SBI PO Prelims Memory Based Paper (Held On: 6 November 2023 Shift 2) (Previous Year Paper)

The correct answer is 'Option 4'.

 

Key Points

• Mumbai Suburban Railway is primarily operated by two divisions.
• These two divisions are mentioned explicitly in the passage as Western Railways (WR) and Central Railways (CR).
• The passage details the historical significance and operational aspects of these railway divisions.
• It emphasizes the role of these two divisions in ensuring the efficient functioning of Mumbai’s extensive railway network.

Therefore, the correct answer is- ‘Central Railways and Western Railways’.

 

Additional Information

• Option 1: Northern Railways and Western Railways
• Incorrect because Northern Railways does not operate the Mumbai Suburban Railway. The passage indicates that it is Central Railways and Western Railways.
• Option 2: Central Railways and Eastern Railways
• Incorrect because the passage does not mention Eastern Railways as an operator of the Mumbai Suburban Railway.
• Option 3: Western Railways and Southern Railways
• Incorrect because Southern Railways is not involved in operating the Mumbai Suburban Railway, as noted in the passage.
• Option 5: Southern Railways and Eastern Railways
• Incorrect for the same reasons above; these divisions are not operators of the Mumbai Suburban Railway according to the passage.

The correct answer is 'Option 1'.

 

Key Points

• The passage states that the first train in Mumbai ran from Bori Bunder (now Chhatrapati Shivaji Maharaj Terminus) to Thane, not Kasara.
• The incorrect statement is option 1, which inaccurately mentions Kasara instead of Thane as the destination of the first train.
• Option 2 is correct as the passage mentions that the Mumbai Suburban Railway serves more than 7.5 million commuters daily.
• Option 3 is correct, as the passage states that the Harbour Line branches off from the Central Line and covers Navi Mumbai.
• Option 4 is accurate because the passage details that the network consists of the Western Line, Central Line, and Harbour Line.
• Option 5 is true since the passage describes the Chhatrapati Shivaji Maharaj Terminus as a UNESCO World Heritage Site.

Therefore, the correct answer is ‘The first train in Mumbai ran from Chhatrapati Shivaji Maharaj Terminus to Kasara’.

 

Additional Information

• Option 1: The first train in Mumbai ran from Chhatrapati Shivaji Maharaj Terminus to Kasara
• Incorrect because the passage specifies that the first train ran from Bori Bunder (now Chhatrapati Shivaji Maharaj Terminus) to Thane, not Kasara.
• Option 2: The Mumbai Suburban Railway serves more than 7.5 million commuters daily.
• This statement is correct as per the passage, which mentions that the suburban trains serve more than 7.5 million commuters daily.
• Option 3: The Harbour Line branches off from the Central Line and covers Navi Mumbai.
• This statement is accurate as the passage clearly states that the Harbour Line branches off from the Central Line and extends to both Panvel and Goregaon, covering Navi Mumbai in the process.
• Option 4: The network consists of the Western Line, Central Line, and Harbour Line.
• This is correct, as the passage describes the network as comprising three main lines: the Western Line, Central Line, and Harbour Line.
• Option 5: The Chhatrapati Shivaji Maharaj Terminus is a UNESCO World Heritage Site.
• This statement is true as per the passage, which highlights that the Chhatrapati Shivaji Maharaj Terminus is a UNESCO World Heritage Site known for its Victorian Gothic architecture.

The correct answer is 'Option 3'.

 

Key Points

• The passage points out that the Mumbai Suburban Railway serves as a cultural microcosm, reflecting the diverse population of Mumbai.
• It emphasizes that the daily commute on these trains brings together people from all walks of life, creating a unique sense of community.
• Vendors, performers, and the presence of historic stations add to the cultural experience on these trains.
• The passage suggests that the railway is not just a mode of transport but also holds cultural importance, highlighting Mumbai's diversity.

Therefore, the correct answer is ‘Reflects the cultural diversity of Mumbai’.

 

Additional Information

• Option 1: Is primarily used by tourists.
• Incorrect because the passage mentions the suburban railway is the lifeline for daily commuters, implying it's mainly used by locals, not primarily tourists.
• Option 2: Is disliked by the majority of commuters.
• Incorrect as the passage does not suggest that commuters dislike the service; rather, it highlights the importance and efficiency of the railway system despite challenges like overcrowding.
• Option 4: Has no specific facilities for different segments of the population.
• Incorrect because the passage explicitly states that the trains include coaches for women, senior citizens, and disabled passengers, addressing the needs of different population segments.
• Option 5: Is less crowded during peak hours.
• Incorrect because the passage states that trains run as often as every three minutes during peak hours to handle high traffic, implying that they are, in fact, very crowded during these times.

The correct answer is 'Option 1'.

 

Key Points

• The passage primarily focuses on the Mumbai Suburban Railway, detailing its historical origins, its critical role in the daily lives of millions, and its current operations.
• It highlights the railway's vast network, the various lines it operates, and its significant role in the cultural and economic life of Mumbai.
• The passage also touches upon recent developments like the Mumbai Metro and Monorail, but emphasizes that the suburban railway remains unmatched in reach and utility.
• Additionally, it describes the daily experiences and challenges of commuting on these trains, as well as the cultural significance of the railway system in Mumbai.

Therefore, the correct answer is ‘The history and current significance of the Mumbai Suburban Railway’.

 

Additional Information

• Option 2: The introduction of the Mumbai Metro and the Monorail.
• Incorrect because while the passage mentions the Mumbai Metro and the Monorail, they are only discussed in the context of their relation to the existing suburban railway system and not the central focus.
• Option 3: The architectural heritage of Chhatrapati Shivaji Maharaj Terminus.
• Incorrect because although the passage briefly discusses the Chhatrapati Shivaji Maharaj Terminus and its architectural significance, this is only a part of the broader discussion about the Mumbai Suburban Railway.
• Option 4: The financial markets and skyline of Mumbai.
• Incorrect because the main focus of the passage is on the railway system, not the financial markets or the skyline.
• Option 5: The role of vendors and performers on Mumbai suburban trains.
• Incorrect because while vendors and performers are mentioned, this detail is part of a broader discussion about the cultural importance of the railway and not the central theme.

The correct answer is 'Option 4'.

 

Key Points

• Statement A: "The Mumbai Suburban Railway played a role in the establishment of Mumbai's impressive skyline."
• Incorrect. The passage does not state that the railway played a role in establishing Mumbai's skyline. The skyline is mentioned separately in the introductory context.
• Statement B: "Efforts have been made to improve safety standards on the railway."
• Correct. The passage mentions that there have been continuous efforts to improve safety standards, including the introduction of advanced signaling systems, improved station facilities, and increased security measures.
• Statement C: "The Western Line runs from Churchgate to Dahanu Road."
• Correct. The passage clearly states that the Western Line runs from Churchgate to Dahanu Road.

Therefore, the correct answer is 'B and C'.

The correct answer is 'Option 1'.

 

Key Points

• Statement A: "The Harbour Line does not extend to Navi Mumbai."
• Incorrect. The passage states that the Harbour Line branches off from the Central Line and extends to both Panvel and Goregaon, covering Navi Mumbai in the process. Therefore, the Harbour Line does extend to Navi Mumbai, making this statement incorrect.
• Statement B: "The Mumbai Metro and Monorail are designed to complement the suburban railway."
• Correct. The passage mentions that one of the significant developments in recent years has been the introduction of the Mumbai Metro and the Monorail, which are designed to complement the existing railway system and ease congestion.
• Statement C: "Chhatrapati Shivaji Maharaj Terminus was built in 1887."
• Correct. The passage states that among the most famous stations is the Chhatrapati Shivaji Maharaj Terminus, which was built in 1887 and is known for its Victorian Gothic architecture.

Therefore, the incorrect statement is 'Only A'.

The correct answer is: Option 2.

Key Points

• The word "bustling" means full of activity, energy, and movement; lively and busy. (चहल-पहल से भरा हुआ)
• Example: The marketplace was bustling with shoppers and vendors.
• "Busy" refers to being actively engaged in activities, full of people, movement, and noise. (व्यस्त)
• Example: The city streets were busy with traffic and pedestrians.

Therefore, the correct answer is: Busy.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Quiet (शांत): Free from noise or disturbance.
• Example: The library is a quiet place where people come to read and study.
• Uninhabited (निर्जन): Not lived in; without inhabitants.
• Example: The island was uninhabited, making it a perfect spot for a peaceful retreat.
• Tranquil (शांत): Calm, peaceful, and quiet.
• Example: The tranquil garden was an ideal place for meditation and relaxation.
• Dull (नीरस): Lacking interest or excitement.
• Example: The lecture was so dull that several students fell asleep.

The correct answer is: Option 3.

Key Points

• The word "substantial" means something that is of considerable importance, size, or worth. (महत्‍वपूर्ण, ठोस)
• Example: They made substantial progress in their research.
• "Insignificant" refers to something that is too small or unimportant to be worth consideration. (तुच्छ)
• Example: The error was so insignificant that it went unnoticed.
• Hence, we can infer that the opposite of 'substantial' is 'insignificant'.

