SBI PO Prelims Memory Based Paper (Held On: 4 November 2023 Shift 2) (Previous Year Paper)

The correct answer is: Option 5 i.e., 'Conducted'.

Key Points

• The word "ran" in this context means to perform an action or carry out a task. (काम को अंजाम देना)
• Example: He ran a quick diagnostic check on the computer system before starting his work.
• "Conducted" means to lead or direct a particular activity. (संचालित करना)
• Example: The scientist conducted an experiment to test the hypothesis.
• Hence, we can infer that "ran" in the given passage is synonymous with "conducted".

​Therefore, the correct answer is: Conducted.

Additional Information

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

• Walked (चला): Move at a regular pace by lifting and setting down each foot in turn.
• Example: She walked to the store to buy some groceries.
• Managed (प्रबंधित करना): Be in charge of an activity or work.
• Example: She managed the entire project from start to finish.
• Rushed (जल्दी करना): Move with urgent haste.
• Example: They rushed to the hospital after hearing the news.
• Operated (संचालित किया): Control the functioning of a machine, process, or system.
• Example: He operated the machinery with great skill.

The correct answer is Option 2.

 

Key Points

• The passage states that the management of plantations is essential for balancing economic viability with environmental sustainability, highlighting the overarching goal of plantation management.
• Sustainable practices are emphasized as critical not just for productivity but for maintaining the health of the ecosystem, thereby supporting the primary goal mentioned in Option 2.

Therefore, the correct answer is Option 2.

The correct answer is 'conserving'.

 

Key Points

• The word "conserving" means to protect from loss or harm; preserve. (संरक्षण)
• The context refers to using water efficiently while protecting or saving resources from being depleted.
• The other options: "expending," "depleting," "wasting," and "ignoring" do not fit the context as they imply the reduction or inefficient use of resources.

​Therefore, the correct answer is 'Option 3'.

Complete Sentence: Techniques like drip irrigation and rainwater harvesting ensure optimal water use while conserving resources.

Additional Information

• Expending (व्यय): involves spending or using up a resource.
• Depleting (कम होना): means reducing the quantity of something, especially resources.
• Wasting (बर्बाद): means to use or expend carelessly, extravagantly, or to no purpose.
• Ignoring (अनदेखा): means refusing to take notice of or acknowledge something.

The correct answer is: Option 1.

Key Points

• In the passage, the word "crucial" is used to emphasize the importance of various management strategies for the success and sustainability of plantations. The word implies something that is critical or essential to achieving a specific outcome, which aligns closely with the meaning of "vital."

Additional Information

• B) Insignificant: This term suggests something that is not important, which is the opposite of "crucial."
• C) Minor: Refers to something of lesser importance, again opposite to what "crucial" implies.
• D) Optional: Indicates that something is not mandatory, which contradicts the essential nature suggested by "crucial."
• E) Unnecessary: Implies that something is not needed, which is contrary to the indispensable quality denoted by "crucial."

The correct answer is Option 2.

 

Key Points

• According to the passage, technology plays a significant role in modern plantation management by helping to monitor plant health and manage irrigation systems more effectively.
• This technological integration allows for swift, informed decision-making, which enhances overall productivity and sustainability.

Therefore, the correct answer is Option 2.

The correct answer is 'Both A and B.'

Key Points

• Statement A: "Plantations often face challenges that require innovative strategies."
• The passage mentions, "Plantations... must navigate various challenges through innovative strategies." This indicates that the statement is true.
• Statement B: "Efficient water management is crucial for plantations, especially those in water-scarce regions."
• The passage states, "Efficient water management is also crucial, especially in regions facing water scarcity." This confirms that the statement is true.
• Statement C: "The passage states that technological advances have completely eliminated the need for traditional agricultural practices."
• The passage does not make such a claim. Instead, it emphasizes the integration of technology with traditional practices, indicating that both are necessary.

Thus, the correct answer is: Both A and B

The correct answer is Option 3.

 

Key Points

• The passage highlights that ensuring fair labor practices and adequate living conditions for workers remains a significant challenge in plantation management.
• It discusses the necessity of safeguarding workers’ rights and improving their living conditions as fundamental to fostering a productive work environment.

Therefore, the correct answer is Option 3.

**The correct answer is 5) Only B.

Key Points

• Option B is false according to the passage. It states that technology in plantations is only used to enhance worker productivity and not to manage irrigation systems. However, the passage clearly mentions that modern plantations use advanced technology to monitor plant health and manage irrigation systems.
• Options A and C are true based on the passage:
• • A is true as the passage mentions that drip irrigation and rainwater harvesting are techniques used to ensure optimal water use.
• • C is true as the passage states that plantations maintain soil health through organic practices and nutrient replenishment.

The correct answer is: Option 4.

Key Points

• The original phrase "keeps being easy" does not align with the context presented in the passage. The passage describes the ongoing difficulty of ensuring fair labor practices in remote plantation locations despite technological advances**. The correct phrase should reflect the ongoing challenges in managing labor practices effectively under these circumstances.**
• The passage underscores the complexities and challenges of managing labor practices in plantation settings, where technological advancements alone are not sufficient to address all issues. The phrase "remains a challenge" concisely and accurately reflects the ongoing efforts needed to improve labor conditions, aligning with the broader themes of sustainable management and ethical practices in the plantation industry.
• Option 4 (remains a challenge): This is the correct choice because it fits both grammatically and contextually. It properly reflects the ongoing struggle to ensure fair labor practices despite technological advances, matching the passage’s description of these efforts.

Additional Information

• Option 1 (continues to be easy): This option is grammatically correct but does not fit the context as it suggests that ensuring fair labor practices is easy, which contradicts the passage's indication of ongoing challenges.
• Option 2 (are still challenging): This choice, while contextually relevant, is grammatically incorrect due to the verb "are," which does not agree with the singular subject "ensuring."
• Option 3 (persisting as a problem): This option, although it captures the ongoing nature of the issue, is grammatically awkward and does not smoothly integrate into the sentence structure.

The correct answer is 'A-D.'

Key Points

• The given sentence talks about a wounded man who survived his painful or unpleasant experience despite what doctors described as hopeless or impossible odds.
• Let us explore the meaning of the highlighted words:
• Ordeal - A very unpleasant or difficult experience. (अत्‍यंत अप्रिय या कठिन अनुभव, अग्नि-परीक्षा)
• Wounded - Inflicted with a wound; injured. (घायल, ज़ख्‍़मी)
• Survived - To continue to live or exist, especially in spite of danger or hardship. (कठिन या संकटपूर्ण स्थिति में या उसके बाद जीवित या अस्तित्‍व में बने रहना)
• Insuperable - A difficulty or obstacle impossible to overcome. (अजेय; असमाधेय)
• Thus, (A) and (D) must be interchanged.
  

Hence, the correct answer is option 1.

Correct Sentence: Despite what doctors described as insuperable odds, the wounded man survived his ordeal.

The correct answer is 'C-B.'

