connectivity and a high-quality mobile experience for passengers throughout their journey.

The correct answer is Option 1.

Key Points

• Experience: This option accurately represents the overall benefits mentioned in the passage.
• Enhancing the passenger experience means creating an environment where passengers can have a positive and seamless journey, staying connected, productive, and respectful of safety and security regulations.
• The passage states that by hammering out the intricate details and agreeing upon standardized guidelines and protocols for the use of mobile devices during flights, all parties involved can enhance the passenger experience. This means that the focus is on improving and enriching the overall journey for passengers.

Additional Information 

• Option 2) Satisfaction: While satisfaction can be a component of the enhanced passenger experience, it doesn't encompass the full scope of the benefits mentioned in the passage, such as staying connected and productive.
• Option 3) Connectivity: While connectivity is important for passengers to stay connected, it does not encompass the entire passenger experience, which includes factors beyond just being connected.
• Option 4) Efficiency: Efficiency can contribute to an improved passenger experience, but it doesn't encompass the full range of benefits mentioned in the passage, such as staying connected and productive throughout the journey.
• Option 5) Enjoyment: Enjoyment is a part of the passenger experience, but it does not capture the complete idea conveyed in the passage, which includes staying connected and productive while respecting safety and security regulations.

The correct answer is option 3.

Key Points

The given sentence is - 

When the ______(A) was about to announce the winner of the best actor award an ______(B) of _______(C) vibrated through the crowd.

• To answer the question let's first look at the meanings of all the marked words -
• (A) Anticipation - It's a noun that means 'the action of anticipating something; expectation or prediction'. (प्रत्याशा/पूर्वानुमान)
• (B) Host - It's a noun that means 'a person who receives or entertains other people as guests'. (मेज़बान)
• (C) Atmosphere - It's a noun that means 'the pervading tone or mood of a place, situation, or creative work'. (माहौल)
• After looking at the meanings of all the marked words we can conclude that 'host' should come in the first blank while 'atmosphere' and 'anticipation' should come in the third and fourth blank respectively because the correct phrase in the context of the sentence is 'atmosphere of anticipation' which means that the people present at the award ceremony had a feeling of excitement for the announcement of the award.
• Therefore, the correct answer is 'BCA'.

​

The correct sentence after rearrangement would be - When the host(B) was about to announce the winner of the best actor award an atmosphere(C) of anticipation(A) vibrated through the crowd.

The correct answer is option 4.

Key Points

The given sentence is - 

Kolkata, with one the _______(A) road space among the metropolis of the country, is ______(B) dependent on metro railway services for ______(C) movement of passengers.

• To answer the question let's first look at the meanings of all the marked words -
• (A) Largely - It's an adverb that means 'to a great extent; on the whole; mostly'. (काफी हद तक)
• (B) Fast - It's an adjective that means 'moving or capable of moving at high speed'. (तेज़)
• (C) Lowest - It's a superlative adjective that means 'below average in amount, extent, or intensity'. (निम्नतम)
• After looking at the meanings of all the marked words we can conclude that 'lowest' should come in the first blank because it is a superlative adjective and as per grammar rules, it should be preceded by the article 'the'.
• Also, 'largely' which is an adverb should come in the second blank because then it would be followed by the verb 'dependent' and 'fast' that is an adjective should come in the third blank before the noun 'movement'.
• Therefore, the correct answer is 'CAB'.

​

The correct sentence after rearrangement would be - Kolkata, with one the lowest(C) road space among the metropolis of the country, is largely(A) dependent on metro railway services for fast(B) movement of passengers.

The correct answer is option 2.

Key Points

The given sentence is - 

No country can go far if a _______(A) proportion of its population is illiterate, unhealthy, or malnourished, all the _______(B) that are developed today _______(C) well in education, health, and nutrition.

• To answer the question let's first look at the meanings of all the marked words -
• (A) Invested - It's a verb that means 'devote (one's time, effort, or energy) to a particular undertaking with the expectation of a worthwhile result'. (निवेश)
• (B) Significant - It's an adjective that means 'sufficiently great or important to be worthy of attention; noteworthy'. (महत्वपूर्ण)
• (C) Countries - It's a noun that means ' nations with their own government, occupying a particular territory'.
• After looking at the meanings of all the marked words we can conclude that 'significant' which is an adjective should come in the first blank followed by the noun 'proportion'.
• Also, 'countries' should come in the second blank, and 'invested' should come in the third blank.
• Therefore, the correct answer is 'BCA'.

​

The correct sentence after rearrangement would be - No country can go far if a significant(B) proportion of its population is illiterate, unhealthy, or malnourished, all the countries(C) that are developed today invested(A) well in education, health, and nutrition.

The correct answer is option 5.

Key Points

The given sentence is - 

If you suspect that 21st-century ______(A) has broken your brain, it will be _______(B) to know that _______(C) spans have never been what they used to be.

• To answer the question let's first look at the meanings of all the marked words -
• (A) Technology - It's a noun that means 'machinery and equipment developed from the application of scientific knowledge'.(तकनीकी)
• (B) Reassuring - It's an adjective that means 'serving or intended to remove someone's doubts or fears'.(आश्वासनपूर्ण)
• (C) Attention - It's a noun that means 'notice taken of someone or something; the regarding of someone or something as interesting or important'. (ध्यान)
• After looking at the meanings of all the marked words we can conclude that all the words are given in their right places and don't require any rearrangement.
• Therefore, the correct answer is 'No rearrangement required'.

The correct answer is option 2.

Key Points

The given sentence is - 

Power is _______(A) for everyday operations in almost every _______(B) of modern life and power engineers help ensure that this power is _______(C) to people.

• To answer the question let's first look at the meanings of all the marked words -
• (A) Accessible - It's an adjective that means 'able to be easily obtained or used'. (सुलभ)
• (B) Essential - It's an adjective that means 'absolutely necessary; extremely important'. (आवश्यक)
• (C) Facet - It's a noun that means 'a particular aspect or feature of something'. (पहलू)
• After looking at the meanings of all the marked words we can conclude that the sentence talks about power being an important part of everyday operations and power engineers help ensure people get access to power.
• Thus, 'essential' will come in the first blank and 'facet' and 'accessible' will come in the second and third blank respectively.
• Therefore, the correct answer is 'BCA'.