Therefore, the correct answer is: Insignificant.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Ample (पर्याप्‍त): Enough or more than enough; plentiful.
• Example: There was ample evidence to support the theory.
• Significant (महत्वपूर्ण): Sufficiently great or important to be worthy of attention.
• Example: The discovery was significant in the field of medicine.
• Considerable (काफी): Notably large in size, amount, or extent.
• Example: The project required considerable investment.
• Extensive (व्यापक): Covering or affecting a large area.
• Example: The hurricane caused extensive damage to the town.

The correct answer is 'Ruckus.'

Key Points

• The given sentence says the effects of the fight or disturbance from the angry citizens left many people arrested for disturbing the peace.
• Therefore, the most appropriate word to be filled in the blank is 'Ruckus'.
• Also, the use of the word ''disturbing'' in the sentence indicates the use of the word 'ruckus' in the blank.
• The word 'Ruckus' means A noisy fight or disturbance. (हंगामा) 
• Example: Due to the ruckus in the motel room next door, it woke my whole family up.

Hence, the correct answer is option 4.

Complete Sentence: The effects of the ruckus from the angry citizens left many people arrested for disturbing the peace.

Additional Information

• Let us explore the other options:
• Contentment means A feeling of happiness and satisfaction. (मधुर संतुष्टि, संतोष)
• Ecstasy means A feeling or state of great happiness. (आह्लाद और आनंद की भावना; हर्षोन्माद)
• Elation means Great happiness and exhilaration. (अति प्रसन्‍नता, उल्‍लास, हर्ष)
• Gratification means Pleasure, especially when gained from the satisfaction of a desire. (संतोष, आनंद)

The correct answer is 'Derogatory.'

Key Points

• The given sentence talks about the public who criticized the basketball team owner after he made poor opinions or remarks about minorities.
• Therefore, the most appropriate word to be filled in the blank is 'Derogatory'.
• Also, the use of the word ''criticized'' in the sentence indicates the use of the word 'derogatory' in the blank.
• The word 'Derogatory' means Conveying a poor opinion of something or someone. (प्रतिष्ठा रहित, अपमानजनक, अनादरपूर्ण)
• Example: Once you finish insulting me with derogatory words, we can have a peaceful conversation.

Hence, the correct answer is option 2.

Complete Sentence: The public criticized the basketball team owner after he made derogatory remarks about minorities.

Additional Information

• Let us explore the other options:
• Mandatory means Required by a law or rule. (अनिवार्य)
• Victory means Success in winning a battle, game, competition, etc. (युद्घ, खेल, स्‍पर्धा आदि में सफलता, विजय, जीत, फ़तह)
• Possession means Something that someone owns or has with them at a particular time. (अधिकार)
• Advisory means Giving advice only; not having the power to make decisions. (केवल सलाहकारी; निर्णय करने के अधिकार से वंचित)

The correct answer is 'overture'.

Key Points

• The given sentence talks about the government's economic policies to attract foreign investments.
• Therefore, the most appropriate word for the given blank would be 'overture'.
• 'Overture' refers to an introduction or opening move, often in the context of music, diplomacy, or literature. (प्रस्ताव, प्रारंभिक प्रस्ताव)
• Example: The peace talks began with a diplomatic overture, signalling a willingness to negotiate.
• Hence, the correct answer is 'Option 5'.

The complete sentence would be: The government's economic policies can be seen as an overture to attract foreign investments.

Additional InformationLet's understand the meaning of the other options:

• Bolster: To support, strengthen, or reinforce; a long, narrow pillow or cushion. (सहारा देना, समर्थन करना)
• Aggression: Hostile or violent behaviour or attitudes; the act of initiating an attack or confrontation. (प्रकोप, हमला)
• Deception: The act of deceiving or misleading; the action of causing someone to believe something that is not true. (धोखा, छल)
• Abrogation: The repeal or abolition of a law, rule, or agreement; the act of officially ending or canceling something. (समाप्ति, अधिनियमन का समाप्त होना)

The correct answer is 'inflamed'.

Key Points

• The given sentence talks about the politician's controversial statement that sparked protests.
• Therefore, the most appropriate word for the given blank would be 'inflamed'.
• 'Inflamed' describes a condition characterized by redness, swelling, or heightened emotions. (सूजा हुआ, भड़कानेवाला)
• Example: The injured area became inflamed, causing pain and swelling.
• Hence, the correct answer is 'Option 4'.

The complete sentence would be: The politician's controversial statement inflamed public opinion and sparked protests.

Additional InformationLet's understand the meaning of the other given options:

• Suppressed: Kept under control or restrained; subdued or stifled. (दबाया हुआ, नियंत्रित)
• Angered: Made angry or provoked; filled with resentment or displeasure. (क्रोधित, गुस्साया हुआ)
• Engraved: Carved, etched, or incised with a design or inscription on a hard surface. (खुदाई किया हुआ, नक्काशी किया हुआ)
• Settled: Resolved, established, or decided conclusively; firmly established in a place. (निश्चित, स्थायी)

The correct answer is BADEC​.

 Key Points

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

• The first blank requires an adjective, which modifies the noun 'years''. Therefore, 'few' is the correct answer here.
• The second blank requires an adverb that is used with a measurement of time. Therefore, 'ago' is the correct answer here.
• The third blank requires an adjective that describes the characteristic of the action of operating a patient. Therefore, 'impossible' is the correct answer here.
• The fourth blank requires a noun that should be related to the patient and able to get operated on. Therefore 'heart' is the correct answer.
• The fifth blank requires a verb that describes the action of the noun 'heart'. Therefore, 'working' is the correct answer

Therefore, the correct answer is,

A few years ago it was impossible to operate on a patient whose heart was not working properly.

The correct answer is BAECD​.

 Key Points

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

• The first blank requires an adverb, which shows the fact. Therefore, 'actually' is the correct answer here.
• The second blank requires a noun that the adverb 'actually' is mentioning. Therefore, 'drama' is the correct answer here.
• The third blank requires a verb that describes the action and that too third form of the verb 'be'. Therefore, 'been' is the correct answer here.
• The fourth blank requires an adjective that describes the noun 'people'. Therefore 'Indian' is the correct answer.
• The fifth blank requires a noun that goes along with another noun 'politicians'. Therefore, 'actors' is the correct answer

Additional Information

• Let's look at the meaning of the given word.
• legends: 

an extremely famous or notorious person, especially in a particular field

Therefore, the correct answer is,

Actually, the drama has always been the life of Indian people, as it deals with legends of actors and politicians.

The correct answer is BCEAD​.

 Key Points

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

• The first blank requires a noun, and that too a person's name because an adverb 'according' is used for this noun which means 'something stated by someone'. Therefore, 'Gandhiji' is the correct answer here.
• The second blank requires a noun that is a plural one because the pronoun 'all' is used before it. Therefore, 'religions' is the correct answer here.
• The third blank requires an adverb that modifies the adjective 'true. Therefore, 'equally' is the correct answer here.
• The fourth blank requires a pronoun that can be used for the noun 'scripture'. Therefore 'each' is the correct answer.
• The fifth blank requires an adjective that describes the quality of the noun 'religion'. Therefore, 'worthy' is the correct answer

Additional Information

• Let's look at the meaning of the given words.
• scripture: religious text
• worthy:  

having or showing the qualities that deserve the specified action or regard.

​

Therefore, the correct answer is,

According to Gandhiji, all religions are equally true and each scripture is worthy of respect.

The correct answer is BDEAC​.

 Key Points

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

• The first blank requires a noun which is a part of the noun 'officer' describing the specific kind of officer. Therefore, 'police' is the correct answer here.
• The second blank requires a pronoun that is used for the noun 'police'. Therefore, 'whose' is the correct answer here.
• The third blank requires a verb describing the action related to the citizens. Therefore, 'protect' is the correct answer here.
• The fourth blank requires a verb that describes the action which is related to the noun 'crimes'. Therefore 'solve' is the correct answer.
• The fifth blank requires a noun that goes along in combination with another noun which is joined by the conjunction 'and. Therefore, 'rules' is the correct answer

Therefore, the correct answer is,

Police officers are law enforcement professionals whose job is to protect citizens, solve crimes, and assure that rules and regulations are followed

The correct answer is E.

Key Points

• The given paragraph is about the Lotte World Tower in South Korea.
• Sentence E is the first sentence as it introduces the Lotte World Tower and its various features like retail outlets, offices, residences, hotel and Lotte World Mall.
• Sentence F is the second sentence as it explains further about the significance of the Tower to South Korea and its national pride.
• Sentence B is the third sentence as it details which companies were primarily involved in the construction of the tower.
• Sentence D is already in the correct place, as the fourth sentence describing the tower's impressive height.
• Sentence A would serve as the fifth sentence, elaborating on unique additional features like a helipad and a maximum capacity of over 500 residents.
• Sentence C is the sixth sentence as it concludes the paragraph by talking about the history and completion of the Tower.
• The correct sequence is EFBDAC.