Key Points

• The given sentence talks about the semi-finalist who cleared the elimination round and took the crown even though there was a strong careful examination.
• Let us explore the meaning of the highlighted words:
• Scrutiny - Critical observation or examination. (अति सावधानी से की गई जाँच; सूक्ष्‍म परीक्षण)
• Passed - To achieve the necessary standard in an exam, test, etc. (परीक्षा में पास या सफल होना)
• Intense - Very great, strong, or serious. (बहुत अधिक, उग्र या गंभीर)
• Elimination - The exclusion of someone or something from consideration or further participation. (निकाल देना)
• Thus, (C) and (B) must be interchanged.
  

Hence, the correct answer is option 3.

Correct Sentence: Even though the scrutiny was intense, the semi-finalist passed the elimination round and took the crown.

The correct answer is 'D-A.'

Key Points

• The given sentence talks about someone whose strength or energy is at an all-time low because of a recent stomach virus and he can hardly walk to the bathroom.
• Let us explore the meaning of the highlighted words:
• Barely - Only just; almost not. (मुश्किल से, कठिनाई से)
• Stamina - The ability to do something that involves a lot of physical or mental effort for a long time. (दम-ख़म, दम, ऊर्जस्विता; जीवट)
• Low - Below the usual or normal level or amount. (सामान्‍य स्‍तर या मात्रा से कम)
• Recent - Having happened, begun, or been done not long ago. (हालिया; कुछ ही देर पहले का, हाल का)
• Thus, (D) and (A) must be interchanged.
  

Hence, the correct answer is option 2.

Correct Sentence: Because of a recent stomach virus, my stamina is at an all-time low, and I can barely walk to the bathroom.

The correct answer is 'C-A.'

Key Points

• The given sentence talks about someone who is in a frightening mood due to studying intensively 100 words for his vocabulary exam, but he is firm about achieving success.
• Let us explore the meaning of the highlighted words:
• Determined - Having firmly decided to do something or to succeed, even if it is difficult. (कठिन होने के बावजूद किसी काम में सफलता प्राप्त करने का संकल्प, कृतसंकल्‍प, दृढ़निश्‍चयी)
• Formidable - Inspiring fear. (डर पैदा करने वाला)
• Cramming - To study intensively over a short period just before an examination. (रटना)
• Succeed - To manage to achieve what you want; to do well. (सफल होना; कामयाब होना)
• Thus, (C) and (A) must be interchanged.
  

Hence, the correct answer is option 3.

Correct Sentence: Cramming 100 words for my vocabulary exam puts me in a formidable mood, but I am determined to succeed.

The correct answer is ABECD.

Key Points

• A is the part that establishes the subject of the matter i.e. 'someone'. Hence, it'll be the first part after rearrangement.
• Part B talks about an offering done by that someone mentioned in A. Hence, B follows A.
• Part E talks about something good which is offered. Hence, E follows B.
• Part C talks about something which is so good that it is difficult to believe that it is true. So, C follows E.
• Part D tells us that something which is hard to believe to be true must be considered as a warning sign. Hence, D follows C.
  

Correct rearrangement of segments is: Whenever someone offers you something too good to be true, it is a warning sign.

Hint

• While solving jumbles, one must first look for any independent sentences/segments or the option which establishes the subject matter.
• Then, one must look for connections between the sentences/segments.
• Some sentences/segments might have some concluding notion. So those options will be always at the end.

The correct answer is EDBCA.

Key Points

• E is the segment that establishes the subject matter i.e ‘People' who perform yoga. Hence, it'll be the first segment after rearrangement.
• Segment D mentions the place i.e. 'world' from where the people come from. Hence, D follows E.
• In segment B, it mentions Yoga which is performed by people all over the world which was mentioned in segment D and E**.** Hence**, B** follows D.
• In segment C, it is explained the benefits of Yoga which was mentioned in segment B. Hence, C follows B.
• Segment A explained more on the benefits of Yoga which is a continuation of segment C. Hence, A follows C.
  

Correct rearrangement of segments is:  People from all over the world perform yoga to relax their minds and keep their bodies fit.

Additional Information

• Segments A, B, C are about Yoga.
• Segment B says 'perform' which means there must be a subject before it. The subject in this sentence is 'People'. So, segment E is first.
• Segment E and D are connected as it talks about the place where people perform Yoga.

The correct answer is CDEBA.

Key Points

• C is the part that establishes the subject of the matter i.e. 'Telling a person about something'. Hence, it'll be the first part after rearrangement.
• Part D talks about what a person must not tell others which is to get over cancer. Hence, D follows C.
• Part E is a continuation of part D as 'it' talks about cancer mentioned in part D. It says that  Hence, D follows B.
• Part B talks about a comparison that is made between cancer which is already made and depression in part A. Hence, B follows E and A follows B.
  

Correct rearrangement of segments is: For instance, you never tell a person with cancer to get over it and that it’s all in their head in comparison to someone dealing with depression. 

Hint

• While solving jumbles, one must first look for any independent sentences/segments or the option which establishes the subject matter.
• Then, one must look for connections between the sentences/segments.
• Some sentences/segments might have some concluding notion. So those options will be always at the end.

The correct answer is option 2.

 Key Points The correct phrase is "particularly in the realm of biofuels."

• The phrase "particular to the realm of biofuels" is grammatically incorrect because it doesn't convey the intended meaning. It suggests that the pursuit of sustainability is specific only to biofuels, which is not the intended idea.
• The correct phrase, "particularly in the realm of biofuels," accurately conveys that sustainability efforts are focused within the broader context of biofuels.

 

Thus, the correct sentence after phrase replacement would be: "In the pursuit of genuine sustainability, particularly in the realm of biofuels, it is crucial to thoroughly assess strategies within the broader ecosystem to prevent unforeseen adverse outcomes."

The correct answer is option 5.

 Key Points

• The underlined phrase "To achieve food self-sufficiency" is grammatically and contextually correct.
• The sentence is given in the present tense and it discusses the need for advanced crop varieties and hybrids that have increased yields, adaptability, and reduced resource requirements to achieve food self-sufficiency and enhance production.
• Let's understand some important vocab given in the question:
• Advanced - having been developed to a higher level; more sophisticated or improved (उन्नत)
• For Example -
• The advanced technology in the new smartphone allows for faster processing and better graphics.
• Hybrid - a plant or animal resulting from a crossbreeding or mixture of different species or varieties 
• For Example -
• This tomato plant is a hybrid of two different tomato varieties, resulting in a more disease-resistant and productive crop.
• Yield - the amount of a product or crop that is harvested or produced (पैदावार)
• For Example -
• The wheat field had a high yield this year, producing more grain than expected.
• Adaptability - the ability to adjust or change in response to different conditions or circumstances (अनुकूलनशीलता)
• For Example -
• The success of this species lies in its adaptability to a wide range of environmental conditions.

The correct answer is option 1.

Key Points 

• The correct phrase is "with elders often occupying it."
• The phrase "with elders often occupied it" is grammatically incorrect because it uses the past tense "occupied" when it should use the present participle "occupying" to match the present tense implied by the word "often."
• Thus, the correct sentence after phrase replacement would be: "In the past, our homes remained unlocked, trust in neighbours prevailed, and the sit-out served as a bustling hub for family needs, with elders often occupying it."

The correct answer is "Is set to bear away".