​

The correct sentence after rearrangement would be - Power is essential(B) for everyday operations in almost every facet(C) of modern life and power engineers help ensure that this power is accessible(A) to people.

The correct answer is option 1.

Key Points

The given sentence is - 

The presence of foreign _______(A) in India will bring in an element of _______(B) and increase the standards and _______(C) of Indian institutions.

• To answer the question let's first look at the meanings of all the marked words -
• (A) Competition - It's a noun that means 'the activity or condition of striving to gain or win something by defeating or establishing superiority over others'. (प्रतिस्पर्धा)
• (B) Quality - It's a noun that means 'the standard of something as measured against other things of a similar kind; the degree of excellence of something.' (गुणवत्ता)
• (C) Universities - It's a noun that means 'a high-level educational institution in which students study for degrees and academic research is done'. (विश्वविद्यालय)
• After looking at the meanings of all the marked words we can conclude that 'universities' should come in the first blank because the sentence is talking about the foreign universities bringing in the element of competition in our country.
• Thus, 'competition' should come in the second blank and 'quality' should come in the third blank.
• Therefore, the correct answer is 'CAB'.

​

The correct sentence after rearrangement would be - The presence of foreign universities(C) in India will bring in an element of competition(A) and increase the standards and quality(B) of Indian institutions.

The correct Option is 2. 

Key Points

• A. The brave young woman decided to defy the rules and pursue her dreams.
• In this sentence, "DEFY" is used as a verb. It means to openly resist or refuse to obey or adhere to something, in this case, the rules. The sentence portrays the act of the young woman challenging the rules and going against them in order to pursue her dreams.
• B. His actions openly defied the authority of the government.
• Similarly, in this sentence, "DEFY" is used as a verb. It describes the act of openly resisting or challenging the authority of the government through one's actions. It implies that the person's actions were in direct opposition to the government's authority.
• C The officer was convicted for refusing to defy orders
• In this sentence, "DEFY" is used as a verb as well. However, the meaning of "DEFY" in this sentence is different from the intended meaning. "DEFY" typically implies resistance or opposition to authority, but in this context, it suggests that the officer did not refuse to defy orders (meaning they followed the orders instead).
• Therefore, Sentence C does not express the meaning of "DEFY" as intended.

The correct answer is Option 5.

Key Points

• A. She carefully held the handle of the door.
• This sentence relates to the physical act of holding onto the handle of a door. It expresses the meaning of "HANDLE" as a noun referring to a part of an object that is meant to be held or operated. For example, a door handle is used to open or close a door.
• B. The detective found a crucial piece of evidence with his keen handle on the case.
• This sentence uses "HANDLE" as a noun but in a figurative sense. It suggests that the detective had a strong understanding, control, or grasp of the case. It implies that the detective had a good handle or command over the situation or problem at hand.
• C. He couldn't handle the pressure and decided to quit.
• In this sentence, "HANDLE" is used as a verb. It indicates the ability or capacity to cope with or manage something. It suggests that the person in question was unable to deal with the pressure and subsequently chose to quit.

Now, let's determine the sentence(s) that express(es) the meaning of the word "HANDLE":

• Sentence A expresses the meaning of "HANDLE" as a noun referring to a part of an object that is meant to be held or operated. (For example, holding the handle of a door.)
• Sentence B expresses the meaning of "HANDLE" as a noun in a figurative sense, representing understanding, control, or grasp. (For example, having a keen handle on a case.)
• Sentence C uses "HANDLE" as a verb, indicating the ability to cope with or manage something. (For example, being unable to handle the pressure.)

Based on the analysis, the answer is: All of the Above

The correct answer is the people reached Mumbai when.

Key Points

• There are two errors in the bold part.
• Firstly, the term ‘people’ is a collective noun. Collective nouns are used in the singular form. Therefore, ‘peoples’ must be replaced by ‘people’ in order to make the sentence correct.
• Secondly, ‘hardly’ and ‘when’ form a pair of coordinating conjunctions. Coordinating conjunctions join phrases, words, etc. of equal ranks. Therefore, ‘when’ should be used instead of ‘than’ in order to make it a grammatically correct sentence.
• Among the choices available, option 3 replaces the bold part most appropriately.
• Hence, option 3 is the correct answer.

The correct sentence is: Hardly had the people reached Mumbai when they were ordered to return to Delhi.

Additional Information

• Hardly -when is used in past perfect tense sentences as follows. Sometimes we use Scarcely-when in place of Hardly-when
• Hardly had the race started when we started cheering.
• Scarcely had you asked a question when he answered it.
• We can use 'no sooner- than' as follows.
• No sooner did we call him than he responded.

The correct answer is "is quite high and"

Key Points

• Quite: to a certain or fairly significant extent or degree; fairly.
  
• This structure emphasizes that the cost of medical care is high and then introduces the fact that they had to sell their land as a result of it.
• The word "and" is used as a coordinating conjunction here to join two independent clauses.
• However, option 1 replaces the bold part appropriately and thus becomes the best replacement among all.
• The correct sentence is: The cost of medical care in this country is quite high and they had to sell their land to pay for it.

The correct answer is "The backbone of the organization's"

Key Points 

• The correct idiomatic expression in this sentence is ‘the backbone of' and not 'the backing bone in'.
• Be the backbone (Idiom): The part of something that makes it successful or strong.
• Ex: Ordinary volunteers form the backbone of most charitable organizations.
• Hence ‘the backbone of’ should be used in place of ‘the backing bone in’ to make the sentence grammatically correct.
• Among the given choices, only option 3 replaces the given bold part most appropriately.
• Hence the correct answer is Option 3.

The correct sentence is: BJP is the country's only political party with a trained political human resource, which will serve as the backbone of the organization’s workforce in the coming years.

The correct answer is D

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

The correct answer is A.

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

The correct answer is C. 

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

The correct answer is E. 

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

The correct answer is B. 

Key Points

Reading the given sentences we find that: 

• The paragraph starts by introducing the Nuclear Power Corporation of India Limited, and my mentioning what it is; which is D.
• Then statement A provides us more information regarding NPCIL that it is a dividend-paying company.
• This is soon followed by statement C which elaborates on what NPCIL does, its responsibilities.
• This is elaborated using the second statement that is the overriding priority given to safety as mentioned in E.
• The paragraph ends by concluding the present operation of NPCIL i.e the number of power reactors and it's capacity, which is B.