 

Correct Paragraph: The comprehensive Lotte World Tower complex includes retail outlets, offices, residences, a hotel, and a podium with the Lotte World Mall. The Tower is a new symbol for the national pride of South Korea and its aspiration to be at the forefront of global trends in architecture and technology. The project was completed primarily by the South Korean construction company Hyundai Engineering & Construction and High-Tech Industrial Development. The Lotte World Tower situated in Seoul, South Korea, is one of the tallest buildings in the world with an impressive height of 1,819 feet. The unique construction features a helipad and has a maximum capacity of over 500 residents. Despite being renowned for its elegance and luxury, the Tower had a bleak history and was completed after 11 years of persistent efforts.

The correct answer is F.

Key Points

• The given paragraph is about the Lotte World Tower in South Korea.
• Sentence E is the first sentence as it introduces the Lotte World Tower and its various features like retail outlets, offices, residences, hotel and Lotte World Mall.
• Sentence F is the second sentence as it explains further about the significance of the Tower to South Korea and its national pride.
• Sentence B is the third sentence as it details which companies were primarily involved in the construction of the tower.
• Sentence D is already in the correct place, as the fourth sentence describing the tower's impressive height.
• Sentence A would serve as the fifth sentence, elaborating on unique additional features like a helipad and a maximum capacity of over 500 residents.
• Sentence C is the sixth sentence as it concludes the paragraph by talking about the history and completion of the Tower.
• The correct sequence is EFBDAC.

 

Correct Paragraph: The comprehensive Lotte World Tower complex includes retail outlets, offices, residences, a hotel, and a podium with the Lotte World Mall. The Tower is a new symbol for the national pride of South Korea and its aspiration to be at the forefront of global trends in architecture and technology. The project was completed primarily by the South Korean construction company Hyundai Engineering & Construction and High-Tech Industrial Development. The Lotte World Tower situated in Seoul, South Korea, is one of the tallest buildings in the world with an impressive height of 1,819 feet. The unique construction features a helipad and has a maximum capacity of over 500 residents. Despite being renowned for its elegance and luxury, the Tower had a bleak history and was completed after 11 years of persistent efforts.

The correct answer is B.

Key Points

• The given paragraph is about the Lotte World Tower in South Korea.
• Sentence E is the first sentence as it introduces the Lotte World Tower and its various features like retail outlets, offices, residences, hotel and Lotte World Mall.
• Sentence F is the second sentence as it explains further about the significance of the Tower to South Korea and its national pride.
• Sentence B is the third sentence as it details which companies were primarily involved in the construction of the tower.
• Sentence D is already in the correct place, as the fourth sentence describing the tower's impressive height.
• Sentence A would serve as the fifth sentence, elaborating on unique additional features like a helipad and a maximum capacity of over 500 residents.
• Sentence C is the sixth sentence as it concludes the paragraph by talking about the history and completion of the Tower.
• The correct sequence is EFBDAC.

 

Correct Paragraph: The comprehensive Lotte World Tower complex includes retail outlets, offices, residences, a hotel, and a podium with the Lotte World Mall. The Tower is a new symbol for the national pride of South Korea and its aspiration to be at the forefront of global trends in architecture and technology. The project was completed primarily by the South Korean construction company Hyundai Engineering & Construction and High-Tech Industrial Development. The Lotte World Tower situated in Seoul, South Korea, is one of the tallest buildings in the world with an impressive height of 1,819 feet. The unique construction features a helipad and has a maximum capacity of over 500 residents. Despite being renowned for its elegance and luxury, the Tower had a bleak history and was completed after 11 years of persistent efforts.

The correct answer is A.

Key Points

• The given paragraph is about the Lotte World Tower in South Korea.
• Sentence E is the first sentence as it introduces the Lotte World Tower and its various features like retail outlets, offices, residences, hotel and Lotte World Mall.
• Sentence F is the second sentence as it explains further about the significance of the Tower to South Korea and its national pride.
• Sentence B is the third sentence as it details which companies were primarily involved in the construction of the tower.
• Sentence D is already in the correct place, as the fourth sentence describing the tower's impressive height.
• Sentence A would serve as the fifth sentence, elaborating on unique additional features like a helipad and a maximum capacity of over 500 residents.
• Sentence C is the sixth sentence as it concludes the paragraph by talking about the history and completion of the Tower.
• The correct sequence is EFBDAC.

 

Correct Paragraph: The comprehensive Lotte World Tower complex includes retail outlets, offices, residences, a hotel, and a podium with the Lotte World Mall. The Tower is a new symbol for the national pride of South Korea and its aspiration to be at the forefront of global trends in architecture and technology. The project was completed primarily by the South Korean construction company Hyundai Engineering & Construction and High-Tech Industrial Development. The Lotte World Tower situated in Seoul, South Korea, is one of the tallest buildings in the world with an impressive height of 1,819 feet. The unique construction features a helipad and has a maximum capacity of over 500 residents. Despite being renowned for its elegance and luxury, the Tower had a bleak history and was completed after 11 years of persistent efforts.

The correct answer is C.

 Key Points

• The given paragraph is about the Lotte World Tower in South Korea.
• Sentence E is the first sentence as it introduces the Lotte World Tower and its various features like retail outlets, offices, residences, hotel and Lotte World Mall.
• Sentence F is the second sentence as it explains further about the significance of the Tower to South Korea and its national pride.
• Sentence B is the third sentence as it details which companies were primarily involved in the construction of the tower.
• Sentence D is already in the correct place, as the fourth sentence describing the tower's impressive height.
• Sentence A would serve as the fifth sentence, elaborating on unique additional features like a helipad and a maximum capacity of over 500 residents.
• Sentence C is the sixth sentence as it concludes the paragraph by talking about the history and completion of the Tower.
• The correct sequence is EFBDAC.

 

Correct Paragraph: The comprehensive Lotte World Tower complex includes retail outlets, offices, residences, a hotel, and a podium with the Lotte World Mall. The Tower is a new symbol for the national pride of South Korea and its aspiration to be at the forefront of global trends in architecture and technology. The project was completed primarily by the South Korean construction company Hyundai Engineering & Construction and High-Tech Industrial Development. The Lotte World Tower situated in Seoul, South Korea, is one of the tallest buildings in the world with an impressive height of 1,819 feet. The unique construction features a helipad and has a maximum capacity of over 500 residents. Despite being renowned for its elegance and luxury, the Tower had a bleak history and was completed after 11 years of persistent efforts.

The correct answer is 'B' i.e. the error lies in part B of the sentence. 

Key Points

Let us have a look at few words given in the sentence:

• Returns is a verb.
• Slow is an adjective.
• A verb should be preceded by an adverb.
• Hence, slow should be replaced with slowly.

So the correct sentence is The southern state of Kerala slowly returns to normalcy, days after devastating floods claimed over 450 lives and caused massive destruction.

Additional Information

Let us understand the following about adverb:

• An adverb is a word that modifies (describes)
• a verb
• Example: She sings loudly.
• an adjective
• Example: She is very tall.
• another adverb
• Example: The episode ended too quickly.
• a whole sentence
• Example: Fortunately, I had brought an umbrella.
• Adverbs often end in -ly. 
• Example: beautifully, carefully, quickly, etc.
• However, some adverbs look exactly the same as their adjective counterparts.
• Example: fast.

The erroneous part is D i.e. this part of the sentence has an error.

Key Points

• The last part (D) of the sentence is erroneous because the word 'feasting' is grammatically incorrect.
• The preposition 'to' is used before the word 'feasting'. Therefore, infinitive should be used here.
• Hence, the base form of the word 'feasting' should be used here.
• So, the word 'feast' should replace 'feasting'.
• Hence, option 4) is the answer.

Correct sentence: Researchers have found a whale species that typically migrates away from solid sea ice each autumn and returns every summer to feast on tiny crustaceans.

Additional Information 

• An infinitive is the base form of the verb. 
• Example: He likes to eat apple.

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

Key Points

• The error lies in part C.
• The word 'loosing' used here is incorrect. The correct word will be 'losing' in this context.
• Lose is a verb that means to be without (lose a sock), to fail (lose the game), or to be deprived of (lose a job). Other forms of this verb are lost and losing.
• Loose is most often an adjective that means not tight (a loose belt) or unbound and unconstrained (loose lips). It can also be used as an adverb or verb with similar meanings of being unconstrained.

So, the correct sentence is,

With Casper and Glossier venturing into new product ranges, their regular customers start losing trust in the companies and their products.

The correct answer is Option 5 i.e. No correction required.

Key Points

• The original sentence is grammatically correct, so the correct answer is "No correction required."
• The sentence follows the correct structure of a sentence with a subject, verb, and object.
• The subject is "The government," the verb is "has announced," and the object is "plans to launch a new initiative aimed at reducing plastic waste in the oceans."
• The phrase "aimed at reducing plastic waste in the oceans" is a prepositional phrase that modifies "initiative."
• The phrase "aimed at" shows the purpose of the initiative, which is to reduce plastic waste in the oceans.
• Therefore, the sentence is already grammatically correct, and we don't need to make any changes.

The correct answer is Option 2 i.e. to move into a larger office space

Key Points

• We can improve the given sentenec by replacing "to a larger office space" with "into a larger office space."
• The verb "to move" is a transitive verb, which means it requires a direct object. In this case, the direct object is "its headquarters."
• The prepositional phrase "to a larger office space" functions as an adverb to modify the verb "move."
• However, when we use "to move" with a destination that is an enclosed space, like an office, it is more appropriate to use the preposition "into." So, the correct sentence would use "into" instead of "to."
• Therefore, option 2) "to move into a larger office space" is the correct choice, and the corrected sentence is grammatically accurate and more precise.
• Here's the corrected sentence: "The company has decided to move its headquarters into a larger office space in the downtown area."