Key Points

• In the underlined segment, the phrasal verb 'bear down​' is incorrect.
• The phrasal verb 'bear down' means to push or press downwards.
• Example: The enemy warship tried to bear down on our small airboat.
• The phrasal verb 'bear up' means to remain cheerful in the face of adversity.
• Example: It's not easy to bear up under such circumstances.
• The phrasal verb 'bear out' means to show that someone is right or that something is true.
• Example: Close examination fails to bear out the argument.
• The phrasal verb 'bear with' means to be patient with someone or something.
• Example: If you will bear with me a little longer, I'll answer your question.
• The phrasal verb 'bear away' which means to carry off in victory would be suitable in this context.
• Example: The colonel gave the soldiers permission to bear away the spoils after winning the battle!
• The underlined part hence must be replaced with ''is set to bear away'' to make it a grammatically correct sentence.
  

Hence, the correct answer is option 4.

Correct Sentence: The Indian football team is set to bear away the Asian Cup trophy for the first time.

The correct answer is 'Have pulled down.'

Key Points

• In the underlined segment, the phrasal verb ''pulled out'' is incorrect.
• The given sentence talks about so many demolished buildings.
• The phrasal verb ''pulled out'' means (of a vehicle) move out from the side of the road, or from its normal position in order to overtake. (कार आदि का) सड़क के किनारे से आगे बढ़ जाना)
• The phrasal verb ''pulled down'' means demolish a building. (एक इमारत को ध्वस्त करना)
• Therefore, the phrasal verb ''pulled down'' should be used in place of the phrasal verb ''pulled out''.
  

Hence, the correct answer is option 4.

Correct Sentence: They have pulled down so many buildings around here it looks like a bomb site.

Additional Information

• The phrasal verb ''pulled up'' means (to cause a car, etc.) to stop. (कार आदि को रोक देना)
• The phrasal verb ''pulled over'' means (used about a vehicle or its driver) to slow down and move to the side of the road. (कार या उसके चालक का) गति मंद करते हुए सड़क के किनारे हो जाना

The correct answer is radical.

Key Points

The sentence suggests that there is has been an intrinsic change in doing business.

The word ‘radical’ means ‘affecting the fundamental nature of thing’ and hence, is the correct fit.

Additional Information

• Unusual means not habitually or commonly occurring or done.
• Exception means a person or a thing excluded from general consensus and non considered normal.
• Affluent means wealthy; rich

The correct answer is outlets.

Key Points

The sentence suggests how individual owners use their channels to target a specific audience.

The word ‘outlets’ mean ‘pipes or canals through which water can escape or a channel’ and hence, is the correct fit.

Key Points

• Edifice means a large and imposing building
• Sanatorium means an institution for the treatment of people having chronic illnesses.
• Inlet means a vent for the inward flow of a particular thing, especially water.

The correct answer is dispense.

Key Points

The sentence suggests that how the different owners invest money in a complex system.

The word ‘Dispense’ means ‘to spend or distribute’ and hence, is the correct fit.

Additional Information

• Exhume means to dig up something buried under the earth.
• Forsake means abandon or leave
• Islet means a small island
• Onset means the beginning of something

The correct answer is  perils.

Key Points

The sentence suggests that there are certain threats to the current system.

The word ‘Perils’ mean ‘dangers’ and hence, is the correct fit.

Additional Information

• Impel means drive, force or urge someone to do something.
• Foreboding means a feeling that something bad will happen.
• Elucidations mean explanations which make something clear or easy to understand.
• Console means comfort someone at the time of grief or pain.

The correct answer is stark.

Key Points

The sentence suggests that there has noticeable relief from previous dangers.

The word ‘stark’ means ‘complete or sheer’ and hence, is the correct fit.

Additional Information

• Exquisite means extremely beautiful and delicate
• Rustic means belonging to or related to a village/countryside; rural
• Rubicund means having a ruddy facial complexion
• Prominent means important or famous

The correct answer is option (1).

Key Points

• Option 1-Mr Singh's son has applied to the post of supervisor in a construction company. Here in the place of "to" we will use "for" as for is always used with a noun and to is always used with a verb, so it is having an error.

• Option 2-As compared to many developing countries, India and Bangladesh have a large number of educated workers. Here "as" preposition is used,  we use as with a noun to refer to the role or purpose of a person or thing hence grammatically correct. 

• **Option 3-**In his opinion, every senior citizen will benefit from the taxation policy of the new government. Here "of" is used which usually shows a connection or belonging hence grammatically correct.

• **Option 4-**Over fifty per cent of people in the country may not be part of financial inclusion. Here "of" is used which usually shows a connection or belonging hence grammatically correct.

• **Option 5-**All are correct is not the right option.

Option (1) is the correct answer.

The correct answer is option 1.

Key Points

To answer this question, let's break down each sentence to identify the grammatically and contextually correct ones:

• 1. In recent years Government has failed to reignite the economy partly because of economic slowdown and partly due to failure of failure to raise the tax revenue.
• This sentence contains a grammatical error due to the unnecessary repetition of the phrase "failure of".
• The sentence is erroneous.
• The correct sentence would be: "In recent years, the Government has failed to reignite the economy partly because of the economic slowdown and partly due to the failure to raise tax revenue."
• 2. India is more reliant on Indirect Taxes instead of direct taxes compared to its peers.
• This sentence is grammatically acceptable.
• Although "more reliant on... than" is stylistically better than "instead of", the sentence does not contain a grammatical error.
• 3. Direct taxes are taxed on income so they hurt the poor less and are more progressive.
• This sentence is grammatically correct.
• It correctly conveys that direct taxes are imposed on income and are generally considered more progressive.
• 4. GST was meant to be one good structural reform but even that has been plagued by implementation issues.
• This sentence is grammatically and contextually correct.
• Only sentence 1 contains a grammatical error, while sentences 2, 3, and 4 are grammatically correct.
• Therefore, the correct answer is Option 1.

• Option 1-History is full of examples of successful personalities who displayed their gut feeling in the time of crisis. This sentence is correct as "who" is used to ask questions and introduce relative clauses.
• Option 2-I must speak to the boss regarding the juniors as these days they are making much noise about tea supply in the office. This sentence is also grammatically correct for juniors "they" pronoun is used in the second part of the sentence.
• Option 3-When the bomb went off, the impact was powerful enough to break all of our windows and ceilings. This sentence is correct as "when" is used to mean at that time and the consequences are discussed in the next part.
• Option 4- The teacher asked, "why you are late for the lecture?". Here the answer will be, "why are you late for the lecture". After why the auxiliary verb is used and why is used for asking questions hence it has the error.
• Option 5-All are correct is not correct

Option (4) is the correct answer.

Explanation:

• Option 1- V1 form of verb is used shows the sentence is in simple present tense which is wrong as the sentence should be in simple past tense so we will use V2 form of the verb.
• Option 2- Data from budget document shows that the total amount under tax dispute has more than quadrupled from 11% to 46% from FY 08 to FY 19. As this sentence is in simple present tense so correct form of verb show with s is used.
• Option 3- And within this, the bulk of the disputes centre around personal income and corporate income-tax issues. This sentence is also in simple present tense so the verb dispute is used with s.
• Option 4-For addressing this issue,the government has announced a new amnesty scheme Vivad se Vishwas, seeking to dispose of nearly 5 lakh disputed cases.Here present perfect tense is used so the verb is used in third form.
• Option 5-All are correct is not correct.

