SBI Clerk Prelims Memory Based Paper (Held On: 21 September 2025 Shift 2) (Previous Year Paper)

The correct answer is option 1.

Key Points

To answer this question, let's have a look at all the given sentences as options:

• Option 1: A flock of birds were flying south for the winter.
• This sentence is erroneous because the subject 'a flock' is singular, and the verb should therefore also be singular: 'was' instead of 'were'.
• The correct sentence would be: "A flock of birds was flying south for the winter."
• Option 2: She writes every day to improve her storytelling skills.
• This sentence is grammatically and contextually correct.
• Option 3: Driving carefully in rainy weather can prevent many accidents.
• This sentence is grammatically and contextually correct.
• Option 4: His innovative approach to problem-solving sets him apart from his peers.
• This sentence is grammatically and contextually correct.
• Option 5: It's important to drink plenty of water throughout the day.
• This sentence is grammatically and contextually correct.

So, out of the given sentences, only option 1 is a grammatically/contextually incorrect sentence.

Therefore, the correct answer is "A flock of birds was flying south for the winter."

The correct answer is option 2.

Key Points

To answer this question, let's have a look at all the given sentences as options:

• Option 1: The new store opens at 9 AM every morning.
• This sentence is grammatically and contextually correct.
• Option 2: He always ask interesting questions during the lecture.
• This sentence is incorrect because the verb should agree with the singular subject 'He', thus it should be 'asks' instead of 'ask'.
• The correct sentence would be: "He always asks interesting questions during the lecture."
• Option 3: I enjoy reading books that challenge my understanding of the world.
• This sentence is grammatically and contextually correct.
• Option 4: They played chess until midnight, each move more strategic than the last.
• This sentence is grammatically and contextually correct.
• Option 5: Creativity often thrives under constraints.
• This sentence is grammatically and contextually correct.

So, out of the given sentences, only option 2 is a grammatically/contextually incorrect sentence.

Therefore, the correct answer is "He always asks interesting questions during the lecture."

The correct answer is 'beleive'.

Key Points

• The word 'beleive' has been incorrectly spelled in the given sentence.
• The correct spelling and its meaning has been listed below - 
• believe -  accept that (something) is true, especially without proof.
• Example - You may believe the story that you like best.

​

Hint

• “I before E except after C” is a grammar rule that will help you with remembering the spelling of some words.
• The entire saying is “I before E, except after C or when sounded as A, as in neighbor and weigh. And weird is just weird.”
• It is also important to remember that there are exceptions to this rule like neighbor, Einstein, neither, efficient etc.

Additional Information

The following are the meanings of the other highlighted words in the given sentence - 

• arguments - Plural form of 'argument' which means an exchange of diverging or opposite views, typically a heated or angry one.
• describe - give a detailed account in words of.
• inevitable -  certain to happen.

The correct answer is 'calander'.

Key Points

• The word 'calander' has been incorrectly spelled in the given sentence.
• The correct spelling and its meaning has been listed below - 
• colander -  a perforated bowl used to strain off liquid from food after washing or cooking.
• Example - Shruti said as he strained the spaghetti into a colander.

Additional Information

The following are the meanings of the other highlighted words in the given sentence - 

• drain - cause or allow (liquid) to run off or out of something.
• thoroughly - in a thorough manner.
• rinse -  wash (something) with clean water to remove soap, detergent, dirt, or impurities.

The correct answer is 'desert'.

Key Points

• The word 'desert' has been incorrectly spelled in the given sentence.
• The correct spelling and its meaning has been listed below - 
• dessert -  the sweet course eaten at the end of a meal.
• Example - Guests finish with an indulgent dessert, baked on premises by the resident pastry chef.

Confusion Points

• 'Desert'  spelled in this manner means a water less, desolate area of land with little or no vegetation, typically one covered with sand.
• Hence, although the spelling is correct, the meaning is not valid for the given sentence.

Additional Information

The following are the meanings of the other highlighted words in the given sentence - 

• shines - be exceptionally good.
• among- surrounded by; in the middle of
• foster -  encourage the development of (something, especially something desirable). But in context of the given sentence we need to consider the phrase 'Bananas Foster' which refers to a dessert made from bananas and vanilla ice cream

The correct answer is 'fourt'.

Key Points

• The word 'fourt' has been incorrectly spelled in the given sentence.
• The correct spelling and its meaning has been listed below - 
• fourth -  constituting number four in a sequence; 4^th.
• Example - After the fourth week she knew he wouldn't be back.