The correct answer is Option 4.

 

Key Points

• The original sentence contains the phrase "to be prepare," which is incorrect.
• The correct form should be "to be prepared" to ensure proper grammatical structure.
• Thus, the phrase should be "to be prepared to discuss it in class on Monday" to make the sentence correct.

Therefore, the correct answer is Option 4.

 

Correct Sentence: "The teacher asked her students to read the novel over the weekend and to be prepared to discuss it in class on Monday.

The correct answer is option 3.

Key Points

To answer this question, first, let's look at the given phrases in the table:

• A. The project encapsulated their collective efforts,
• This phrase expresses the combined work and dedication of everyone involved.
• B. The results of the experiment had been inconclusive,
• This phrase mentions that the experiment didn't provide clear or definite findings.
• C. Comprising 14% of the global population,
• This phrase refers to a specific portion of the world's population.
• D. the WHO African region collected only 5% of global donations.
• This phrase highlights the low amount of donations collected in Africa.
• E. making it unsuitable for beginners.
• This phrase mentions that something is not good for beginners.
• F. they embarked on the adventurous hike into the remote, snow-covered mountains.
• This phrase describes a daring journey through isolated snowy mountains.

 

Now, let's understand the meanings of the given connectors in the question:

• i. despite
• It means "regardless of" or "in spite of."
• For Example:
• Despite the storm, she went out for a run.
• ii. moreover
• It means "furthermore" or "in addition to what has been said."
• For Example:
• She aced her exams; moreover, she volunteered at the shelter.
• iii. conversely
• It means "on the contrary" or "in contrast."
• For Example:
• He expected failure; conversely, he achieved great success.
• So, after understanding the given phrases and the connectors, we can conclude that only the combination C-i-D can make a grammatically and contextually meaningful sentence.
• The complete coherent sentence would be: "Despite comprising 14% of the global population, the WHO African region collected only 5% of global donations."
• This sentence points out that although Africa has 14% of the world's population, it received only 5% of global donations.
• Therefore, the correct answer is "C-i-D."

The correct answer is option 2.

Key Points

To answer this question, first, let's look at the given phrases in the table:

• A. The findings supported the hypothesis;
• This phrase suggests the hypothesis was backed by evidence or results.
• B. Phones stimulate our dopamine circuit,
• This phrase mentions that phones trigger our pleasure centre, causing excitement.
• C. She implemented a new strategy;
• This phrase indicates the introduction of a fresh plan or approach by her.
• D. failing to provide the long-term happiness humans seek from experiences.
• This phrase suggests experiences do not deliver lasting happiness to people.
• E. her husband set the table for the family.
• This phrase describes the husband setting the family dinner table.
• F. they persisted in their plan to explore the mountains.
• This phrase highlights determination in pursuing mountain exploration despite obstacles.

 

Now, let's understand the meanings of the given connectors in the question:

• i. meanwhile
• It means "at the same time" or "during that period."
• For Example:
• She was cooking; meanwhile, he set the table for dinner.
• ii. thus
• It means "as a result" or "in this way," indicating a consequence or conclusion.
• For Example:
• He studied hard; thus, he aced the exam.
• iii. albeit
• It means "although" or "even though," introducing a concession or contrast.
• For Example:
• She was tired; albeit, she finished the project on time.
• So, after understanding the given phrases and the connectors, we can conclude that only the combination B-ii-D can make a grammatically and contextually meaningful sentence.
• The complete coherent sentence would be: "Phones stimulate our dopamine circuit, thus failing to provide the long-term happiness humans seek from experiences."
• The sentence suggests that phone use triggers short-term pleasure but doesn't fulfil our deeper, lasting happiness from real-life experiences.
• Therefore, the correct answer is "B-ii-D."

The correct answer is option 1.

Key Points

To answer this question, first, let's look at the given phrases in the table:

• A. They departed from the quaint village,
• This phrase describes leaving a charming, old-fashioned village.
• B. The project's success relied heavily on teamwork,
• This phrase highlights how the project depended on a collaborative effort.
• C. Winning the war against NCDs is vital for individual well-being,
• This phrase emphasizes the importance of defeating non-communicable diseases for personal health.
• D. he reached the picturesque village nestled in the valley.
• This phrase describes arriving at a beautiful village in a valley.
• E. safeguarding the health of the nation.
• This phrase emphasizes protecting the overall well-being of the country.
• F. he faced various health issues later in life.
• This phrase refers to the health problems he encountered as he aged.

 

Now, let's understand the meanings of the given connectors in the question:

• i. notwithstanding
• It means "despite" or "in spite of" and indicates a contrast or exception to a previous statement.
• For Example:
• She continued working, notwithstanding her exhaustion from the long day.
• ii. be that as it may
• It means "nevertheless" or "however," acknowledging a point but continuing the argument or discussion.
• For Example:
• The weather was bad, but, be that as it may, they still enjoyed their vacation.
• iii. as well as
• It means "in addition to" or "along with," indicating inclusion or a parallel point.
• For Example:
• She bought apples as well as oranges for the fruit salad.
• So, after understanding the given phrases and the connectors, we can conclude that only the combination C-iii-E can make a grammatically and contextually meaningful sentence.
• The complete coherent sentence would be: "Winning the war against NCDs is vital for individual well-being, as well as safeguarding the health of the nation."
• This sentence emphasizes the importance of fighting Non-Communicable Diseases for personal health and the nation's well-being.
• Therefore, the correct answer is "C-iii-E."

General solution:

Number of tables sold in shop A = x

Number of chairs sold in shop A = y

Number of tables sold in shop B = (x - 20)

Number of chairs sold in shop A is 70% of number of chairs sold in shop B

Number of chairs sold in shop B = y/(70) ×  100 = (10y/7)

Number of tables sold in shop C = (x - 40)

Number of tables sold in shop D = (60/100) ×  x = 0.6x

Number of chairs sold in shop C = 80/100 ×  (10y/7) = 8y/7

Number of chairs sold in shop D = (8y/7) ×  (75/100) = 6y/7

Total tables sold in all the shops is 170 more than total chairs sold in all the shops

[x + (x - 20) + (x - 40) + 0.6x] - [y + 10y/7 + (8y/7)y + (6y/7)] = 170

(3.6x - 60) - (y + 24y/7) = 170

(3.6x - 60) - (7y + 24y)/7 = 170

25.2x - 420 - (7y + 24y) = 1190

25.2x - 31y = 1610 —----> 1

2 ×  31→ x + y = 220 —----->2

25.2x - 31y = 1610

31x + 31y = 6820

56.2x = 8430

x = 150

y = 70

Number of tables sold in shop A = x = 150

Number of chairs sold in shop A = y = 70

Number of tables sold in shop B = (x - 20) = (150 - 20) = 130

Number of chairs sold in shop A is 70% of number of chairs sold in shop B

Number of chairs sold in shop B = y/(70) ×  100 = (10y/7) = 10 ×  70/7 = 100

Number of tables sold in shop C = (x - 40) = (150 - 40) = 110

Number of tables sold in shop D = (60/100) ×  x = 0.6x = 150 ×  (0.6) = 90

Number of chairs sold in shop C = 80/100 ×  (10y/7) = 8y/7 = 8 ×  (70/7) = 80

Number of chairs sold in shop D = (8y/7) ×  (75/100) = 6y/7 = 6 ×  (70/7) = 60

Solution:

Price of each table in shop A = Rs. a

Price of each chair in shop A = Rs. (a + 100)

Total revenue generated = Rs. 73000

a×  150 + (a + 100) ×  70 = 73000

150a + 70a + 7000 = 73000

220a = 66000

a = 300

General solution:

Number of tables sold in shop A = x

Number of chairs sold in shop A = y

Number of tables sold in shop B = (x - 20)

Number of chairs sold in shop A is 70% of number of chairs sold in shop B

Number of chairs sold in shop B = y/(70) ×  100 = (10y/7)

Number of tables sold in shop C = (x - 40)

Number of tables sold in shop D = (60/100) ×  x = 0.6x

Number of chairs sold in shop C = 80/100 ×  (10y/7) = 8y/7

Number of chairs sold in shop D = (8y/7) ×  (75/100) = 6y/7

Total tables sold in all the shops is 170 more than total chairs sold in all the shops