 

Correct Sentence: "Earlier this month,In his speech PM Modi claimed that only 15 million Indians paid income tax. 

Since Option (1) has error so this is the correct option.

Calculation∶

The series follows following pattern

3 - 14 = -11

-11 + 28 = 17

17 - 56 = -39

-39 + 112 = 73

73 - 224 = -151

∴ The value of ? is -151

GIVEN:

?, 4000, 3500, 3250, 3125, 3062.5

Calculation:

The series follows the following pattern:

⇒ ? - 1000/1 = 4000

⇒ 4000 - 1000/2 = 3500

⇒ 3500 - 1000/4 = 3250

⇒ 3250 - 1000/8 = 3125

⇒ 3125 - 1000/16 = 3062.5

Value of ?:

⇒ ? - 1000/1 = 4000

⇒ ? = 4000 + 1000

⇒ ? = 5000

∴ The required value of "?" is 5000.

 

∴ The required value of "?" is 5000.

Given:

Series is 2, 5, 11, 23, 44, 77, ?

Calculation:

Pattern of the given series can be explained as,

∴ 125 will come in the place of "?"

The correct answer is: 5

Given:

 110, 121, 143, 176, ? , 275, 341

Calculation:

The given series follows the following pattern:

 ⇒ 121 - 110 = 11

 ⇒ 143 - 121 = 22

 ⇒ 176 - 143 = 33

 ⇒ 220 - 176  = 44

 ⇒ 275 - 220 = 55

 ⇒ 341 - 275 = 66

 Hence, 220 will come in place of '?'.

Calculation:

The pattern of the given series is:

⇒ 111.5 - (1 × 6.5) = 105

⇒ 105 + (2 × 6.5) = 118

⇒ 118 - (1 × 6.5) = 111.5

⇒ 111.5 + (2 × 6.5) = 124.5

⇒ 124.5 - (1 × 6.5) = ? = 118

∴ the missing number in the series is 118.

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying arts in college A and B = (192 + 168) = 360

Total number of students studying science in all the colleges = (2000 - 1200) = 800

Required percentage = 360/800 ×  100 = 45%.

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying arts in college D = 336

Number of students studying arts in college E = 264

Number of students studying arts in college F = (336 + 264)/2 = 300 + 20

Number of students studying science in college D = 114

Number of students studying science in college E = 236

Number of students studying science in college F = (350)/2 = 175 + 25

Required ratio = (320 : 200) = 8: 5

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying arts in college B = 168

If 25% of students studying arts in college B is increased = 168 ×  (125/100) = 210

If y numbers of students studying in college B studying science stream is increased by y = (110 + y)

Then the ratio becomes 7: 4.

To find the value of y

210/(110 + y) = 7/4

840 = 770 + 7y

70 = 7y

y = 10

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying arts from college C = 240

Number of students studying arts from college C attending seminar = 240 ×  (75/100) = 180

Number of students studying arts from college C does not attend seminar = (240 - 180) = 60

Number of students studying science from college C attending seminar = 110 × 4/11 = 40

Number of students studying Science from college C does not attend seminar = (110 - 40) = 70

Required sum = (60 + 70) = 130

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying Arts in college A = 192

Number of boys  studying arts in college A = 192/3 = 64

Number of boys studying arts in college A having two wheelers = 64 ×  (25/100) = 16

Number of students studying science in college A = 208 

Number of boys studying science in college A = 208 ×  3/8 = 78

Number of boys studying science in college A having two wheelers = 78 ×  (50/100) = 39

Required sum = (39 + 16) = 55

Shortcut Trick

Breadth of rectangle = 750 ÷ 30 = 25 m.

Perimeter of rectangle = 2 × (30 + 25) = 110 m.

Ratio 11 units = 110 m ⇒ 1 unit = 10 m.

Perimeter of square = 8 units = 8 × 10 = 80 m.

Fencing cost = 80 × 20 = ₹1600.

∴ The correct answer is ₹1600.

Alternate Method

Given: Length (L) = 30 m, Area = 750 m², Rate = ₹20/m, Ratio P_s:P_r = 8:11

Formula: Area = L × B | Perimeter = 2(L + B)

⇒ Breadth of rectangle (B) = Area ÷ L = 750 ÷ 30 = 25 m

⇒ Perimeter of rectangle (P_r) = 2(30 + 25) = 2 × 55 = 110 m

⇒ According to ratio, 11 units = 110 m

⇒ 1 unit = 10 m

⇒ Perimeter of square (P_s) = 8 units = 8 × 10 = 80 m

⇒ Total Cost of fencing = Perimeter × Rate = 80 × 20 = ₹1600

∴ The correct answer is ₹1600.

Additional Information

Square Properties

Perimeter = 4 × side, Area = side². The diagonal of a square is side × √2.

Rectangle Properties

Perimeter = 2(length + breadth), Area = length × breadth. Diagonal = √(L² + B²).

Fencing Cost

Fencing is always done along the boundary, so total cost = Perimeter × Rate per unit length.

Shortcut Trick

Total distance (Train + Platform) = 180 + 1.25 × 180 = 180 + 225 = 405 m

Initial speed = 405 ÷ 32.4 = 12.5 m/s

New speed = 12.5 × (4/3) = 50/3 m/s (since 33.33% increase → 4/3 factor)

New distance (Train + Tunnel) = 180 + 200 = 380 m

Required time = 380 ÷ (50/3) = (380 × 3) ÷ 50 = 22.8 seconds

∴ The correct answer is 22.8 sec.

Alternate Method

Given:

Length of Train (L₁) = 180 m

Length of Platform (L₂) = 180 + 25% of 180 = 180 + 45 = 225 m

Length of Tunnel (L₃) = 200 m

Formula Used:

Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance₁ = L₁ + L₂ = 180 + 225 = 405 m

⇒ Initial Speed (S₁) = 405 ÷ 32.4 = 12.5 m/s

⇒ New Speed (S₂) = 12.5 + (33.33% of 12.5) = 12.5 + (1/3 × 12.5) = 12.5 × (4/3) = 50/3 m/s

⇒ Total Distance₂ = L₁ + L₃ = 180 + 200 = 380 m

⇒ Required Time = 380 ÷ (50/3) = (380 × 3) ÷ 50

⇒ Required Time = 1140 ÷ 50 = 22.8 seconds

∴ The correct answer is 22.8 sec.

Additional Information

Train Crossing Stationary Object with Length

When a train crosses a platform, bridge, or tunnel, the total distance covered is the sum of the length of the train and the object.

Fractional Equivalent of Percentages

Memorizing 33.33% = 1/3 and 25% = 1/4 helps in faster calculation. An increase of 33.33% means multiplying by (1 + 1/3) = 4/3.

Unit Conversion

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

Given:

(27.02)% of 300.08 + 19% of 120 + 29.8% of 500

Concept:

We have to follow the BODMAS rule

Calculation:

Taking the approximate values

27% of 300 + 19% of 120 + 30% of 500 = ?

⇒ 81 + 22.8 + 150 = ?

⇒ 253.8 = ?

⇒ ? ≈ 254

∴ The value of ? is 254.