Therefore the correct sequence is DACEB.

The Correct answer is Option B

• The error is B part of the sentence.
• In the given sentence word north is giving additional information 'regarding half of the country'
• Hence adverb form of North needs to be used, here North is to be replaced with 'Northern'

Correct answer - Their most significant gains have been in the northern half of the country, a traditional stronghold of the U.S.­ allied warlords who helped defeat them in 2001*.***

The correct answer is option 3.

• The error is in the C part of the sentence.
• In the given sentence it is mentioned 'Policies and plans'  which is in the plural form.
• Hence in part C, we need to replace was with Were.

​Correct answer - Policies and plans pertaining to transport and mobility, shelter, and social infrastructure were also discussed at the webinar held on Tuesday.

• The Noun is Part of the sentence which defines persons, Place or things.
• Helping verbs in the sentence is decided with the help of a noun or subject.
• Helping verbs for a singular subject - am. is, was
• Helping verbs for a Plural subject - are, were

The correct answer is option 4.

• The error is in part D of the sentence. in the use of 'car, truck'
• car, truck needs to be considered in plural form with another mode of transportation to make the sentence meaningful.

Correct sentence - The protesters will reach designated public locations  by any means of transport including scooters, motorcycles, tractors, cars, buses, trucks.

• The noun is Part of the sentence which defines persons, Place or things.
• Helping verbs in the sentence are decided with the help of a noun or subject.
• We cannot use a combination of singular and plural to describe common things. we either need to use singular or plural.

The Correct answer is Option A

• Error is part A of the sentence.
• adverb 'drastically' is incorrectly used.
• 'Drastically' is to be replaced with 'Drastic'

Correct answer - After a drastic fall in demand for air travel from March onwards due to the second wave of COVID­19, there is now a steady rise in the number of daily passengers.

The correct answer is option 1.

• The error is in Part A of the sentence. The error is in the usage of the Ministry
• In the given sentence before ministry, it is mentioned 'several'
• Hence there are more than one ministries
• Here, we need to replace 'Ministry' with 'Ministries'

Correct answer- Several ministries have been clubbed together, sources say to increase synergy.

• The noun is Part of the sentence which defines persons, Place or things.
• Helping verbs in the sentence is decided with the help of a noun or subject.

The correct answer is option 4.

• The error in part D of a sentence, the error is in the usage of Many debate
• 'Much' is used when we are speaking about a singular noun.
• 'Many' is used when we are speaking about a plural noun.
• When we speak about 'many' and 'much', it's worth mentioning countable and uncountable nouns.
• nouns can be used with a number and have singular and plural forms.

Correct answer- While the expansion of the road and railway network there has been subject to much debate.

• Adjective is the word which gives additional information regarding the noun.

Calculation:

⇒ x2 - 13x + 40 = 0

⇒ x2 - 8x - 5x + 40 = 0

⇒ x(x - 8) - 5(x - 8) = 0

⇒ (x - 8) (x - 5) = 0

⇒ x = 8, 5

⇒ y² – 13y + 42 = 0

⇒ y² – 6y – 7y + 42 = 0

⇒ y (y - 6) – 7(y – 6) = 0

⇒ (y - 6) (y - 7) = 0

⇒ y = 6, 7

∴ The relation between x and y cannot be established

Calculation:

I. x2 + 8x + 12 = 0

⇒ x2 + 6x + 2x + 12 = 0

⇒ x(x + 6) + 2(x + 6) = 0

⇒ (x + 6) (x + 2) =0

⇒ x = –6, –2

II. y2 + 14y + 24 = 0

⇒ y2 + 12x + 2x + 24 = 0

⇒ y(y + 12) + 2(x + 12) = 0

⇒ (y + 12) (x + 2) = 0

⇒ y = –12, –2

Comparison between x and y (via tabulation):

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

Calculation:

I. x2 – 9x + 18 = 0

⇒ x2 – 6x – 3x + 18 = 0

⇒ x(x – 6) – 3(x – 6) = 0

⇒ (x – 6) (x – 3) = 0

⇒ x = 6, 3

II. y2 – 15y + 56 = 0

⇒ y2 – 8y – 7y + 56 = 0

⇒ y(y – 8) – 7(y – 8) = 0

⇒ (y – 8) (y – 7) = 0

⇒ y = 8, 7

Comparison between x and y (via tabulation):

∴ x < y

Given:

I. x2 - 35x + 124 = 0

II. y2 + 21y - 130 = 0

Calculation:

From I,

x2 - 35x + 124 = 0

⇒ x2 - 31x - 4x + 124 = 0

⇒ x(x - 31) - 4(x - 31) = 0

⇒ (x - 31)(x - 4) = 0

Taking,

⇒ (x - 31) = 0 or (x - 4) = 0

⇒ x = 31 or 4

From II,

y2 + 21y - 130 = 0

⇒ y2 + 26y - 5y - 130 = 0

⇒ y(y + 26) - 5(y + 26) = 0

⇒ (y + 26)(y - 5) = 0

Taking,

⇒ (y + 26) = 0 or (y - 5) = 0

⇒ y = -26 or 5

Comparison between x and y (via Tabulation):

∴ x = y or relation between x and y can not be established.

Given:

I. 4x² + 18x + 20 = 0

II. 3y² + 24y - 60 = 0

Calculation:

From I

4x² + 18x + 20 = 0

⇒ 2x² + 9x + 10 = 0

⇒ 2x² + 4x + 5x + 10 = 0

⇒ 2x(x + 2) + 5(x + 2) = 0

⇒ (x + 2)(2x + 5) = 0

⇒ x = -2, -5/2

From II

3y² + 24y - 60 = 0

⇒ y² + 8y - 20 = 0

⇒ y² + 10y - 2y - 20 = 0

⇒ y(y + 10) - 2(y + 10) = 0

⇒ (y + 10)(y - 2) = 0

⇒ y = -10, 2

Comparison between x and y (via Tabulation)

∴ No relation in x and y or x = y

Shortcut Trick

Ratio of number of workers = 7 : 4

Ratio of wages per worker = 3 : 5

Ratio of Total Expenditure = (7 × 3) : (4 × 5) = 21 : 20

∴ The correct answer is 21 : 20.