Additional Information

The following are the meanings of the other highlighted words in the given sentence - 

• work - activity involving mental or physical effort done in order to achieve a purpose or result.
• stove - an apparatus for cooking or heating that operates by burning fuel or using electricity.
• supper -  an evening meal, typically a light or informal one.

The correct answer is 'vacum '.

Key Points

• The word 'vacum' has been incorrectly spelled in the given sentence.
• The correct spelling and its meaning has been listed below - 
• vacuum -  a space or container from which the air has been completely or partly removed. A 'vacuum cleaner' is an electrical apparatus that by means of suction collects dust and small particles from floors and other surfaces.
• Example - There is no such thing really as a vacuum, any more than there are atoms or ultimate indivisible particles.

​​                           You'll have to do a lot more stooping when you use an upright vacuum cleaner.

Additional Information

The following are the meanings of the other highlighted words in the given sentence - 

• particles - the least possible amount.
• receptacle - a hollow object used to contain something.
• process -   a series of actions or steps taken in order to achieve a particular end.

The correct answer is 'found'

Key Points

• In the given blank, we need to use a third form of the verb because there is a usage of 'been' and 'have' is an auxiliary verb so in this sense, we need to use a third form of the verb which is written only in Option 2 i.e. 'found'
• So the correct sentence is- A radiological examination of an ancient mummy said to have been found in royal tombs in Thebes

The correct answer is 'mummified'.

Key Points

• The passage describes an ancient Egyptian mummy of a pregnant woman who was carefully preserved according to burial customs.
• The blank requires a word that describes the process of preserving a dead body, especially in ancient Egypt.
• "Mummified" means preserved a dead body by embalming, drying, and wrapping it in cloth. This fits perfectly in the context of Egyptian burial practices. (ममीकृत)
• The sentence "She came from the elite of the Theban community and was carefully mummified" is grammatically and contextually correct.

Therefore, the correct answer is 'Option 3'.

Complete Sentence: She came from the elite of the Theban community and was carefully mummified*, wrapped in fabrics, and equipped with a rich set of amulets.*

Additional Information

• Mummification (ममीकरण): The process of preserving a body; it is a noun, so it does not fit grammatically in the blank.
• Typified (प्रतिनिधित्व करना): Means represented or symbolized; it does not suit the context of body preservation.
• Decomposified: This is not a standard English word and is incorrect in this context.
• Nourishment (पोषण): Means food or nutrition, which is unrelated to the context of preserving a mummy.

The correct answer is 'and'

Key Points

• According to the rule of grammar, between...and is correlative conjunction hence we need to use Option 5 i.e. 'and'
• Let's see an example-
• The Ministry plans to construct between 50 and 60 cyclone shelters.

So the correct sentence is- Closer examination has revealed that the woman died between 20 and 30 years

The correct answer is 'embalmed'

Key Points

• Let's see the meanings of the given words-
• Embalmed- preserve from decay.
• Decay- rot or cause to rot through the action of bacteria or fungi.
• Embank- protect or provide with an embankment.
• Neglect- Fail to give proper care or attention to.
• Embodiment- A tangible or visible form of an idea or quality.
• Hence, according to the meaning of the given words, the correct answer is 'Embalmed'.
• We use the mummification process to preserve the body of the person hence, we need to use Option 1 as the answer.

The correct answer is 'Egyptian'

Key Points

• Since the passage is talking about Egyptian burial customs hence, we need to use the word Egyptian in the blank because no other religion has been mentioned in the passage. So the correct answer is Option 4 i.e. Egyptian.

So the correct sentence is- Furthermore, this specimen sheds a light on an unresearched aspect of ancient Egyptian burial customs and interpretations of pregnancy in the context of ancient Egyptian religion.

The correct answer is None of these.

Key Points

None of the combinations in the given options can be used to make a meaningful sentence.

Let us take a look at the sentence combinations:

• A is combined with R to form a meaningful sentence: A crane is used to lift heavy objects.
• A cannot be used with either P or Q because it would not make a meaningful sentence.

A crane is used to highest mountain in India.

A crane is used to to the exam hall.

• The next combination would have to be B-P: The Kanchenjunga is the​ highest mountain in India.
• The combination B-Q does not make any meaningful sentence:

The Kanchenjunga is the to the exam hall.

• Then, the final combination is C-Q: She was on her way to the exam hall.