[x + (x - 20) + (x - 40) + 0.6x] - [y + 10y/7 + (8y/7)y + (6y/7)] = 170

(3.6x - 60) - (y + 24y/7) = 170

(3.6x - 60) - (7y + 24y)/7 = 170

25.2x - 420 - (7y + 24y) = 1190

25.2x - 31y = 1610 —----> 1

2 ×  31→ x + y = 220 —----->2

25.2x - 31y = 1610

31x + 31y = 6820

56.2x = 8430

x = 150

y = 70

Number of tables sold in shop A = x = 150

Number of chairs sold in shop A = y = 70

Number of tables sold in shop B = (x - 20) = (150 - 20) = 130

Number of chairs sold in shop A is 70% of number of chairs sold in shop B

Number of chairs sold in shop B = y/(70) ×  100 = (10y/7) = 10 ×  70/7 = 100

Number of tables sold in shop C = (x - 40) = (150 - 40) = 110

Number of tables sold in shop D = (60/100) ×  x = 0.6x = 150 ×  (0.6) = 90

Number of chairs sold in shop C = 80/100 ×  (10y/7) = 8y/7 = 8 ×  (70/7) = 80

Number of chairs sold in shop D = (8y/7) ×  (75/100) = 6y/7 = 6 ×  (70/7) = 60

Solution:

Number of tables sold at discount in shop A = 150 ×  (3/5) = 90

Number of tables sold at discount in shop C = 110 ×  (4/11) = 40

Number of chairs sold at discount in shop A = 70 ×  (3/7) = 30

Number of chairs sold at discount in shop C = 80 ×  (1/2) = 40

Total number of chairs and tables in shop A and C sold at the discount = (90 + 40 +30 + 40) = 200

General solution:

Number of tables sold in shop A = x

Number of chairs sold in shop A = y

Number of tables sold in shop B = (x - 20)

Number of chairs sold in shop A is 70% of number of chairs sold in shop B

Number of chairs sold in shop B = y/(70) ×  100 = (10y/7)

Number of tables sold in shop C = (x - 40)

Number of tables sold in shop D = (60/100) ×  x = 0.6x

Number of chairs sold in shop C = 80/100 ×  (10y/7) = 8y/7

Number of chairs sold in shop D = (8y/7) ×  (75/100) = 6y/7

Total tables sold in all the shops is 170 more than total chairs sold in all the shops

[x + (x - 20) + (x - 40) + 0.6x] - [y + 10y/7 + (8y/7)y + (6y/7)] = 170

(3.6x - 60) - (y + 24y/7) = 170

(3.6x - 60) - (7y + 24y)/7 = 170

25.2x - 420 - (7y + 24y) = 1190

25.2x - 31y = 1610 —----> 1

2 ×  31→ x + y = 220 —----->2

25.2x - 31y = 1610

31x + 31y = 6820

56.2x = 8430

x = 150

y = 70

Number of tables sold in shop A = x = 150

Number of chairs sold in shop A = y = 70

Number of tables sold in shop B = (x - 20) = (150 - 20) = 130

Number of chairs sold in shop A is 70% of number of chairs sold in shop B

Number of chairs sold in shop B = y/(70) ×  100 = (10y/7) = 10 ×  70/7 = 100

Number of tables sold in shop C = (x - 40) = (150 - 40) = 110

Number of tables sold in shop D = (60/100) ×  x = 0.6x = 150 ×  (0.6) = 90

Number of chairs sold in shop C = 80/100 ×  (10y/7) = 8y/7 = 8 ×  (70/7) = 80

Number of chairs sold in shop D = (8y/7) ×  (75/100) = 6y/7 = 6 ×  (70/7) = 60

Solution:

Number of tables sales in shop D is increased by p

(90 + p)/60 = 2/1

120 = 90 + p

p = 30

Value of b = (30/90) ×  100 = 33.33%

Therefore the value of b = 33.33%

General solution:

Number of tables sold in shop A = x

Number of chairs sold in shop A = y

Number of tables sold in shop B = (x - 20)

Number of chairs sold in shop A is 70% of number of chairs sold in shop B

Number of chairs sold in shop B = y/(70) ×  100 = (10y/7)

Number of tables sold in shop C = (x - 40)

Number of tables sold in shop D = (60/100) ×  x = 0.6x

Number of chairs sold in shop C = 80/100 ×  (10y/7) = 8y/7

Number of chairs sold in shop D = (8y/7) ×  (75/100) = 6y/7

Total tables sold in all the shops is 170 more than total chairs sold in all the shops

[x + (x - 20) + (x - 40) + 0.6x] - [y + 10y/7 + (8y/7)y + (6y/7)] = 170

(3.6x - 60) - (y + 24y/7) = 170

(3.6x - 60) - (7y + 24y)/7 = 170

25.2x - 420 - (7y + 24y) = 1190

25.2x - 31y = 1610 —----> 1

2 ×  31→ x + y = 220 —----->2

25.2x - 31y = 1610

31x + 31y = 6820

56.2x = 8430

x = 150

y = 70

Number of tables sold in shop A = x = 150

Number of chairs sold in shop A = y = 70

Number of tables sold in shop B = (x - 20) = (150 - 20) = 130

Number of chairs sold in shop A is 70% of number of chairs sold in shop B

Number of chairs sold in shop B = y/(70) ×  100 = (10y/7) = 10 ×  70/7 = 100

Number of tables sold in shop C = (x - 40) = (150 - 40) = 110

Number of tables sold in shop D = (60/100) ×  x = 0.6x = 150 ×  (0.6) = 90

Number of chairs sold in shop C = 80/100 ×  (10y/7) = 8y/7 = 8 ×  (70/7) = 80

Number of chairs sold in shop D = (8y/7) ×  (75/100) = 6y/7 = 6 ×  (70/7) = 60

Solution:

Number of tables sold in shop A = 150

Number of tables sold in shop B = 130

Number of tables sold in the shop E = (150 + 130)/2 = 280/2 = 140 + 25 = 165

Number of chairs sold in shop A = 70

Number of chairs sold in shop D = 60

Number of chairs sold in shop E = (60 + 70)/2 = 130/2 = 65 + 35 = 100

Required total = (165 + 100) = 265

The pattern of the given series can be explained as:

4 × 1.5 = 6

6 × 3 = 18

18 × 6 = 108 ≠ 110

108 × 12 = 1296

1296 × 24 = 31104

∴ The wrong term is 110.

Given:

24, 26, 36, 62, 112, 196, 316

Calculation:

⇒ 24 + 2 (1² +1) = 26

⇒ 26 + 10 (32 +1) = 36

⇒ 36 + 26 (52 +1) = 62

⇒ 62 + 50 (72 +1) = 112

⇒ 112 + 82 (92 +1) = 194

⇒ 194 + 122 (112 +1) = 316

∴ The wrong term is 196.

Given:

155, 298, 493, 748,1069, 1470

Calculation:

⇒ 155 + (12² - 1) = 298

⇒ 298 + (14² - 1) = 493

⇒ 493 + (162 - 1) = 748

⇒ 748 + (182 - 1) = 1071

⇒ 1071 + (202 - 1) = 1470

∴ The wrong term is 1069.

Given:

25, 200, 45, 320, 64, 512

Calculation:

⇒ 25 × 8 = 200

⇒ 200 ÷ 5 = 40

⇒ 40 × 8 = 320

⇒ 320 ÷ 5 = 64

⇒ 64 × 8 = 512

∴ The wrong term is 45.

Given:

119, 138, 195, 290, 432, 594

Calculation:

⇒ 119 + 19 × 1 = 138

⇒ 138 + 19 × 3 = 195

⇒ 195 + 19 × 5 = 290

⇒ 290 + 19 × 7 = 423 

⇒ 423 + 19 × 9 = 594.

∴ The wrong term is 432.

Shortcut Trick

Let efficiencies of typists be x and y. Total work = 18(x + y).

Work done: 9x + 18y = 2/3 of 18(x + y) ⇒ 9x + 18y = 12x + 12y.

⇒ 6y = 3x ⇒ x = 2y. Ratio of efficiencies x : y = 2 : 1.

Total Work = 18 × (2 + 1) = 54 units.

Time for faster typist (x) = 54 ÷ 2 = 27 minutes.

∴ The correct answer is 27 min.

Alternate Method

Given: First typist works for 9 min, Second for 18 min, remaining work is 1/3.

⇒ Work completed = 1 − 1/3 = 2/3 of total work.

⇒ Let efficiency of first typist be a and second be b.

⇒ Total Work = 18(a + b)

⇒ 9a + 18b = (2/3) × 18(a + b)

⇒ 9a + 18b = 12a + 12b

⇒ 18b − 12b = 12a − 9a

⇒ 6b = 3a ⇒ a = 2b (First typist is faster)

⇒ Total Work = 18(2b + b) = 18 × 3b = 54b

⇒ Time for faster typist = 54b ÷ 2b = 27 minutes.

∴ The correct answer is 27 min.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to time taken. If the ratio of efficiencies is a : b, then the ratio of time taken is b : a.

Combined Work Formula

If two people with efficiencies E₁ and E₂ work together for T days, the Total Work = T × (E₁ + E₂).

Shortcut Trick

Students passed in only Political Science = Total passed in Pol. Science − passed in Both

Percentage in only Pol. Science = 72% − 35% = 37%

Given, 37% of N = 666

N = 666 ÷ 37 × 100 = 18 × 100 = 1800

∴ The correct answer is 1800 students.

Alternate Method

Given:

Passed in History H = 59%

Passed in Political Science P = 72%

Passed in Both (H ∩ P) = 35%

Number of students passed in only Political Science = 666

Calculations:

⇒ Percentage of students passed in only Political Science = P − (H ∩ P)

⇒ Percentage = 72% − 35% = 37%

⇒ According to the question, 37% of N = 666

⇒ (37/100) × N = 666

⇒ N = (666 × 100) ÷ 37

⇒ N = 18 × 100

⇒ N = 1800

∴ The correct answer is 1800 students.