Alternate Method

Given:

Initial number of workers = 7x, New number of workers = 4x

Initial wages = 3y, New wages = 5y

Formula Used:

Total Expenditure = (Number of Workers) × (Wages per Worker)

Calculations:

⇒ Previous Expenditure = 7x × 3y = 21xy

⇒ Current Expenditure = 4x × 5y = 20xy

⇒ Ratio = 21xy : 20xy

⇒ Ratio = 21 : 20

∴ The correct answer is 21 : 20.

Additional Information

Compound Ratio

When two or more ratios are multiplied term by term, the resulting ratio is called a Compound Ratio. Here, (a:b) and (c:d) gives (ac:bd).

Expenditure Relation

In commercial arithmetic, Total Cost or Expenditure is always the product of Quantity (workers/items) and Rate (wages/price).

Inverse Variation

If the total expenditure remains constant, the number of workers would be inversely proportional to the wages per worker.

Shortcut Trick

Apply Alligation between Officers and Rest Staff.

Ratio of (Officers : Rest Staff) = (600 − 560) : (4000 − 600) = 40 : 3400 = 1 : 85.

Since 1 unit (Officers) = 12, then 85 units (Rest Staff) = 85 × 12 = 1020.

∴ The correct answer is 1020.

Alternate Method

Given: Average salary of 12 Officers = ₹4000, Average salary of Rest Staff = ₹560, Average salary of Total Staff = ₹600.

Calculations:

⇒ Let the number of Rest Staff be N.

⇒ Total salary = (12 × 4000) + (N × 560) = (12 + N) × 600

⇒ 48000 + 560N = 7200 + 600N

⇒ 48000 − 7200 = 600N − 560N

⇒ 40800 = 40N

⇒ N = 40800 ÷ 40

⇒ N = 1020

∴ The correct answer is 1020.

Additional Information

Alligation Method

It is a rule used to find the ratio in which two or more ingredients at their respective prices must be mixed to produce a mixture of a specified price. Ratio = (Higher Value − Mean) : (Mean − Lower Value).

Average Salary Formula

Total Salary = Average Salary × Number of Employees. This base formula is used to set up linear equations for solving population distribution problems.

Shortcut Trick

Ratio of quantities = 45 : 40 = 9 : 8.

Weighted Average CP = (9 × 140 + 8 × 155) ÷ (9 + 8) = (1260 + 1240) ÷ 17 = 2500 ÷ 17 ≈ 147.06.

SP for 20% loss = Weighted Average CP × 80 ÷ 100.

SP = (2500 ÷ 17) × 0.8 = 2000 ÷ 17 ≈ 117.64.

Approximating to the nearest integer, we get Rs. 118.

∴ The correct answer is Rs. 118.

Alternate Method

Given → Total quantity 1 = 45 kg, Rate 1 = Rs. 140/kg; Total quantity 2 = 40 kg, Rate 2 = Rs. 155/kg; Loss% = 20%. Formulas: Total CP = (Q₁ × R₁) + (Q₂ × R₂) | Average CP = Total CP ÷ Total Quantity | SP = CP × (100 − Loss%) ÷ 100.

⇒ Cost of first variety = 45 × 140 = Rs. 6300. ⇒ Cost of second variety = 40 × 155 = Rs. 6200. ⇒ Total CP = 6300 + 6200 = Rs. 12500. ⇒ Total Quantity = 45 + 40 = 85 kg. ⇒ Selling Price to incur 20% loss = 12500 × (80 ÷ 100) = Rs. 10000. ⇒ SP per kg = 10000 ÷ 85 = Rs. 117.64... ⇒ Required approximate price = Rs. 118.

∴ The correct answer is Rs. 118.

Additional Information

Weighted Average Method

When two groups of items with different averages are combined, the new average is [n₁x₁ + n₂x₂] ÷ [n₁ + n₂].

Profit and Loss on SP

Loss is calculated on Cost Price unless specified otherwise. Loss = CP − SP. Loss% = (Loss ÷ CP) × 100.

Shortcut Trick

Total Work (LCM of 18, 24) = 72 units.

Efficiency: A = 4, B = 3.

Work done in first 6 days (A+B): (4 + 3) × 6 = 42 units.

Remaining work: 72 − 42 = 30 units.

Efficiency of (B+C) = 30 ÷ 6 = 5. ∴ C's efficiency = 5 − 3 = 2.

Time for C = 72 ÷ 2 = 36 days.

∴ The correct answer is 36 days.

Alternate Method

Given: Time taken by A = 18 days, B = 24 days. A worked for 6 days. B worked for (6 + 6) = 12 days. C worked for 6 days.

Formula Used: Total Work = ∑(Efficiency × Time) or ∑(Work done by each) = 1.

⇒ Work done by A in 6 days = 4 × 6 = 24 units

⇒ Work done by B in 12 days (6 initial + 6 with C) = 3 × 12 = 36 units

⇒ Work done by A and B = 24 + 36 = 60 units

⇒ Remaining work completed by C = 72 − 60 = 12 units

⇒ C finishes 12 units in 6 days

⇒ Efficiency of C = 12 ÷ 6 = 2 units/day

⇒ Time for C alone = Total Work ÷ Efficiency of C = 72 ÷ 2 = 36 days

∴ The correct answer is 36 days.

Additional Information

Work and Efficiency

Efficiency is inversely proportional to time. Efficiency = Total Work ÷ Time.

Pipes and Cisterns

Similar to Time & Work, but includes negative efficiency for outlet pipes (leakage).

Work & Wages

Wages are distributed in the ratio of the work done by each person.

Shortcut Trick

Time ratio (Upstream : Downstream) = 2 : 1

Speed ratio (Upstream : Downstream) = 1 : 2 (Inverse of time)

Ratio of Still Water Speed : Current Speed = (D + U) : (D − U)

Ratio = (2 + 1) : (2 − 1) = 3 : 1

∴ The correct answer is 3 : 1.

Alternate Method

Given: Time taken upstream (A to B) = 2 × Time taken downstream (B to A).

Formula Used: Speed = Distance ÷ Time; Upstream Speed (U) = u − v; Downstream Speed (D) = u + v.

⇒ Let speed of boat in still water = u and speed of current = v.

⇒ Distance (d) is constant, so (u − v) × 2t = (u + v) × t.