​The correct combination of sentences from the given options is A-R, B-P, and C-Q - none of which are given in the options.

Thus, the correct answer is: None of these.

Additional Information

We use both 'tall' and 'high' as adjectives for the height of an object.

But when referring to the height measurement of mountains, there is a slight difference.

• The peak of the highest mountain is the furthest away from sea level.

The highest mountain in the world is Mount Everest. Its peak is 29,035 feet above sea level.

• The peak of the tallest mountain is the furthest away from the base of the mountain.

The tallest mountain in the world is Mauna Kea. Its height from its base below sea level to its peak is 33,465 feet.

Here is an illustration of this difference:

The correct answer is C-R.

Key Points

The right combination from the given options that makes a meaningful sentence is C and R.

Let us take a look at the sentence combinations:

• A is combined with P to form a meaningful sentence: The school is closed for the summer break.
• A cannot be used with either Q or R because it would not make a meaningful sentence.

The school is closed from Mussoorie.

The school is closed their thick skin.

• The next combination would have to be B-Q: I sent him a postcard from Mussoorie.
• If we consider the combination B-R, it does not make any meaningful sentence:

I sent him a postcard their thick skin.

• Then, the final combination is C-R: Rhinoceros are known for their thick skin.

Thus, the correct combination of sentences from the given options is: (C) Rhinoceros are known for (R) their thick skin.

Additional Information

There are some animal names that remain the same in both singular and plural forms. Whether referring to one animal or a group of them, we use the same word.

• Some examples include: deer, moose, sheep, elk, walrus, antelope, buffalo, salmon.

The correct answer is A-R.

Key Points

The right combination from the given options that makes a meaningful sentence is A and R.

Let us take a look at the sentence combinations:

• A is combined with R to form a meaningful sentence: Please wash your hands before having food.
• A cannot be used with either P or Q because it would not make a meaningful sentence.

Please wash your hands as large as a city.

Please wash your hands in case it rained.

• The next combination would have to be B-P: An asteroid can be as large as a city.
• Next, if we consider the combination B-Q, it does not make any meaningful sentence:

An asteroid can be in case it rained.

• Then, the final combination is C-Q: I carried an umbrella in case it rained.

Thus, the correct combination of sentences from the given options is: (A) Please wash your hands (R) before having food.

The correct answer is Option 2.

Key Points

• The passage explicitly states that GlamourThreads gained popularity among fashion enthusiasts across North America and Asia.
• The brand was originally recognized for its avant-garde designs and sustainable approach, which attracted attention in these regions.
• There is no mention of its initial popularity in South America, Europe, Australia, or Africa.

Therefore, the correct answer is Option 2.

Reference Sentence: "Originally recognized for its avant-garde designs and sustainable approach, the brand quickly gained popularity among fashion enthusiasts across North America and Asia."

Additional Information

• Option 1: South America and Europe are not mentioned as the initial markets where GlamourThreads gained popularity.
• Option 3: Australia and Africa are also not mentioned as initial target markets for the brand.
• Option 4: Europe and Africa do not fit the description provided in the passage regarding the brand's early popularity.
• Option 5: Australia and South America are not listed as regions where the brand initially found success.

The correct answer is Option 3.

Key Points

• The passage mentions that GlamourThreads was originally recognized for its avant-garde designs and sustainable approach, which contributed to its early popularity and success.
• The brand's commitment to quality and innovation also played a significant role in setting it apart as a trendsetter in the fashion industry.
• Options such as late delivery of products, exclusivity agreements, partnerships with emerging brands in Africa, or high pricing are not mentioned as factors contributing to the brand's initial success.

Therefore, the correct answer is Option 3.

Reference Sentence: "Originally recognized for its avant-garde designs and sustainable approach, the brand quickly gained popularity among fashion enthusiasts across North America and Asia."

Additional Information

• Option 1: Late delivery of products is generally a negative factor and is not mentioned in the passage as contributing to the brand's success.
• Option 2: Exclusivity agreements with American designers are not mentioned in the passage.
• Option 4: Partnerships with emerging brands in Africa are not discussed as a factor in the passage.
• Option 5: High pricing of products is not mentioned as a contributing factor to the brand's initial success.

The correct answer is Option 2.