Given:

(43.12 × 6 ÷ 2 – 63) – {6.2 of 8 + 48.89 – (11)² + 25}

Concept used:

We have to follow the BODMAS rule

Calculation:

Taking the approximate values

(43 × 6 ÷ 2 – 63) – {6 of 8 + 49 – (11)² + 25} = ?

⇒ (43 × 3 – 63) – {48 + 49 – 121 + 25} = ?

⇒ (129 – 63) – {122 – 121} = ?

⇒ 66 – 1 = 65

⇒ ? = 65

∴ The value of ? is 65.

Given:

{(86.01)² + (120.03)² + (150.02) × 143}/300

Concept used:

We have to follow the BODMAS rule

Calculation:

Taking approximate values

{(86)² + (120)² + 150 × 143}/300

⇒ {7396 + 14400 + 21450}/300

⇒ 43246/300 = 144.15 ≈ 144

∴ The value of ? is 144.

Concept:

Calculation:

Giving expression is,

38.73 × 15.11 - 27.88 × 10.23 = ( 20 + ?) × 2 + 11.1 - 9.8

Taking approximate values as,

⇒ 39 × 15 - 28 × 10 = (20 + ?) × 2 + 11 - 10

⇒ 585 - 280 = 40 + 2? + 1

⇒ 305 = 41 + 2?

⇒ 264 = 2?

⇒ ? = 132

∴ Correct answer is 132

Given:

12.12 – 8.11 + 2.99 × (14.28%) of 1190.1 ÷ 16.99 = ?

Concept used:

We have to follow the BODMAS rule

Calculation:

Taking approximate values

12.12 – 8.11 + 2.99 × (14.28%) of 1190.1 ÷ 16.99 = ?

⇒ 12 – 8 + 3 × (1/7) of 1190 ÷ 17 = ?

⇒ 12 – 8 + 3 × (1/7) of 1190 ÷ 17 = ?

⇒ 12 – 8 + 3 × 170 ÷ 17 = ?

⇒ 12 – 8 + 3 × 10 = ?

⇒ ? = 34

∴ The value of ? is 34.

Shortcut Trick

Net discount = 25 + 20 − (25 × 20) ÷ 100 = 40%.

SP = MP × (100 − 40) ÷ 100 = 0.6 MP.

Since loss is 10%, SP = 0.9 CP ⇒ 0.6 MP = 0.9 CP ⇒ MP = 1.5 CP.

Given MP − CP = 900 ⇒ 0.5 CP = 900 ⇒ CP = 1800, MP = 2700.

To get Profit 360, new SP = 1800 + 360 = 2160. New MP × 0.6 = 2160 ⇒ New MP = 3600.

Increase in MP = (3600 − 2700) ÷ 2700 × 100 = 100 ÷ 3%.

∴ The correct answer is (100/3)%.

Alternate Method

Formulas: SP = CP × (100 − L%) ÷ 100 | MP = SP ÷ (1 − Total Discount) | Profit = SP − CP

⇒ Let Cost Price (CP) be x. Marked Price (MP) = x + 900. ⇒ Successive discounts of 25% and 20% ⇒ Single discount = 25 + 20 − (25 × 20)/100 = 40%. ⇒ Selling Price (SP) = (x + 900) × 0.6. ⇒ Loss of 10% means SP = 0.9x. ⇒ Equating SP: 0.6(x + 900) = 0.9x ⇒ 0.6x + 540 = 0.9x ⇒ 0.3x = 540 ⇒ x = 1800. ⇒ Initial MP = 1800 + 900 = 2700. ⇒ To earn Profit of Rs. 360, new SP = 1800 + 360 = 2160. ⇒ New MP = 2160 ÷ 0.6 = 3600. ⇒ % increase in MP = [(3600 − 2700) ÷ 2700] × 100 = (900 ÷ 2700) × 100 = 100/3 %.

∴ The correct answer is (100/3)%.

Additional Information

Successive Discounts

When two discounts a% and b% are given, the equivalent single discount is (a + b − ab/100)%.

Marked Price and Selling Price

SP is the price after applying the discount on MP. SP = MP × (100 − D%)/100.

Shortcut Trick

Apply Alligation: Boys (38) and Girls (39) with Mixture Average (38.49).

Ratio of Boys to Girls = (39 − 38.49) : (38.49 − 38) = 0.51 : 0.49 = 51 : 49.

Difference in ratio parts = 51 − 49 = 2 units. Given difference (x − (x − 2)) = 2 students.

Total students = (51 + 49) units = 100 students.

∴ The correct answer is 100 students.

Alternate Method

Given: Boys = x, Girls = x − 2, Avg Boys = 38, Avg Girls = 39, Avg Class = 38.49.

Formula: Total Score = Average × Number of Students

⇒ 38x + 39(x − 2) = 38.49(x + x − 2)

⇒ 38x + 39x − 78 = 38.49(2x − 2)

⇒ 77x − 78 = 76.98x − 76.98

⇒ 77x − 76.98x = 78 − 76.98

⇒ 0.02x = 1.02

⇒ x = 102 ÷ 2 = 51

⇒ Total Students = x + (x − 2) = 51 + 49 = 100

∴ The correct answer is 100 students.

Additional Information

Alligation Rule

Quantity₁ : Quantity₂ = (Value₂ − Mean) : (Mean − Value₁). It is the fastest way to find ratios in mixtures.

Weighted Average

The average of a whole group is calculated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Deviation Method

Total sum of deviations from the mean is always zero. This can be used to find missing values in a dataset.

Shortcut Trick

Let Son's age = 100 units → Man's age = 250 units → Ratio Man : Son = 5 : 2.

Total age = 30 × 3 = 90 years.

Substitute options: Check for ratio 5 : 2 (or 20 : 8) between Man and Son.

Only Option (1) 20 : 17 : 8 satisfies Man : Son = 20 : 8 = 5 : 2 and total sum 20+17+8=45 units, where 45 units = 90 years.

∴ The correct answer is 20 : 17 : 8.

Alternate Method

Given: Average age = 30, Man = 250% of Son, Wife = Man − 6.

Formula: Total Age = Average × Number of members

⇒ Let Son's age = x

⇒ Man's age = 2.5x

⇒ Wife's age = 2.5x − 6

⇒ Total Age = x + 2.5x + (2.5x − 6) = 30 × 3

⇒ 6x − 6 = 90

⇒ 6x = 96 → x = 16

⇒ Son = 16, Man = 2.5 × 16 = 40, Wife = 40 − 6 = 34

⇒ Ratio = 40 : 34 : 16 = 20 : 17 : 8

∴ The correct answer is 20 : 17 : 8.

Additional Information

Average Age Concept

The sum of ages of n members is Average × n. If each person's age increases by k years, the average also increases by k.

Ratio and Proportion

To find the ratio of three quantities A:B:C, ensure all values are in the same unit and simplify by dividing by their HCF.

Percentage to Ratio Conversion

250% can be written as 250/100 or 5/2. Thus, if the base is 2 parts, the resultant is 5 parts.

General solution:

Number of persons who participated in only swimming and only fencing are in the ratio 4x: 3x

Number of persons who participated in only skating is 2 less than the number of persons who participated in only fencing = (3x - 2)

Number of persons who participated in all the three = 5

Number of persons who participated in both swimming and fencing but not skating =  (5 + 5) = 10

Number of persons who participated in both fencing and swimming but not skating and the number of persons who participated in swimming and skating but not fencing are in the ratio 2 : 3

Number of persons who participated in swimming and skating but not fencing = 10/2 ×  3 = 15

Number of person who participated in both fencing and skating but not swimming is 80% of the number of persons who participated in swimming and skating but not fencing.