⇒ 2u − 2v = u + v

⇒ 2u − u = v + 2v

⇒ u = 3v

⇒ u : v = 3 : 1

∴ The correct answer is 3 : 1.

Additional Information

Upstream and Downstream Speed

Downstream Speed (D) = u + v and Upstream Speed (U) = u − v, where u is boat speed and v is current speed.

Still Water Speed Calculation

The speed of the boat in still water (u) is the average of downstream and upstream speeds: u = (D + U) ÷ 2.

Current Speed Calculation

The speed of the current (v) is half the difference between downstream and upstream speeds: v = (D − U) ÷ 2.

From the Pie chart data,

Total number of employees in company D = 18%*3000 = 540

Number of Male in Company D = (3/5)*540 = 324

Number of Female in Company D = (2/5)*540 = 215

Similarly, 

Solution:

Total number of Employees in company C = 600

Total number of Employees in company F is 110% of Employees in company C

Therefore, total number of Employees in company F = 110%*600 = 660

Hence, number of Female Employees in company F = (2/5)*660 = 264

From the Pie chart data,

Total number of employees in company D = 18%*3000 = 540

Number of Male in Company D = (3/5)*540 = 324

Number of Female in Company D = (2/5)*540 = 216

Similarly, 

The total % distribution of Company D is 18% out of total number of Employees in all the company.

Total angle formed at the center of the pie chart is 360o 

Hence, Central Angle of Company D = (18/100)*360^o = 64.8

From the Piechart data,

Total number of Employees in company B = 16%*3000 = 480

number of males in company B = (3/5)*480 = 288

Total number of Employees in Company E = 22%*300 = 660

number of Male Employees in copmany E = (3/5)*660 = 396

Average number of Male Employees in company B and E = (288 + 396)/2 = 342

From the Pie chart data,

Total number of employees in company D = 18%*3000 = 540

Number of Male in Company D = (3/5)*540 = 324

Number of Female in Company D = (2/5)*540 = 215

Similarly, 

Therefore, Required % = (240-216)/216 = 1/9 = 11.11%

From the Pie chart data,

Total number of employees in company D = 18%*3000 = 540

Number of Male in Company D = (3/5)*540 = 324

Number of Female in Company D = (2/5)*540 = 216

Similarly, 

 difference between number of Male and Female in Company D = 324 - 216 = 108.

Shortcut Trick

Total Expenditure % = 13% + 27% + 35% + 5% = 80%

Remaining Savings % = 100% − 80% = 20%

20% of Income = ₹13200

100% (Total Income) = 13200 × 5 = ₹66,000

∴ The correct answer is ₹66,000.

Alternate Method

Given:

⇒ Traveling = 13%

⇒ Household expenses = 27%

⇒ Medical expenses = 35%

⇒ Insurance = 5%

⇒ Remaining Cash = ₹13200

Calculations:

⇒ Total spending = (13 + 27 + 35 + 5)% = 80%

⇒ Savings % = 100% − 80% = 20%

⇒ Let Total Income be 'X'

⇒ 20% of X = 13200

⇒ (20/100) × X = 13200

⇒ X = 13200 × 5

⇒ X = 66,000

∴ The correct answer is ₹66,000.

Additional Information

Percentage Base Change

When expenditures are given as a % of the total income, simply add the percentages. If given as % of remaining income, use successive multiplication: Remaining = Income × (1 − r₁) × (1 − r₂).

Income, Expenditure, and Savings Relationship

Income = Expenditure + Savings. If Income increases by x% and Expenditure by y%, the change in Savings depends on their initial ratio.

Shortcut Trick

Profit ratio Kamal : Raju = (3000 − 1400) : 1400 = 1600 : 1400 = 8 : 7.

Time ratio = 24 months : (42 − 24) months = 24 : 18 = 4 : 3.

Investment ratio = (Profit ÷ Time) ⇒ (8 ÷ 4) : (7 ÷ 3) = 2 : 7/3 = 6 : 7.

Since 6 units = Rs. 7500, then 1 unit = Rs. 1250.

Raju investment = 7 × 1250 = Rs. 8750.

∴ The correct answer is Rs. 8750.

Alternate Method

Given → Kamal Investment (C_k) = Rs. 7500, Time (T_k) = 24 months. Total time = 3.5 years = 42 months. Raju Time (T_r) = 42 − 24 = 18 months. Total profit = Rs. 3000, Raju Profit (P_r) = Rs. 1400. Formulas: Profit Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂)

Steps: ⇒ Profit of Kamal (P_k) = Total Profit − Raju Profit = 3000 − 1400 = Rs. 1600. ⇒ Ratio of profits (P_k / P_r) = (C_k × T_k) / (C_r × T_r). ⇒ 1600 / 1400 = (7500 × 24) / (X × 18). ⇒ 8 / 7 = (7500 × 4) / (X × 3). ⇒ 8 × 3 × X = 7 × 7500 × 4. ⇒ 24X = 210000. ⇒ X = 210000 / 24 = Rs. 8750.

∴ The correct answer is Rs. 8750.

Additional Information

Partnership Basic Concept

In a partnership, the profit is distributed among partners in the ratio of the product of their invested capital and the duration of investment.

Investment Calculation

If profits and time periods are known, the investment ratio can be found by Investment = Profit ÷ Time.

Shortcut Trick

For 2 years, the percentage by which Compound Interest (CI) is greater than Simple Interest (SI) is given by the formula: (r ÷ 2)%.

Given Rate (r) = 10%.

Percentage difference = (10 ÷ 2)% = 5%.

∴ The correct answer is 5%.

Alternate Method

Given:

Simple Interest (SI) = ₹400, Rate (r) = 10%, Time (t) = 2 years.

Formula Used:

SI = (P × r × t) ÷ 100

CI = P[(1 + r/100)^t − 1]

Calculations:

⇒ 400 = (P × 10 × 2) ÷ 100

⇒ 400 = P × 0.2 ⇒ P = ₹2000

⇒ CI for 2 years = 2000 × [(1 + 10/100)² − 1]

⇒ CI = 2000 × [1.21 − 1] = 2000 × 0.21 = ₹420

⇒ Difference = CI − SI = 420 − 400 = ₹20

⇒ Percentage greater = (Difference ÷ SI) × 100

⇒ Percentage greater = (20 ÷ 400) × 100 = 5%

∴ The correct answer is 5%.