Additional Information

Venn Diagram Principle

For two sets A and B, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). This represents students who passed in at least one subject.

Only One Subject Calculation

To find only A, subtract the intersection from total A: n(only A) = n(A) − n(A ∩ B).

Failed in Both Subjects

Percentage failed in both subjects = 100% − [Percentage passed in at least one subject].

General Solution:

 

College A:

Total number of students (Male + Female) participated in exam = 1100

Number of males participated in exam = 1100/11 ×  7 = 700

Number of females participated in exam = (1100 - 700) = 400

Percentage of students failed in exam = 1100 ×  (30/100) = 330

Number females failed in exam = 330 - 210 = 120

Number of males passed in exam = 700 - 210 = 490

Number of females passed in exam = 400 - 120 = 280

 

College B:

Total number of students (Male + Female) participated in exam = 900

Number of males participated in exam = 900/3 ×  2 = 600

Number of females participated in exam = (900 - 600) = 300

Percentage of students failed in exam = 900 ×  (40/100) = 360

Number females failed in exam = 360 - 240 = 120

Number of males passed in exam = 600 - 240 = 360

Number of females passed in exam = 300 - 120 = 180

 

College C:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/3 ×  4 = 800

Number of females participated in exam = (1400 - 800) = 600

Percentage of students failed in exam = 1140 ×  (50/100) = 700

Number females failed in exam = 700 - 500 = 200

Number of males passed in exam = 800 - 500  = 300

Number of females passed in exam = 600 - 200 = 400

 

College D:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/28 ×  17 = 850

Number of females participated in exam = (1400 - 850) = 550

Percentage of students failed in exam = 1400 ×  (45/100) = 630

Number females failed in exam = 630 - 255 = 375

Number of males passed in exam = 850 - 255 = 595

Number of females passed in exam = 550 - 375 = 175

 

College E:

Total number of students (Male + Female) participated in exam = 1600

Number of males participated in exam = 1600/16 ×  9 = 900

Number of females participated in exam = (1600 - 900) = 700

Percentage of students failed in exam = 1600 ×  (60/100) = 960

Number females failed in exam = 960 - 450 = 510

Number of males passed in exam = 900 - 450 = 450

Number of females passed in exam = 700 - 510 = 190

 

Solution:

Number of males who passed in college A = 490

Number of male who passed in college A passed in distinction = 490 ×  (3/7) = 210

Number of females passed in college A = 280

Number of females who passed in college A in distinction = (280 ×  3/5) = 168

Required total = (210 + 168) = 378

General Solution:

 

College A:

Total number of students (Male + Female) participated in exam = 1100

Number of males participated in exam = 1100/11 ×  7 = 700

Number of females participated in exam = (1100 - 700) = 400

Percentage of students failed in exam = 1100 ×  (30/100) = 330

Number females failed in exam = 330 - 210 = 120

Number of males passed in exam = 700 - 210 = 490

Number of females passed in exam = 400 - 120 = 280

 

College B:

Total number of students (Male + Female) participated in exam = 900

Number of males participated in exam = 900/3 ×  2 = 600

Number of females participated in exam = (900 - 600) = 300

Percentage of students failed in exam = 900 ×  (40/100) = 360

Number females failed in exam = 360 - 240 = 120

Number of males passed in exam = 600 - 240 = 360

Number of females passed in exam = 300 - 120 = 180

 

College C:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/3 ×  4 = 800

Number of females participated in exam = (1400 - 800) = 600

Percentage of students failed in exam = 1140 ×  (50/100) = 700

Number females failed in exam = 700 - 500 = 200

Number of males passed in exam = 800 - 500  = 300

Number of females passed in exam = 600 - 200 = 400

 

College D:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/28 ×  17 = 850

Number of females participated in exam = (1400 - 850) = 550

Percentage of students failed in exam = 1400 ×  (45/100) = 630

Number females failed in exam = 630 - 255 = 375

Number of males passed in exam = 850 - 255 = 595

Number of females passed in exam = 550 - 375 = 175

 

College E:

Total number of students (Male + Female) participated in exam = 1600

Number of males participated in exam = 1600/16 ×  9 = 900

Number of females participated in exam = (1600 - 900) = 700

Percentage of students failed in exam = 1600 ×  (60/100) = 960

Number females failed in exam = 960 - 450 = 510

Number of males passed in exam = 900 - 450 = 450

Number of females passed in exam = 700 - 510 = 190

 

Solution:

Number of males failed in college B = 240

Number of females failed in college B = 120

Number of males failed in college B increased by 30% = 240 ×  (130/100) = 312

Number of females failed in college B increased by 40% = 120 ×  (140/100) = 168

Total students passed in the college B = 540

Required difference = 540 - 480 = 60

General Solution:

 

College A:

Total number of students (Male + Female) participated in exam = 1100

Number of males participated in exam = 1100/11 ×  7 = 700

Number of females participated in exam = (1100 - 700) = 400

Percentage of students failed in exam = 1100 ×  (30/100) = 330

Number females failed in exam = 330 - 210 = 120

Number of males passed in exam = 700 - 210 = 490

Number of females passed in exam = 400 - 120 = 280

 

College B:

Total number of students (Male + Female) participated in exam = 900

Number of males participated in exam = 900/3 ×  2 = 600

Number of females participated in exam = (900 - 600) = 300

Percentage of students failed in exam = 900 ×  (40/100) = 360

Number females failed in exam = 360 - 240 = 120

Number of males passed in exam = 600 - 240 = 360

Number of females passed in exam = 300 - 120 = 180

 

College C:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/3 ×  4 = 800

Number of females participated in exam = (1400 - 800) = 600

Percentage of students failed in exam = 1140 ×  (50/100) = 700

Number females failed in exam = 700 - 500 = 200

Number of males passed in exam = 800 - 500  = 300

Number of females passed in exam = 600 - 200 = 400

 

College D:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/28 ×  17 = 850

Number of females participated in exam = (1400 - 850) = 550

Percentage of students failed in exam = 1400 ×  (45/100) = 630

Number females failed in exam = 630 - 255 = 375

Number of males passed in exam = 850 - 255 = 595

Number of females passed in exam = 550 - 375 = 175

 

College E:

Total number of students (Male + Female) participated in exam = 1600

Number of males participated in exam = 1600/16 ×  9 = 900

Number of females participated in exam = (1600 - 900) = 700

Percentage of students failed in exam = 1600 ×  (60/100) = 960

Number females failed in exam = 960 - 450 = 510

Number of males passed in exam = 900 - 450 = 450

Number of females passed in exam = 700 - 510 = 190

 

 

Solution:

Number of male students passed in college D = 595

Number of female students passed in college D = 175

3/5 of number of males passed in college D = 595 ×  3/5 = 357

4/5 of number of females passed in college D = 175 ×  (4/5) = 140

Total students failed in college D = (255 + 375) = 630

Required percentage = (357 + 140)/630 ×  100= 78.89%~ 79%

General Solution:

 

College A:

Total number of students (Male + Female) participated in exam = 1100

Number of males participated in exam = 1100/11 ×  7 = 700

Number of females participated in exam = (1100 - 700) = 400

Percentage of students failed in exam = 1100 ×  (30/100) = 330

Number females failed in exam = 330 - 210 = 120

Number of males passed in exam = 700 - 210 = 490

Number of females passed in exam = 400 - 120 = 280

 

College B:

Total number of students (Male + Female) participated in exam = 900

Number of males participated in exam = 900/3 ×  2 = 600

Number of females participated in exam = (900 - 600) = 300

Percentage of students failed in exam = 900 ×  (40/100) = 360

Number females failed in exam = 360 - 240 = 120

Number of males passed in exam = 600 - 240 = 360

Number of females passed in exam = 300 - 120 = 180

 

College C:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/3 ×  4 = 800

Number of females participated in exam = (1400 - 800) = 600

Percentage of students failed in exam = 1140 ×  (50/100) = 700

Number females failed in exam = 700 - 500 = 200

Number of males passed in exam = 800 - 500  = 300

Number of females passed in exam = 600 - 200 = 400

 

College D:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/28 ×  17 = 850

Number of females participated in exam = (1400 - 850) = 550

Percentage of students failed in exam = 1400 ×  (45/100) = 630

Number females failed in exam = 630 - 255 = 375

Number of males passed in exam = 850 - 255 = 595

Number of females passed in exam = 550 - 375 = 175

 

College E:

Total number of students (Male + Female) participated in exam = 1600

Number of males participated in exam = 1600/16 ×  9 = 900

Number of females participated in exam = (1600 - 900) = 700

Percentage of students failed in exam = 1600 ×  (60/100) = 960

Number females failed in exam = 960 - 450 = 510

Number of males passed in exam = 900 - 450 = 450

Number of females passed in exam = 700 - 510 = 190

 

 

Solution:

Number of males passed in college C = 300

Number of males passed in college E = 450

Number of females passed in college C = 400

Number of females passed in college E = 190

Required ratio = (450 + 300): (400 + 190) = 750: 590 = 75: 59

General Solution:

 

College A:

Total number of students (Male + Female) participated in exam = 1100

Number of males participated in exam = 1100/11 ×  7 = 700

Number of females participated in exam = (1100 - 700) = 400

Percentage of students failed in exam = 1100 ×  (30/100) = 330

Number females failed in exam = 330 - 210 = 120

Number of males passed in exam = 700 - 210 = 490

Number of females passed in exam = 400 - 120 = 280

 

College B:

Total number of students (Male + Female) participated in exam = 900

Number of males participated in exam = 900/3 ×  2 = 600

Number of females participated in exam = (900 - 600) = 300

Percentage of students failed in exam = 900 ×  (40/100) = 360

Number females failed in exam = 360 - 240 = 120

Number of males passed in exam = 600 - 240 = 360

Number of females passed in exam = 300 - 120 = 180

 

College C:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/3 ×  4 = 800

Number of females participated in exam = (1400 - 800) = 600

Percentage of students failed in exam = 1140 ×  (50/100) = 700

Number females failed in exam = 700 - 500 = 200

Number of males passed in exam = 800 - 500  = 300

Number of females passed in exam = 600 - 200 = 400

 

College D:

Total number of students (Male + Female) participated in exam = 1400

Number of males participated in exam = 1400/28 ×  17 = 850

Number of females participated in exam = (1400 - 850) = 550

Percentage of students failed in exam = 1400 ×  (45/100) = 630

Number females failed in exam = 630 - 255 = 375

Number of males passed in exam = 850 - 255 = 595

Number of females passed in exam = 550 - 375 = 175

 

College E:

Total number of students (Male + Female) participated in exam = 1600

Number of males participated in exam = 1600/16 ×  9 = 900

Number of females participated in exam = (1600 - 900) = 700

Percentage of students failed in exam = 1600 ×  (60/100) = 960

Number females failed in exam = 960 - 450 = 510

Number of males passed in exam = 900 - 450 = 450

Number of females passed in exam = 700 - 510 = 190

 

 

Solution:

Number of males who failed in all the college = (210 + 240 + 500 + 255 + 450)/5 = 331

Number of females who failed in all the college = (120 + 120 + 200 + 375 + 510)/5 = 265

Required difference = (331 - 265) = 66

Shortcut Trick

Initial average of 4 people (A, B, C, D) = 40 inches.

New average with E = 41 inches (increased by 1).

Height of E = 41 + (4 × 1) = 45 inches.

New average of (B, C, D, E, F) = 42 inches.

Sum of (B, C, D, F) = (Sum of B, C, D, E, F) − Height of E = (42 × 5) − 45 = 210 − 45 = 165 inches.

Average of (B, C, D, F) = 165 ÷ 4 = 41.25 inches.

∴ The correct answer is 41.25 inches.

Alternate Method

Given:

Average height (A+B+C+D) = 40 inches

Average height (A+B+C+D+E) = 41 inches

Average height (B+C+D+E+F) = 42 inches

Calculations:

⇒ Total height (A+B+C+D) = 40 × 4 = 160 inches

⇒ Total height (A+B+C+D+E) = 41 × 5 = 205 inches

⇒ Height of E = 205 − 160 = 45 inches

⇒ Total height (B+C+D+E+F) = 42 × 5 = 210 inches

⇒ Total height (B+C+D+F) = Total (B+C+D+E+F) − E = 210 − 45 = 165 inches

⇒ Average height (B+C+D+F) = 165 ÷ 4 = 41.25 inches

∴ The correct answer is 41.25 inches.

Additional Information

Average Calculation

Average = Sum of observations ÷ Number of observations.

Inclusion/Exclusion Rule

Value of new person = New Average + (Old Count × Change in Average).

Weighted Average

Total Sum = Sum₁ + Sum₂. Combined Average = (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂).

Shortcut Trick

Initial ratio Alcohol : Water = 1 : 4. Total units = 5.

After removing 2/3, remaining mixture is 1/3 of Y. Ratio stays 1 : 4.

In remaining part: Alcohol = 1x, Water = 4x. Add 250 ml water → 1x / (4x + 250) = 4 / 19.

⇒ 19x = 16x + 1000 ⇒ 3x = 1000 ⇒ x = 1000/3 ml.

Remaining mixture = 5x = 5000/3 ml. Original Y = 3 × (5000/3) = 5000 ml.

∴ The correct answer is 5 litres.

Alternate Method

Given: Initial Ratio = 1 : 4, Removed = 2/3, Added Water = 250 ml, Final Ratio = 4 : 19.

⇒ Let remaining mixture (Y/3) consist of Alcohol = a and Water = 4a.

⇒ New Alcohol : New Water = a : (4a + 250) = 4 : 19

⇒ 19 × a = 4 × (4a + 250)

⇒ 19a = 16a + 1000

⇒ 3a = 1000 ml ⇒ a = 1000/3 ml

⇒ Total remaining mixture (Y/3) = a + 4a = 5a

⇒ Y/3 = 5 × (1000/3) = 5000/3 ml

⇒ Y = 5000 ml = 5 litres

∴ The correct answer is 5 litres.

Additional Information

Mixture Withdrawal Rule

When a part of a mixture is removed, the ratio of components in the remaining mixture remains the same as the initial ratio.

Alligation Method

Used to find the ratio in which two ingredients are mixed to produce a desired concentration: (Cheaper) : (Dearer) = (d−m) : (m−c).

Replacement Formula

Final Quantity = Initial Quantity × (1 − x/V)ⁿ, where x is quantity replaced, V is total volume, and n is number of operations.

Concept:

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

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

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

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

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

Calculation:

211 + 111 × 210 + 630 × 2 = ?

⇒ 211 + 23310 + 1260 = ?

⇒ ? = 24781

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

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

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

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

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

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

Given expression is

121.98 – [70.98 + {4.14 – (4.98 – (22.98 – 21.12))}] = ?

⇒ 122 – [71 + {4 – (5 – (23 – 21))}] = ?

⇒ 122 – [71 + {4 – (5 – 2)}] = ?

⇒ 122 – [71 + {4 – 3}] = ?

⇒ 122 – [71 + 1] = ?

⇒ 122 – 72 = ?

⇒ 50 = ?

Concept:

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

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

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

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

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

Calculation:

Writing the approximate values to the nearest integer

(65% of 400 + 33 × 22 – 743) = ?

? = (65/100 × 400 + 726 – 743)

= 260 + 726 – 743

= 243

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

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

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

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

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

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

 Given Expression.

49.9% of 499.9 × 19.9% of 99.9 ÷ ? = 49.9% of 1999.9

⇒ 50% of 500 × 20% of 100 ÷ ? = 50% of 2000

⇒ 250 × 20 ÷ ? = 1000

⇒ ? = 5

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

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

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

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

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

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

Given expression is

34.98% of 799.99 + 64.95% of 199.98 = ? + 49.99% of 249.99

⇒ 35% of 800 + 65% of 200 = ? + 50% of 250

⇒ 280 + 130 = ? + 125

⇒ 410 = ? + 125

∴ ? = 285

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.

Shortcut Trick

Effective CI for 2 years at 30% = 30 + 30 + (30 × 30)/100 = 69%

Effective SI for 2 years at 15% = 15 × 2 = 30%

Let investments be 200u and 500u. Interest X = 200 × 69% = 138u; Interest Y = 500 × 30% = 150u

Difference = 150u − 138u = 12u → 10800. So, 1u = 900

Investment in Scheme Y = 500 × 900 = 4,50,000

∴ The correct answer is 4,50,000.

Alternate Method

Given: Ratio of investment X : Y = 2 : 5, Time = 2 years, Rate X = 30% (CI), Rate Y = 15% (SI), Difference in Interest = Rs. 10800.

Formula Used: CI = P[(1 + r/100)^t − 1]; SI = (P × R × T) / 100

⇒ Let Investment in X = 200k and Y = 500k

⇒ Interest from X = 200k × [(1 + 30/100)² − 1] = 200k × [1.69 − 1] = 200k × 0.69 = 138k

⇒ Interest from Y = (500k × 15 × 2) / 100 = 150k

⇒ Difference = 150k − 138k = 12k

⇒ 12k = 10800

⇒ k = 900

⇒ Investment in Scheme Y = 500 × 900 = 4,50,000

∴ The correct answer is 4,50,000.

Additional Information

Effective Rate for Compound Interest

For 2 years at rate r%, the effective CI rate is given by the formula (2r + r²/100)%.

Simple Interest vs Compound Interest

Simple Interest is calculated only on the principal, while Compound Interest is calculated on the principal plus the accumulated interest of previous periods.

Difference for 2 years

For the same principal and rate, the difference between CI and SI for 2 years is P × (R/100)².