Number of person who participated in both fencing and skating but not swimming  =15 ×  (80/100) = 12

Total number of persons who participated in only swimming , only fencing and only skating is 98.

(4x + 3x + 3x - 2) = 98

10x = 100

x = 10

Number of persons who likes swimming only = 40

Number of persons who likes fencing only = 30

Number of persons who likes skating = (30 - 2) = 28

Solution:

Number of males to females who participated only skating = 28

Number of males participated  only skating = 28/7 × 4 = 16

Number of females participated only in skating = (28 - 16) = 12

Number of females participated only swimming = 22 - 12 = 10

Number of males participated only swimming = (40 - 10) = 30

Required difference = (30 - 16) = 14

General solution:

Number of persons who participated in only swimming and only fencing are in the ratio 4x: 3x

Number of persons who participated in only skating is 2 less than the number of persons who participated in only fencing = (3x - 2)

Number of persons who participated in all the three = 5

Number of persons who participated in both swimming and fencing but not skating =  (5 + 5) = 10

Number of persons who participated in both fencing and swimming but not skating and the number of persons who participated in swimming and skating but not fencing are in the ratio 2 : 3

Number of persons who participated in swimming and skating but not fencing = 10/2 ×  3 = 15

Number of person who participated in both fencing and skating but not swimming is 80% of the number of persons who participated in swimming and skating but not fencing.

Number of person who participated in both fencing and skating but not swimming  =15 ×  (80/100) = 12

Total number of persons who participated in only swimming , only fencing and only skating is 98.

(4x + 3x + 3x - 2) = 98

10x = 100

x = 10

Number of persons who likes swimming only = 40

Number of persons who likes fencing only = 30

Number of persons who likes skating = (30 - 2) = 28

Solution:

Number of persons who participated in skating and fencing but not swimming = 12

Number of persons who participated in only swimming = 40

Required percentage = 12/40 ×  100 = 30%

General solution:

Number of persons who participated in only swimming and only fencing are in the ratio 4x: 3x

Number of persons who participated in only skating is 2 less than the number of persons who participated in only fencing = (3x - 2)

Number of persons who participated in all the three = 5

Number of persons who participated in both swimming and fencing but not skating =  (5 + 5) = 10

Number of persons who participated in both fencing and swimming but not skating and the number of persons who participated in swimming and skating but not fencing are in the ratio 2 : 3

Number of persons who participated in swimming and skating but not fencing = 10/2 ×  3 = 15

Number of person who participated in both fencing and skating but not swimming is 80% of the number of persons who participated in swimming and skating but not fencing.

Number of person who participated in both fencing and skating but not swimming  =15 ×  (80/100) = 12

Total number of persons who participated in only swimming , only fencing and only skating is 98.

(4x + 3x + 3x - 2) = 98

10x = 100

x = 10

Number of persons who likes swimming only = 40

Number of persons who likes fencing only = 30

Number of persons who likes skating = (30 - 2) = 28

Solution:

Number of persons who participated in swimming = (40 + 15 + 5+ 10) = 70

Number of persons who participated in fencing = (30 + 10 + 5 + 12) = 57

Required difference  = (70 - 57) = 13

Shortcut Trick

Let Total Income be 100%.

Planned Donation = 25% of Income.

Actual Donation = 85% of 25% = 21.25% of Income.

21.25% → ₹4250

100% → (4250 ÷ 21.25) × 100 = 200 × 100 = ₹20,000.

∴ The correct answer is ₹20,000.

Alternate Method

Given:

Actual donation = ₹4250

Actual donation = 85% of Planned donation

Planned donation = 25% of Monthly Income

Calculations:

⇒ 85% of Planned donation = ₹4250

⇒ Planned donation = (4250 × 100) ÷ 85

⇒ Planned donation = 50 × 100 = ₹5000

⇒ Now, 25% of Monthly Income = ₹5000

⇒ Monthly Income = (5000 × 100) ÷ 25

⇒ Monthly Income = ₹20,000

∴ The correct answer is ₹20,000.

Additional Information

Percentage Change

To find the original value from a percentage part, use: Original = (Given Value ÷ Percentage) × 100.

Successive Percentages

If a value is changed by a% and then b%, the effective percentage of the original is (a × b) ÷ 100.

Income and Savings

Total Income is always treated as the base (100%) when calculating components like expenditure, savings, or donations.

Shortcut Trick

In the final mixture, the milk and water ratio is 5 : 3.

Total volume remains constant at 280 liters because x liters are removed and x liters are added.

Total units in final mixture = 5 + 3 = 8 units.

8 units = 280 liters ⇒ 1 unit = 35 liters.

Water in final mixture = 3 units = 3 × 35 liters = 105 liters.

∴ The correct answer is 105 liters.

Alternate Method

Given: Initial volume = 280 liters, Initial Ratio (M:W) = 5:2, Final Ratio (M:W) = 5:3.

Formula: Ratio × constant = Actual Value.

⇒ When x liters of mixture is removed, the ratio of milk and water remains 5:2.

⇒ When x liters of water is added, the ratio becomes 5:3.

⇒ Since only water is added, the milk quantity stays constant (5 units in both cases).

⇒ Total volume of final mixture = Initial volume = 280 liters.

⇒ Final ratio sum = 5 + 3 = 8 units.

⇒ 8 units = 280 liters.

⇒ 1 unit = 280 ÷ 8 = 35 liters.

⇒ Water in final mixture = 3 units = 3 × 35 = 105 liters.

∴ The correct answer is 105 liters.

Additional Information

Mixture Removal Property

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

Replacement Concept

If x liters are removed and x liters of a single component are added, the total volume of the mixture remains unchanged.

Ratio Balancing

To solve replacement problems, keep the component that was not added constant in the ratio calculations.

Shortcut Trick

Total interest % in first case = 10% × 7 = 70% of x.

Total interest % in second case = 15% × 8 = 120% of (x + 10,100).

Difference: 120% of (x + 10,100) − 70% of x = 34,620.

⇒ 1.2x + 12,120 − 0.7x = 34,620 ⇒ 0.5x = 22,500.

⇒ x = 45,000.

∴ The correct answer is ₹45,000.

Alternate Method

Given: Rate₁ = 10%, Time₁ = 7 yrs, Principal₁ = x. Rate₂ = 15%, Time₂ = 8 yrs, Principal₂ = x + 10,100.

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

⇒ SI₁ = (x × 10 × 7) ÷ 100 = 0.7x

⇒ SI₂ = [(x + 10,100) × 15 × 8] ÷ 100 = 1.2 × (x + 10,100)

⇒ SI₂ − SI₁ = 34,620

⇒ 1.2x + 12,120 − 0.7x = 34,620

⇒ 0.5x = 34,620 − 12,120

⇒ 0.5x = 22,500

⇒ x = 22,500 ÷ 0.5 = 45,000

∴ The correct answer is ₹45,000.