Additional Information

Effective Rate of Interest

The effective rate for Compound Interest for 2 years is r + r + (r × r)/100. For 10%, it is 10 + 10 + 1 = 21%.

Difference between CI and SI

For 2 years, the difference (D) is given by D = P(r/100)².

Simple Interest Property

Simple Interest remains constant every year if the principal and rate are unchanged. Total SI = r × t % of Principal.

Shortcut Trick

Total units = 150. Lost (40%) = 60. Remaining = 90.

Sold 50% of 90 (45 units) at 20% profit and 45 units at 5% loss.

Let CP of 1 t-shirt = x. Total SP = 45 × 1.20x + 45 × 0.95x = 7740.

54x + 42.75x = 96.75x = 7740.

x = 7740 ÷ 96.75 = 80.

∴ The correct answer is Rs. 80.

Alternate Method

Given: Total t-shirts = 150, Loss in transit = 40%, Profit on half remaining = 20%, Loss on other half = 5%, Total SP = Rs. 7740.

Formulas: SP = CP × (100 + P%) ÷ 100 | SP = CP × (100 − L%) ÷ 100

⇒ Let Cost Price (CP) of each t-shirt = Rs. C.

⇒ Number of t-shirts lost = 40% of 150 = 60. Remaining = 150 − 60 = 90.

⇒ Half of remaining sold at 20% profit: 45 × C × 1.20 = 54C.

⇒ Half of remaining sold at 5% loss: 45 × C × 0.95 = 42.75C.

⇒ Total SP = 54C + 42.75C = 96.75C.

⇒ Given 96.75C = 7740 ⇒ C = 7740 ÷ 96.75 = 80.

∴ The correct answer is Rs. 80.

Additional Information

Total Cost vs Net Profit

Net Profit or Loss is calculated on the Total Cost Price of all 150 items, even those lost in transit. Total CP = 150 × 80 = 12000.

Effective Selling Price

Items that are lost/damaged have a Selling Price of 0, contributing to a 100% loss for those specific units.

Shortcut Trick

Let length of Train 1 be 3L and Train 2 be 4L.

From Train 2 crossing platform: Speed × 42 = 4L + 300 ⇒ (x − 6) × (5/18) × 42 = 4L + 300.

From Relative Speed: (x + x − 6) × (5/18) × 21 = 7L.

By substituting L or solving the ratio of distances, we find x = 70.

∴ The correct answer is 70.

Alternate Method

Given: Speed of Train 1 = x km/hr, Speed of Train 2 = (x − 6) km/hr. Length of Train 2 = (4/3) × Length of Train 1. Let length of Train 1 = 3L, then Train 2 = 4L.

Formula: Distance = Speed × Time

⇒ For Train 2 crossing platform: (x − 6) × (5/18) × 42 = 4L + 300

⇒ (x − 6) × (35/3) = 4L + 300 → (Eq 1)

⇒ For trains crossing each other (Relative speed): (x + x − 6) × (5/18) × 21 = 3L + 4L

⇒ (2x − 6) × (35/6) = 7L ⇒ (x − 3) × (35/3) = 7L ⇒ L = 5(x − 3)/3 → (Eq 2)

⇒ Substitute L in (Eq 1): (x − 6) × (35/3) = 4 × [5(x − 3)/3] + 300

⇒ 35x − 210 = 20x − 60 + 900

⇒ 15x = 1050

⇒ x = 70

∴ The correct answer is 70.

Additional Information

Relative Speed

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

Unit Conversion

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

Crossing Distance

When a train crosses another train or platform, the total distance covered is the sum of their respective lengths.

Given,

Total number of boys including those from the five branches

= 500 + 500 + 450 + 200 + 300

= 1950

Required average

= 1950/5

= 390

Given,

Total number to girls including five branches

= 300 + 100 + 250 + 600 + 250

= 1500

Total number of boys including five branches

= 500 + 500 + 450 + 200 + 300

= 1950

Total number of students in College

= 1500 + 1950

= 3450

Required percentage

= (1500/3450) × 100 ≈ 43.48%

Total number of students in Computer branch

= 200 + 600

= 800

Total number of students in Mechanical and Electronics branch

= (500 + 100) + (300 + 250)

= 1150

Required ratio

= 800 : 1150

= 32 : 46

= 16 : 23

Given,

Total number of boys including five branches

= 500 + 500 + 450 + 200 + 300

= 1950

Number of boy’s students in Mechanical branch = 500

Required percentage

= (500/1950) × 100 ≈ 25.64%

Given,

Civil branch = 500 : 300 = 5 : 3 = 1.66

Mechanical branch = 500 : 100 = 5 : 1 = 5

Electrical branch = 450 : 250 = 9 : 5 = 1.8

Computer branch = 200 : 600 = 1 : 3 = 0.33

Electronics branch = 300 : 250 = 6 : 5 = 1.2

From this,

Computer branch has minimum ratio of boys and girls students in College.

Shortcut Trick

Total Capacity (LCM of 7, 10, 15) = 210 units.

Efficiency of P = 210 ÷ 7 = 30, Efficiency of Q = 210 ÷ 10 = 21, Efficiency of R = −(210 ÷ 15) = −14.

Combined Efficiency (P + Q − R) = 30 + 21 − 14 = 37.

Time Taken = Total Capacity ÷ Combined Efficiency = 210 ÷ 37 = 5²⁵⁄₃₇ hours.

∴ The correct answer is 5²⁵⁄₃₇ hr.

Alternate Method

⇒ Net efficiency when all pipes are open = Efficiency of P + Efficiency of Q + Efficiency of R

⇒ Net efficiency = 30 + 21 − 14 = 37 units/hr

⇒ Total time to fill the tank = Total Work ÷ Net efficiency

⇒ Total time = 210 ÷ 37

⇒ Total time = 5²⁵⁄₃₇ hr

∴ The correct answer is 5²⁵⁄₃₇ hr.

Additional Information

Inlet and Outlet Pipes

An inlet pipe fills the tank (positive work), while an outlet pipe (leak) empties it (negative work).

Efficiency Rule

Total Work = Time × Efficiency. If a tank is filled in 'x' hours and emptied in 'y' hours, net work in 1 hour = (1/x − 1/y).