Key Points

• The passage mentions that the merger led to unforeseen challenges, specifically citing differing market dynamics and management conflicts caused by the European and Australian partners expecting different levels of autonomy and control.
• These conflicts resulted in strategic mishaps and misaligned goals, contributing to the eventual fallout of the merger.
• Options such as lack of social media presence, insufficient funding for marketing, inability to create unique designs, or overproduction of fashion items are not mentioned as primary reasons for the merger's failure.

Therefore, the correct answer is Option 2.

Reference Sentence: "Cultural clashes and differing market dynamics led to a series of management conflicts within GlamourThreads. The European and Australian partners expected different levels of autonomy and control, which resulted in strategic mishaps and misaligned goals."

Additional Information

• Option 1: Lack of social media presence is not mentioned in the passage as a factor leading to the merger's fallout.
• Option 3: Insufficient funding for marketing is not mentioned in the passage.
• Option 4: Inability to create unique designs is not cited as a primary reason in the passage.
• Option 5: Overproduction of fashion items is also not mentioned as a contributing factor in the passage.

The correct answer is Option 2.

Key Points

• Statement A: GlamourThreads was able to maintain its market presence in Europe after the merger.
• This statement is incorrect as the passage mentions that by 2018, GlamourThreads had lost its market presence in Europe due to the fallout of the merger.
• Statement B: The merger brought unforeseen challenges due to cultural clashes.
• This statement is correct as it aligns with the information provided in the passage about the cultural clashes and differing market dynamics leading to management conflicts after the merger.
• Statement C: By 2020, GlamourThreads had regained its innovation and quality.
• This statement is incorrect as the passage states that by 2020, GlamourThreads had experienced a steep decline and struggled to regain its footing, leading to a decrease in innovation and quality.
• Hence, the statement B is identified as correct in the context of the passage.

Therefore, the correct answer is: ‘Only B’.

The correct answer is Option 3.

Key Points

• Statement A: GlamourThreads initiated its merger in 2015.
• This statement is correct as per the passage which mentions that GlamourThreads initiated the merger in 2015.
• Statement B: The merger aimed to leverage diverse styles and market strengths.
• This statement is correct according to the passage, which states that the merger aimed to leverage the diverse styles and market strengths of Australia and Europe.
• Statement C: The global fashion market was facing economic growth during the merger.
• This statement is incorrect because the passage mentions that the global fashion market was facing economic downturns during the merger.
• Hence, the statement C is identified as incorrect in the context of the passage.

Therefore, the correct answer is: ‘Only C’.

The correct answer is 'expected'.

Key Points

• The word "expected" means considered likely or anticipated.
• Here, the European and Australian partners anticipated or had different expectations regarding autonomy and control.
• The other options: "tolerated," "ignored," "appreciated," and "compromised" do not fit the context as appropriately.

​Therefore, the correct answer is 'expected'.

Complete Sentence: The European and Australian partners expected different levels of autonomy and control, which resulted in strategic mishaps and misaligned goals.

Additional Information

• Tolerated (सहन करना): means allowing the existence, occurrence, or practice of something that one does not necessarily like.
• Ignored (उपेक्षित): means refusing to take notice of or acknowledge.
• Appreciated (प्रशंसा की): means recognizing the full worth of something.
• Compromised (समझौता किया): means reaching an agreement by making mutual concessions.

The correct answer is: Option 2 i.e., 'Preserve'.

Key Points

• The word "keep" in the context of maintaining the brand's identity means to continue having or holding onto something. (रखना, बनाए रखना)
• Example: It is important to keep your promises to maintain trust.
• "Preserve" refers to maintaining something as it is, especially in order to prevent it from decaying or being damaged. (संरक्षित रखना)
• Example: Efforts are being made to preserve the historic building.
• Hence, we can infer that the meaning of "keep" in this context is similar to "preserve".

​Therefore, the correct answer is: Preserve.

Additional Information

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

• Abandon (त्यागना): To leave something or someone completely.
• Example: He decided to abandon his old lifestyle and start anew.
• Remove (हटाना): To take something away from a place or position.
• Example: Please remove your shoes before entering the house.
• Cease (बंद करना): To stop something.
• Example: The factory will cease operations next month.
• Neglect (अवहेलना करना): To fail to care for something or someone properly.
• Example: He was accused of neglecting his duties.

The correct answer is: Option 4 i.e., 'Conceal'.