Additional Information

Simple Interest Concept

Simple interest is calculated only on the principal amount. SI = P×R×T/100, where P is Principal, R is Rate per annum, and T is Time in years.

Amount Calculation

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

Effective Rate of Interest

For simple interest, the effective rate for the entire duration is simply (R × T)%. This allows for direct percentage-based comparisons between different investment scenarios.

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000 (approx)

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Number of trousers sold in shop D = 1000

Number of trousers sold in shop E = 480

Total shirts sold in all the shops A, B, C, D and E = (720 + 600 + 250 + 400 + 1120) = 3090

Required percentage = (1480)/3090 ×  100 = 47.89% ~ 48%

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Number of cotton trousers sold in shop C =  1000 ×  (20/100) = 200

Number of cotton trousers sold in shop D =  1000 ×  (30/100) = 300

Number of fabric shirts sold in the shop C = 250 ×  (60/100) = 150

Number of fabric shirts sold in the shop D = 400 ×  (70/100) = 280

Required sum = (200 + 300 + 150 + 280) = 930

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Number of trousers sold in shop D = 1000

Number of trousers sold in shop E = 480

Number of trouser sold after 20% increase in shop D = 1000 ×  120/100 = 1200

Number of trouser sold after 25% increase in shop E = 480 ×  125/100 = 600

Number of shirts sold in shop D = 400

Number of shirts sold in shop E = 1120

Number of trouser sold after 50% increase in shop D = 400 ×  (150/100) = 600

Number of trouser sold after 25% increase in shop E = 1120 ×  (125/100) = 1400

Required ratio = (1200 + 600): (600 + 1400) = 1800: 2000 = 9: 10

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Total number of trousers sold in shop B = 900

Total number of shirts sold in shop B = 600

a/100 ×  900 ×  120 + 2a/100 ×  600 ×  180 = 97200

1080a + 2160a = 97200

97200/3240 = a

a = 30

General solution:

 

Total number of trousers and shirts sold in all the shops = 6950

(1200 + 50x + 40x + 50 + (2x + 10)/100 ×  2000 + 1600) = 6950

(1200 + 200 + 50 + 1600 + 130x ) = 6950

130x = 3900

x = 30

 

Shop A:

Total number of shirts and trousers sold = 1200

Number of trousers sold = 1200 ×  (70 - 30)/100 = 480

Number of shirts sold = (1200 - 480) = 720

 

Shop B:

Total number of shirts and trousers sold = 50 ×  30 = 1500

Number of trousers sold = 1500 ×  (30 + 30)/100 = 900

Number of shirts sold = (1500 - 900) = 600

 

Shop C:

Total number of shirts and trousers sold = (40 ×  30 + 50) = 1250

Number of trousers sold = 1250 ×  (2 ×  30 + 20)/100 = 1000

Number of shirts sold = (1250 - 1000) = 250

 

Shop D:

Total number of shirts and trousers sold = (2x + 10)% of 2000 = (2 ×  30 + 10) % of 2000 = 1400

Number of trousers sold = 1400 ×  (71.42/100) = 1000

Number of shirts sold = (1400 - 1000) = 400

 

Shop E:

Total number of shirts and trousers sold = 1600

Number of trousers sold = 1600 ×  30/100 = 480

Number of shirts sold = (1600 - 480) = 1120

 

 

Solution:

Number of trousers sold in shop A = 480

Number of trousers sold in shop A at discount = 480/3 = 160

Number of trousers sold in shop A at marked price = (480 - 160) = 320

Number of branded trousers sold at marked price in shop A = 320/8 = 40

Number of shirts sold in shop A = 720

Number of shirts sold in shop A at discount = 720/4 = 180

Number of shirts sold in shop A at marked price = (720 - 180) = 540

Number of branded shirts sold at marked price in shop A = 540/3 = 180

Required total = (40 + 180) = 220

Shortcut Trick

For 2 years, Simple Interest (SI) = 2x% and Compound Interest (CI) = 2r + r²/100 where r = (x − 2).

Equating interest rates: 2x = 2(x − 2) + (x − 2)²/100 ⇒ 4 = (x − 2)²/100.

√400 = x − 2 ⇒ 20 = x − 2 ⇒ x = 22.

New rate = x − 7 = 15%. SI for 5 years = 15% × 5 = 75%.

Amount = Principal × (100 + 75)% = 3000 × 1.75 = ₹ 5250.

∴ The correct answer is ₹ 5250.

Alternate Method

Given: Principal (P) for both cases is same. Time (T) = 2 years. SI rate = x%. CI rate = (x − 2)%.

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

⇒ Interest from SI = (P × x × 2) / 100 = 2Px / 100

⇒ Interest from CI = P[(1 + (x − 2)/100)² − 1]

⇒ 2x/100 = [1 + (x − 2)/100]² − 1

⇒ 2x/100 + 1 = 1 + 2(x − 2)/100 + ((x − 2)/100)²

⇒ 2x/100 = 2x/100 − 4/100 + (x − 2)²/10000

⇒ 4/100 = (x − 2)² / 10000 ⇒ (x − 2)² = 400

⇒ x − 2 = 20 ⇒ x = 22

⇒ New principal = ₹ 3000, New rate = 22 − 7 = 15%, Time = 5 years

⇒ SI = (3000 × 15 × 5) / 100 = ₹ 2250

⇒ Amount = 3000 + 2250 = ₹ 5250

∴ The correct answer is ₹ 5250.

Additional Information

Effective rate of Compound Interest

For 2 years, the effective CI rate is given by the formula R_eff = 2R + R²/100 %.

Simple Interest Amount

The final amount under SI is A = P(1 + RT/100), where R is the annual rate and T is time in years.

Difference between CI and SI

For a period of 2 years at the same rate R, the difference is CI − SI = P(R/100)².

Shortcut Trick

Profit Ratio = (Capital × Time) ratio.

Ratio of P : Q : R Capitals = 16000 : 20000 : 24000 = 4 : 5 : 6.

Ratio of Time = 12 : (12 − x) : (12 − x).

Profit Ratio = (4 × 12) : 5(12 − x) : 6(12 − x) = 48 : 5(12 − x) : 6(12 − x).

Given Profit Ratio = 48 : 35 : 42.

Comparing Q's share: 5(12 − x) = 35 ⇒ 12 − x = 7 ⇒ x = 5.

∴ The correct answer is 5.

Alternate Method

Given: P's investment = Rs. 16,000 for 12 months; Q's investment = Rs. 20,000 for (12 − x) months; R's investment = Rs. 24,000 for (12 − x) months. Formula: Profit Share = Investment × Time Period

⇒ Profit of P = 16,000 × 12 = 192,000. ⇒ Profit of Q = 20,000 × (12 − x). ⇒ Ratio P : Q = 192,000 : 20,000(12 − x) = 48 : 35. ⇒ 192,000 / [20,000(12 − x)] = 48 / 35. ⇒ 192 / [20(12 − x)] = 48 / 35. ⇒ 4 / (12 − x) = 4 / 7 (after dividing 192 by 48). ⇒ 12 − x = 7. ⇒ x = 12 − 7 = 5.

∴ The correct answer is 5.

Additional Information

Partnership Basics

In a partnership, the profit is distributed in the ratio of the product of Investment and Time Period.