Pipes & Cisterns Concept

This topic follows the same principles as Time and Work, treating the volume of the tank as the total work to be completed.

Shortcut Trick

Ratio of Ram and Rohit: 7 : 8 (Present) → 9 : 10 (After 6 years).

Difference in ratio parts = 9 − 7 = 2 units and 10 − 8 = 2 units.

2 units → 6 years, so 1 unit → 3 years.

Present age of Rohit = 8 units × 3 = 24 years.

Age after 10 years = 24 + 10 = 34 years.

∴ The correct answer is 34 years.

Alternate Method

Given: Present ratio = 7 : 8, Ratio after 6 years = 9 : 10.

Let Ram and Rohit present ages be 7x and 8x.

⇒ (7x + 6) / (8x + 6) = 9 / 10

⇒ 10(7x + 6) = 9(8x + 6)

⇒ 70x + 60 = 72x + 54

⇒ 2x = 6

⇒ x = 3

⇒ Present age of Rohit = 8 × 3 = 24 years.

⇒ Age after 10 years = 24 + 10 = 34 years.

∴ The correct answer is 34 years.

Additional Information

Ratio Difference Equality

If the age difference between ratios is not equal, multiply ratios by the difference of the other ratio to equalize them.

Age Calculations

The difference between the ages of two people remains constant regardless of the number of years passed.

Shortcut Trick

Ratio of covered distance to remaining distance = 2 : 7

Total units = 2 + 7 = 9 units → 48 km

Distance covered = (2 ÷ 9) × 48 = 32/3 km

Time = 1 hour 40 minutes = 1 + 40/60 = 5/3 hours

Speed = (32/3) ÷ (5/3) = 32/5 kmph = (32/5) × (5/18) = 16/9 m/s

∴ The correct answer is 16/9 m/s.

Alternate Method

Given: Total distance = 48 km, Time = 1 hour 40 mins, Covered distance = 2/7 × Remaining distance.

Formula Used: Speed = Distance ÷ Time; 1 kmph = 5/18 m/s.

⇒ Let remaining distance be x km.

⇒ Distance covered = 2/7 × x

⇒ (2x/7) + x = 48 ⇒ 9x/7 = 48 ⇒ x = (48 × 7) ÷ 9 = 112/3 km

⇒ Distance covered = 48 − 112/3 = (144 − 112) ÷ 3 = 32/3 km

⇒ Time = 1 hr + 40/60 hr = 1 + 2/3 = 5/3 hours

⇒ Speed = (32/3) ÷ (5/3) = 32/5 km/h

⇒ Speed in m/s = 32/5 × 5/18 = 16/9 m/s

∴ The correct answer is 16/9 m/s.

Additional Information

Unit Conversion

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

Average Speed

Average speed is defined as the total distance traveled divided by the total time taken (Total Distance ÷ Total Time).

Ratio Application

If a : b is the ratio of two parts, the first part is [a/(a+b)] × Total and the second part is [b/(a+b)] × Total.

Shortcut Trick

Side of square = 120 ÷ 4 = 30 m

Length (L) of rectangle = 6 × 30 = 180 m

Breadth (B) of rectangle = 30 ÷ 3 = 10 m

Perimeter = 2 × (180 + 10) = 380 m

Total Cost = 380 × 20 = ₹7,600

∴ The correct answer is ₹7,600.

Alternate Method

Given: Ratio of length (L) to square side (s) = 6 : 1. Ratio of breadth (B) to square side (s) = 1/3 : 1. Perimeter of square = 120 m. Rate = ₹20/m.

Formula Used: Perimeter of square = 4 × s; Perimeter of rectangle = 2 × (L + B); Total Cost = Perimeter × Rate.

⇒ 4 × side = 120

⇒ Side (s) = 120 ÷ 4 = 30 m

⇒ Length (L) = 6 × 30 = 180 m

⇒ Breadth (B) = (1/3) × 30 = 10 m

⇒ Perimeter of rectangle = 2 × (180 + 10) = 2 × 190 = 380 m

⇒ Total cost of fencing = 380 × 20 = 7600

∴ The correct answer is ₹7,600.

Additional Information

Mensuration Formulas

Area of rectangle = L × B; Area of square = side². Fencing always refers to the Perimeter of the shape.

Unit Conversion

Ensure all dimensions are in the same unit (meters) before calculating costs or areas to avoid calculation errors.

Shortcut Trick

Concentration of milk in A = 3/8, in B = 2/5, and in Resultant = 5/13.

By Alligation: (2/5 − 5/13) : (5/13 − 3/8) ⇒ (26 − 25)/65 : (40 − 39)/104.

Ratio of quantities A : B = (1/65) : (1/104) = 104 : 65 = 8 : 5.

Given 8 units = 32 litres ⇒ 1 unit = 4 litres.

Value of x (5 units) = 5 × 4 = 20 litres.

∴ The correct answer is 20 litres.

Alternate Method

Given: Vessel A (Milk:Water = 3:5), Vessel B (Milk:Water = 2:3), New Mix (5:8), Vol A = 32L.

Formula: Ratio of volumes V_A/V_B = (m_B − m_m) / (m_m − m_A) where m is milk fraction.

⇒ Milk in 32L of A = (3/8) × 32 = 12 L; Water in A = (5/8) × 32 = 20 L.

⇒ Milk in xL of B = 2x/5; Water in B = 3x/5.

⇒ Total Milk / Total Water = (12 + 2x/5) / (20 + 3x/5) = 5/8.

⇒ 8 × (12 + 2x/5) = 5 × (20 + 3x/5)

⇒ 96 + 16x/5 = 100 + 15x/5

⇒ 16x/5 − 15x/5 = 100 − 96

⇒ x/5 = 4 ⇒ x = 20 litres.

∴ The correct answer is 20 litres.

Additional Information

Rule of Alligation

It is a rule used to find the ratio in which two or more ingredients at their respective prices/concentrations must be mixed to produce a mixture at a given mean price/concentration.

Mixture Concentration

When mixing two quantities with concentration c₁ and c₂ to get c_m, the ratio of quantities is (c₂ − c_m) : (c_m − c₁).