Key Points

• The word "mean" in the context of the passage refers to something that conveys or signifies a particular sense or meaning. (अर्थ रखना)
• Example: His words mean that he is unhappy with the current situation.
• "Conceal" refers to keeping something hidden or secret. (छिपाना)
• Example: She tried to conceal her disappointment from her friends.
• Hence, we can infer that the opposite of "mean" in this context is "conceal".

Therefore, the correct answer is: Conceal.

Additional Information

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

• Intend (इरादा रखना): To plan or have in mind to do something.
• Example: I intend to start a new project next month.
• Signify (अर्थ दर्शाना): To indicate or be a sign of something.
• Example: His nod signified his agreement.
• Suggest (सुझाव देना): To put forward an idea or plan for consideration.
• Example: Can you suggest a good place for dinner?
• Represent (प्रतिनिधित्व करना): To stand for or symbolize something.
• Example: The flag represents our country.

The correct answer is option 1) i.e. PQRS.

Key Points

• While arranging the parts of the sentence given in options, we have to find some grammatical or contextual connections between them, so let’s find out.
• 'Suggest' is a verb and here it cannot be the first part of the given sequence.
• PQ is a pair because P ends with “to” and Q starts with Verb's first form i.e. “suggest”. They together make the infinitive.
• If we put S after Q and then R at last, the sentence does not make any sense. The meaning becomes vague.
• But, if R is put after Q and then S at last, the order makes the sentence meaningful.

Thus, the correct order is PQRS.

Correct sentence: “There is strong empirical evidence to suggest that money in the hands of the mother increases expenditure on children.”

The correct answer is option 4) i.e. RQPS.

Key Points

• While arranging the parts of the sentence given in options, we have to find some grammatical or contextual connections between them, so let’s find out.
• An adverb is a word that modifies (describes) a verb, an adjective, another adverb, or even a whole sentence. Adverbs often end in -ly, but some look exactly the same as their adjective counterparts e.g. She spoke softly.
• Part Q starts with the adverb 'so', so we can say that it has been used to modify something. Here, 'so' means to a very great extent or degree i.e. something is too common.
• Auxiliary verb 'are' here in part P signifies that there will be a subject for it. Thus, we cannot start the sentence with either of them.
• R must come at the beginning as it has both the subject (corruption) and the finite verb (has become) of the sentence.
• Next will come Q as it has the starting point, i.e. the conjunction (that), for the subordinating clause. Thus, RQ becomes a pair and comes at the beginning of the sequence.
• We can see that only in the fourth option RQ comes at the beginning.
• Thus, the correct order is RQPS.

Correct sentence: “Corruption in India has become so common that people now are averse to thinking of public life with it.”

The correct answer is option 2) i.e. PSRQ.

Key Points

• While arranging the parts of the sentence given in options, we have to find some grammatical or contextual connections between them, so let’s find out.
• P is the first fragment because it introduces the subject 'literature'.
• S should be put after P because P ends with “so that” which is a conjunction of the subordinate clause and connects with S.
• R follows S contextually.
• Q has “too”, which makes it an additional statement connecting with R.
• Thus, the correct order is PSRQ.

Correct sentence: “Literature exists so that where a man has lived finely ten thousand others may afterward live finely too.”

The correct answer is: 'PQRS'

Key Points

• We need to check the grammatical and contextual connection between the parts of the sentence to find the correct sequence.
• Part P starts with a noun.
• It will become the subject of the sentence.
• So it will be the first part of the sentence.
• Part P ends with 'as'
• Part Q starts with 'if'
• 'As if' is a coordinate conjunction.
• So Q will follow P and will become the second part of the sentence.
• Part Q ends with 'general'
• Part R starts with 'manager'
• 'General Manager' is a proper noun.
• So R will follow Q and will be the third part of the sentence.
• Part S becomes the last part of the sentence maintaining the continuity of the sentence.
• Thus the correct sequence is: PQRS

The complete sentence is: Raman talks to me as if he were the General manager of NIPPO company although all know he is not.

The correct answer is:  option (2).

Key Points

• The sentence has an error: it uses "hand" (INCORRECT) instead of "hands" (CORRECT) after the plural determiner "their."
• This disrupts subject-verb agreement in grammar because "their" indicates more than one person.
• For proper Subject-verb agreement, the verb form should match the number (singular or plural) of the subject.
• The sentence is talking about multiple people raising their hands, so the plural form is required.
• Hence, the correct answer is "during the event, we asked old people to raise their hand".

The correct sentence is: "In our earnest attempt to promote kindness and consideration during the event, we asked old people to raise their hands so that we, with sincere regard for their comfort, could manage their accommodations efficiently and with care."