Ratio Conversion

If Profit Ratio and Investment Ratio are given, Time Ratio = (Profit Ratio ÷ Investment Ratio).

Shortcut Trick

Speed of Steamer (u) = 24 km ÷ (50/60) h = 28.8 km/h.

Using Difference in Time formula: [D × (2v)] ÷ (u² − v²) = ΔT.

[22.5 × 2v] ÷ (28.8² − v²) = 25/60.

By testing Option (2): v = 7.2 km/h ⇒ (45 × 7.2) ÷ (829.44 − 51.84) = 324 ÷ 777.6 = 5/12 h = 25 minutes.

∴ The correct answer is 7.2 km/h.

Alternate Method

Given:

Distance (D) = 22.5 km

Speed of steamer in still water (u) = 24 ÷ (50/60) = 24 × 6/5 = 28.8 km/h

Time difference (ΔT) = 25/60 = 5/12 hours

Formula Used:

Time = Distance ÷ Speed

Upstream Speed = u − v | Downstream Speed = u + v

Calculations:

⇒ [22.5 / (28.8 − v)] − [22.5 / (28.8 + v)] = 5/12

⇒ 22.5 × [(28.8 + v − 28.8 + v) / (28.8² − v²)] = 5/12

⇒ 22.5 × [2v / (829.44 − v²)] = 5/12

⇒ 45v / (829.44 − v²) = 5/12

⇒ 9v × 12 = 829.44 − v²

⇒ v² + 108v − 829.44 = 0

⇒ Solving quadratic equation or verification by options:

⇒ If v = 7.2, then 7.2² + 108(7.2) = 51.84 + 777.6 = 829.44

∴ The correct answer is 7.2 km/h.

Additional Information

Relative Speed in Water

Downstream speed is the sum (u + v) and Upstream speed is the difference (u − v) where u is boat speed and v is stream speed.

Average Speed for Round Trip

The average speed for a round trip in a river is [(u² − v²) / u] which is always less than the speed in still water.

Time Difference Formula

Difference between Upstream and Downstream time ΔT = [2 × Distance × Stream Speed] ÷ [u² − v²].

Shortcut Trick

Efficiency A : B = 2 : 1 → Days A : B = 1 : 2. Let days be x and 2x.

Days C : D = 2 : 3. Combined efficiency (1/x + 1/2x) = (1/2y + 1/3y) where C = 2y, D = 3y.

3/2x = 5/6y ⇒ 18y = 10x ⇒ y = 5x/9.

Given B − C = 16 ⇒ 2x − 2y = 16 ⇒ 2x − 10x/9 = 16 ⇒ 8x/9 = 16 ⇒ x = 18.

∴ The correct answer is 18 days.

Alternate Method

Given: Efficiency of A is twice of B. Time taken by (A+B) = Time taken by (C+D). Ratio of days C : D = 2 : 3. B − C = 16 days.

⇒ Time taken by (A+B) = 2x ÷ 3.

⇒ For C and D, let days be 2y and 3y. Time taken by (C+D) = (2y × 3y) ÷ (2y + 3y) = 6y/5.

⇒ According to question: 2x/3 = 6y/5 ⇒ 10x = 18y ⇒ 5x = 9y ⇒ y = 5x/9.

⇒ Difference in days B − C = 16 ⇒ 2x − 2y = 16 ⇒ x − y = 8.

⇒ Substitute y: x − 5x/9 = 8 ⇒ 4x/9 = 8 ⇒ 4x = 72 ⇒ x = 18.

∴ The correct answer is 18 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a work. If efficiency ratio is a : b, then time ratio is b : a.

Combined Work Formula

If two people take X and Y days respectively, they together take (X × Y) ÷ (X + Y) days to complete the work.

1)  Mehak is senior to Tony. More than four persons have designation between Mehak and Tony, who is not junior to SO. Sita is the Bank Manager. 

 

2) One designation is between Piku and Kavita. Piku is senior to Kavita. Kavita is just senior to Sita. 

 

3) Mehak is senior to Neha. Romi is not junior to Neha. Neha is a senior to Huma. At least two persons are junior to Huma.

In Case 3, the given conditions do not follow. That is why Case 3 is eliminated.

 

4. Tony is a senior to Anu.  More than two designations are there between Romi and Kavita.

In Case 2, the given conditions do not follow. That is why Case 2 is eliminated.

The final arrangement is:

 

Hence, Three persons are senior to Kavita.

1)  Mehak is senior to Tony. More than four persons have designation between Mehak and Tony, who is not junior to SO. Sita is the Bank Manager. 

 

2) One designation is between Piku and Kavita. Piku is senior to Kavita. Kavita is just senior to Sita. 

 

3) Mehak is senior to Neha. Romi is not junior to Neha. Neha is a senior to Huma. At least two persons are junior to Huma.

In Case 3, the given conditions do not follow. That is why Case 3 is eliminated.

 

4. Tony is a senior to Anu.  More than two designations are there between Romi and Kavita.

In Case 2, the given conditions do not follow. That is why Case 2 is eliminated.

The final arrangement is:

 

Tony is a Section Officer. Hence, Tony is the Deputy General Manager is not correct.

1)  Mehak is senior to Tony. More than four persons have designation between Mehak and Tony, who is not junior to SO. Sita is the Bank Manager. 

 

2) One designation is between Piku and Kavita. Piku is senior to Kavita. Kavita is just senior to Sita. 

 

3) Mehak is senior to Neha. Romi is not junior to Neha. Neha is a senior to Huma. At least two persons are junior to Huma.

In Case 3, the given conditions do not follow. That is why Case 3 is eliminated.

 

4. Tony is a senior to Anu.  More than two designations are there between Romi and Kavita.

In Case 2, the given conditions do not follow. That is why Case 2 is eliminated.

The final arrangement is:

 

Hence, Piku is just senior to the Assistant General Manager.

1)  Mehak is senior to Tony. More than four persons have designation between Mehak and Tony, who is not junior to SO. Sita is the Bank Manager. 

 

2) One designation is between Piku and Kavita. Piku is senior to Kavita. Kavita is just senior to Sita. 

 

3) Mehak is senior to Neha. Romi is not junior to Neha. Neha is a senior to Huma. At least two persons are junior to Huma.

In Case 3, the given conditions do not follow. That is why Case 3 is eliminated.

 

4. Tony is a senior to Anu.  More than two designations are there between Romi and Kavita.

In Case 2, the given conditions do not follow. That is why Case 2 is eliminated.

The final arrangement is:

 

Kavita is the Senior Manager. Hence, Senior Manager- Kavita is the correct matched.

1)  Mehak is senior to Tony. More than four persons have designation between Mehak and Tony, who is not junior to SO. Sita is the Bank Manager. 

 

2) One designation is between Piku and Kavita. Piku is senior to Kavita. Kavita is just senior to Sita. 

 

3) Mehak is senior to Neha. Romi is not junior to Neha. Neha is a senior to Huma. At least two persons are junior to Huma.

In Case 3, the given conditions do not follow. That is why Case 3 is eliminated.

 

4. Tony is a senior to Anu.  More than two designations are there between Romi and Kavita.

In Case 2, the given conditions do not follow. That is why Case 2 is eliminated.

The final arrangement is:

 

Hence, Anu is the junior-most person.