Given:

9.78% of 79.94 + ?% of 9.67 = 10.94 × 2.99 + √100 × 2.98

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

9.78% of 79.94 + ?% of 9.67 = 10.94 × 2.99 + √100 × 2.98

⇒ 10% of 80 + ?% of 10 = 11 × 3 + √100 × 3

⇒ (10/100) × 80 + (?/100) × 10 = 33 + 10 × 3

⇒ 8 + (?/10) = 33 + 30

⇒ 8 + (?/10) = 63

⇒ (?/10) = 63 - 8 

⇒ (?/10) = 55 

⇒ ? = 55 × 10 = 550

∴ The value of ? is 550.

Given:

49.97% of 1900.1 + (7.99)3 × 4.97 + ? = (5.03)3 × 27.98

Concept used:

Rules of Approximation:

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

Follow the BODMAS rule according to the table given below:

Calculation:

49.97% of 1900.1 + (7.99)3 × 4.97 + ? = (5.03)3 × 27.98

⇒ 50% of 1900 + 8³ × 5 + ? = 5³ × 28

⇒ (50/100) × 1900 + 512 × 5 + ? = 125 × 28

⇒ 950 + 2560 + ? = 3500

⇒ 3510 + ? = 3500

⇒ ? = 3500 – 3510

⇒ ? = -10

∴ The value of ? is -10.

Given:

15.67 × 62.5% - 12.5 × 7.99% + 24.2 ÷ 6 = 50.01 ÷ 5.12 + ?

Concept used:

Calculation:

15.67 × 62.5% - 12.5 × 7.99% + 24.2 ÷ 6 = 50.01 ÷ 5.12 + ?

⇒ 16 × (5/8) - 12.5 × (8/100) + 24/6 = 50/5 + ?

⇒ 10 - 1 + 4 = 10 + ?

⇒ ? = 10 - 1 + 4 - 10

⇒ ? = 3

∴ The value of ? is 3.

Given:

37.98% of 549.99 + √(49.02) ÷ ? = 7.99 × (2.97)³

Rules of Approximation:

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

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

37.98% of 549.99 + √(49.02) ÷ ? = 7.99 × (2.97)³

⇒ 38% of 550 + √49 ÷ ? = 8 × 3³

⇒ (38/100) × 550 + 7 ÷ ? = 8 × 27

⇒ 209 + 7 ÷ ? = 216

⇒ 7 ÷ ? = 7

⇒ ? = 1

∴ 1 should come in place of the question mark (?).

Solution :

 Concept used :

 Follow the BODMAS rule to solve this question, as per the question is 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 part of the equation that contains 'Division' and 'multiplication' are calculated,

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

 Given :

⇒ (22.03% of 150.01 ) + (361.33)^1/2 + (63.92 ÷ 2.012) + (11.02% of 499.98) = ?

Approximate the number to its nearest value 

⇒ (22% of 150 ) + (361)^1/2 + (64÷ 2) + (11 % of 500) = ?

⇒ 22 × 150 /100 + (19)^2×1/2 + 32 + 11 × 500 /100 = ?

⇒ 33 + 19 + 32 + 55 = ?

⇒ 84 + 55 = ?

⇒ ? = 139

Hence 139 is the correct answer.

Given:

6 people – A, B, C, P, Q, and R

6 subjects – Physics, History, Maths, Biology, English, and Chemistry

1. B had his performance review on the 26^th of July.
   
2. 2 people had their reviews between the Physics teacher and B.
   
3. The English teacher had his review in December.

4. The Biology teacher had his performance review after the Maths teacher in the same month.
   
5. The History teacher had his review before A, who did not teach Chemistry.
   
6. 4 people had their reviews between P and C, who did not teach Physics.

7. C was not the English teacher but had his review immediately after Q.
   
8. R did not teach Biology.

(A is allocated on July 14 because Point 5 state ‘the History teacher had his review before A’.)

(Case 1 (a.2) and Case 1(b) will not be possible as it will not satisfy point 7.)

Final arrangement:

Hence, A is the Maths teacher.

Given:

6 people – A, B, C, P, Q, and R

6 subjects – Physics, History, Maths, Biology, English, and Chemistry

1. B had his performance review on the 26^th of July.
   
2. 2 people had their reviews between the Physics teacher and B.
   
3. The English teacher had his review in December.

4. The Biology teacher had his performance review after the Maths teacher in the same month.
   
5. The History teacher had his review before A, who did not teach Chemistry.
   
6. 4 people had their reviews between P and C, who did not teach Physics.

7. C was not the English teacher but had his review immediately after Q.
   
8. R did not teach Biology.

(A is allocated on July 14 because Point 5 state ‘the History teacher had his review before A’.)

(Case 1(a.2) and Case 1(b) will not be possible as it will not satisfy point 7.)

Final arrangement:

R is the History teacher.

C is the Chemistry teacher.

Hence, 3 people had their review between R and C.

Given:

6 people – A, B, C, P, Q, and R

6 subjects – Physics, History, Maths, Biology, English, and Chemistry

1. B had his performance review on the 26^th of July.
   
2. 2 people had their reviews between the Physics teacher and B.
   
3. The English teacher had his review in December.

4. The Biology teacher had his performance review after the Maths teacher in the same month.
   
5. The History teacher had his review before A, who did not teach Chemistry.
   
6. 4 people had their reviews between P and C, who did not teach Physics.

7. C was not the English teacher but had his review immediately after Q.
   
8. R did not teach Biology.

(A is allocated on July 14 because Point 5 state ‘the History teacher had his review before A’.)

(Case 1 (a.2) and Case 1(b) will not be possible as it will not satisfy point 7.)

Final arrangement:

Hence, C is the Chemistry teacher.

Given:

6 people – A, B, C, P, Q, and R

6 subjects – Physics, History, Maths, Biology, English, and Chemistry

1. B had his performance review on the 26^th of July.
   
2. 2 people had their reviews between the Physics teacher and B.
   
3. The English teacher had his review in December.

4. The Biology teacher had his performance review after the Maths teacher in the same month.
   
5. The History teacher had his review before A, who did not teach Chemistry.
   
6. 4 people had their reviews between P and C, who did not teach Physics.

7. C was not the English teacher but had his review immediately after Q.
   
8. R did not teach Biology.

(A is allocated on July 14 because Point 5 states ‘the History teacher had his review before A’.)

(Case 1 (a.2) and Case 1(b) will not be possible as it will not satisfy point 7.)

Final arrangement:

Hence, Q - the English teacher, had his review on December 14.