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

 Number of metallic products manufactured by company C = 240 ×  (150/100) = 360

Number of non metallic products manufactured by company C = 480 ×  (80/100) = 384

Number of products manufactured = (360 + 384) = 744

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

Number of metallic products manufactured by company D = 312

Number of non metallic products manufactured by company D = 168

(312 + x)/(168 - x) = 2/1

312 + x = 336 - 2x

3x = 24

x = 8

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

Number of metallic products made by company A = 204

Number of metallic products made by company B = 156

Total nonmetallic in all the companies = (3000 - 1200) = 1800

Required percentage = (204 + 156) = 360/1800 ×  100 = 20%

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

Number of metallic products manufactured by company A = 204

Number of defective metallic products manufactured by company A= 204/3 = 68

Number of non - metallic products manufactured by company A = 456

Number of defective non - metallic products manufactured by company A = 456/4 = 114

Number of non - defective products manufactured by company A = (204 - 68) + (456 - 114) = (136 + 342) = 478

General solution:

 

Company A:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (22/100) = 660

Number of metallic products manufactured = 1200 ×  (17/100) = 204

Number of non- metallic products manufactured = (660 - 204) = 456

Company B:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (18/100) = 540

Number of metallic products manufactured = 1200 ×  (13/100) = 156

Number of non- metallic products manufactured = (540 - 156) = 384

Company C:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (24/100) = 720

Number of metallic products manufactured = 1200 ×  (20/100) = 240

Number of non- metallic products manufactured = (720 - 240) = 480

Company D:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (16/100) = 480

Number of metallic products manufactured = 1200 ×  (26/100) = 312

Number of non- metallic products manufactured = (480 - 312) = 168

Company E:

Total number of metallic and nonmetallic products manufactured = 3000 ×  (20/100) = 600

Number of metallic products manufactured = 1200 ×  (24/100) = 288

Number of non- metallic products manufactured = (600 - 288) = 312

 

Solution:

Number of metallic products manufactured by company D = 312

NUmber of metallic products manufactured by company E = 288

Number of metallic products manufactured by company D = 168

Number of metallic products manufactured by company E = 312

Required ratio = (312 + 288): (168 + 312) = (600:480) = 5: 4

Shortcut Trick

Total Casting Votes = 80% of 25000 = 20000.

Ratio of votes (A : B : C) = 8 : 7 : 5. Total ratio units = 8 + 7 + 5 = 20 units.

Value of 1 unit = 20000 ÷ 20 = 1000 votes.

Winner is A (8 units) and Second runner-up is C (5 units).

Difference (A − C) = (8 − 5) × 1000 = 3000 votes.

∴ The correct answer is A, 3000.

Alternate Method

Given → Total Voters = 25000 | Non-voters = 20% | Ratio A:B:C = 8:7:5. Formulas: Casting Votes = Total × (100 − Non-voter%) ÷ 100 | Difference = (Ratio Diff ÷ Total Ratio) × Total Casting.

⇒ Casting Votes = 25000 − (20% of 25000) = 25000 − 5000 = 20000. ⇒ Ratio components: A = 8x, B = 7x, C = 5x. ⇒ 8x + 7x + 5x = 20x = 20000 ⇒ x = 1000. ⇒ Winner is A because he has the highest ratio (8 units). ⇒ Second runner-up is C (5 units). Note: B is the first runner-up. ⇒ Difference = A − C = 8000 − 5000 = 3000.

∴ The correct answer is A, 3000.

Additional Information

Election Terminology

Winner: The candidate with the maximum number of votes. Runner-up: The candidate with the second-highest votes. Second Runner-up: The candidate with the third-highest votes.

Ratio Distribution

To find an individual share: Share = (Individual Ratio ÷ Sum of Ratios) × Total Quantity.

Shortcut Trick

Circumference 44 cm → Radius = 7 cm (Standard circle ratio 7 : 44).

Length = 2 × 7 + 2 = 16 cm.

Breadth = Area ÷ Length = 192 ÷ 16 = 12 cm.

Side of Triangle = Breadth − 8 = 12 − 8 = 4 cm.

Perimeter = 3 × 4 = 12 cm.

∴ The correct answer is 12 cm.

Alternate Method

Given: Area of rectangle = 192 cm², Circumference of circle = 44 cm.

Formula Used: Circumference = 2πr; Area = L × B; Perimeter of Triangle = 3a.

⇒ 2 × (22/7) × r = 44

⇒ r = 7 cm

⇒ Length (L) = 2r + 2 = 2(7) + 2 = 16 cm

⇒ Breadth (B) = Area ÷ L = 192 ÷ 16 = 12 cm

⇒ Side of triangle (a) = B − 8 = 12 − 8 = 4 cm

⇒ Perimeter = 3 × a = 3 × 4 = 12 cm

∴ The correct answer is 12 cm.

Additional Information

Equilateral Triangle Properties

All sides are equal (a) and Area = (√3/4) × a². Height h = (√3/2) × a.

Circle Relations

Area = πr². For r = 7, Circumference = 44 and Area = 154.

Rectangle Perimeter

Perimeter = 2(L + B). Diagonal d = √(L² + B²).

Combining statements I and II:

Suppose quantities of milk and honey initially were 5a and 4a respectively.

According to the given statements

(4a + 9) = 45

⇒ a = 9

⇒ Quantity of milk initially = 45 litres

Quantity of honey initially = 36 litres

Now,

(45 + x) : 45 = 7 : 5

⇒ x = 18

∴ Statements I and II together are required to answer the question.

Statement I: 

Number of males in town B is 11520 which is 80% of the number of females in town A.

⇒ Number of females in town A = 11520/0.8 = 14400

There are 4880 more males in town A as compared to town B.

Number of males in town A = 11520 + 4880 = 16400

⇒ Total population of town A = 14400 + 16400 = 30800

Statement II: 

The ratio of number of males and females in town A is 41 : 36 and difference of number of males and females is 2000.

Suppose number of males and females in town A are 41x and 36x respectively.

⇒ 41x – 36x = 2000

⇒ 5x = 2000

⇒ x = 400

⇒ Total population of town A = 41x + 36x = 77x = 30800

∴ Either statement I or statement II alone is sufficient to answer the question.

Statement I:

Volume of the cuboid = lbh

Let length be 3x, breadth be 4x, height be 2x

5184 = 3x × 4x × 2x

⇒ 5184 = 24x³

⇒ 216 = x³

⇒ x = 6

Length = 18 cm, Breadth = 24 cm, Height = 12 cm

Total Surface Area of cuboid = 2 (lb + bh + hl)

⇒ 2 × (18 × 24 + 24 × 12 + 12 × 18)

⇒ 2 × (432 + 288 + 216)

⇒ 1872 cm²

Statement II:

Total surface area of the upper and lower faces of the cuboid is 864 cm²

2lb = 864

⇒ lb = 432

height (h) = 12 cm

Now,

Total Surface Area of cuboid = 2 (lb + bh + hl)

We can’t find the total surface area as we do not have the values of length and breadth.

∴ Statement I alone is sufficient to answer the question.

1) The one who likes Hiking is not the senior person but two designations senior to Tejas. Vyas is junior to Tejas.  The one who likes Hiking is two designations senior to the one who likes Archery. 

 

2) Jubal, who likes Polo is junior to the one who likes Surfing. Jubal is not at the Manager designation. The position of the person who likes Surfing cannot be fixed at this point.

 

3) The one who likes Fencing is just senior to Avyan. In Case 4, this condition cannot be satisfied which is why Case 4 is eliminated.

 

4) Kelvin is just junior to Avyan but does not like Surfing. Jubal, who likes Polo is junior to the one who likes Surfing. The one who likes Rugby is not a Manager.

These conditions are not satisfied in Case 1, Case 2, and Case 3(a) which is why Case 1, Case 2, and Case 3(a) are eliminated.

The final arrangement is:

 

Hence, The one who likes Polo (Jubal) is immediate senior to the person who likes Archery.

1) The one who likes Hiking is not the senior person but two designations senior to Tejas. Vyas is junior to Tejas.  The one who likes Hiking is two designations senior to the one who likes Archery. 

 

2) Jubal, who likes Polo is junior to the one who likes Surfing. Jubal is not at the Manager designation. The position of the person who likes Surfing cannot be fixed at this point.

 

3) The one who likes Fencing is just senior to Avyan. In Case 4, this condition cannot be satisfied which is why Case 4 is eliminated.

 

4) Kelvin is just junior to Avyan but does not like Surfing. Jubal, who likes Polo is junior to the one who likes Surfing. The one who likes Rugby is not a Manager.

These conditions are not satisfied in Case 1, Case 2, and Case 3(a) which is why Case 1, Case 2, and Case 3(a) are eliminated.

The final arrangement is:

 

Hence, Only III statement is true.

1) The one who likes Hiking is not the senior person but two designations senior to Tejas. Vyas is junior to Tejas.  The one who likes Hiking is two designations senior to the one who likes Archery. 

 

2) Jubal, who likes Polo is junior to the one who likes Surfing. Jubal is not at the Manager designation. The position of the person who likes Surfing cannot be fixed at this point.

 

3) The one who likes Fencing is just senior to Avyan. In Case 4, this condition cannot be satisfied which is why Case 4 is eliminated.

 

4) Kelvin is just junior to Avyan but does not like Surfing. Jubal, who likes Polo is junior to the one who likes Surfing. The one who likes Rugby is not a Manager.

These conditions are not satisfied in Case 1, Case 2, and Case 3(a) which is why Case 1, Case 2, and Case 3(a) are eliminated.

The final arrangement is:

 

Hence, The one who likes Archery has a Probationary Officer designation.