Additional Information

• Let's check the other correct parts:
• The nouns "kindness"  and "consideration" fit coherently in the sentence.
• The adjectives "sincere" and "old" modify the nouns "regard" and "people" respectively. The adverb "efficiently" correctly modifies the verb "manage."​
• Accommodations : (आवास) - A place to live, work, stay, etc.
• Example: The hotel we stayed in during our vacation offered excellent accommodations.

The correct answer is: of capital and financially

Key Points

• The error in this sentence is the use of the adverb "financially" to qualify the noun "aid."
• "Financially" is an adverb and cannot be used to describe a noun. Instead, an adjective is needed.
• Adjectives, are used to modify nouns, providing information about the qualities or attributes of the noun.
• In this sentence, "financially" is used to modify the noun "aid," which is incorrect.
• The adjective form "financial" should be used to correctly describe "aid."
• The sentence discusses the need for "financial aid," which means assistance in terms of money or funds. (वित्तीय सहायता)

Therefore, the correct answer is option 3.

The correct sentence is: "Travelling is a leisure hobby that requires a lot of capital and financial aid to do it regularly."

Additional Information 

• Adverbs are used to modify verbs, adjectives, or other adverbs. They provide information about how, when, where, or to what degree an action is performed.
• Example: The man became financially stable after years of hard work.

The correct answer is: option (2).

Key Points

• The error is in the segment "that I saved". The correct version should be "that I had been saving".
• "I saved" suggests a one-time, completed action in the past, which doesn't match the ongoing action implied by "for the last 4 months".
• "Had been saving" is the past perfect continuous tense, depicting an action that started and continued in the past.
• The ongoing nature of saving over a period of time is best captured by using "had been saving" rather than "saved".
• Hence, the correct answer is  "that I saved".

Therefore, the correct and complete sentence is "My sister spent all the money "that I had been saving" for my father's new laptop for the last 4 months."

Total shoes sold by Retailer E = 620 + 580 = 1200

Total shoes sold by Retailer A = 450 + 320 = 770

Percentage = (Total E ÷ Total A) × 100 = (1200 ÷ 770) × 100 ≈ 155.84%

Hence, the correct answer is 155.84%.

Total Non-leather shoes sold by all retailers:

320 + 480 + 500 + 450 + 580 = 2330

Number of retailers = 5

Average = Total ÷ Number of retailers = 2330 ÷ 5 = 466

Hence, the correct answer is 466.

Total Leather shoes sold by A and B:

Leather (A + B) = 450 + 510 = 960

Total Non-leather shoes sold by B and C:

Non-leather (B + C) = 480 + 500 = 980

Leather (A + B) : Non-leather (B + C) = 960 : 980 = 48 : 49

Hence, the correct answer is 48 : 49.

Leather shoes sold:

Retailer B = 510

Retailer D = 550

Difference = 550 − 510 = 40

Percentage less = (Difference ÷ D) × 100 = (40 ÷ 550) × 100 ≈ 7.27%

Hence, the correct answer is ≈ 7.27%.

Retailer C → Leather = 480, Non-leather = 500 → Total = 480 + 500 = 980  

Retailer E → Leather = 620, Non-leather = 580 → Total = 620 + 580 = 1200  

Combined total = 980 + 1200 = 2180

Hence, the correct answer is 2180.

Shortcut Trick

Downstream Speed (u) = 11 ÷ 2 = 5.5 km/h

Upstream Speed (v) = 11 ÷ 4 = 2.75 km/h

Boat Speed = (u + v) ÷ 2 = (5.5 + 2.75) ÷ 2 = 8.25 ÷ 2 = 4.125 km/h

Current Speed = (u − v) ÷ 2 = (5.5 − 2.75) ÷ 2 = 2.75 ÷ 2 = 1.375 km/h

∴ The correct answer is 4.125 km/h and 1.375 km/h.

Alternate Method

Given:

Distance (D) = 11 km

Time taken along the stream (t₁) = 2 hours

Time taken against the stream (t₂) = 4 hours

Formula Used:

Speed = Distance ÷ Time

Downstream Speed (u) = x + y | Upstream Speed (v) = x − y

Speed of boat in still water (x) = (u + v) ÷ 2

Speed of current (y) = (u − v) ÷ 2

Calculations:

⇒ Downstream Speed (u) = 11 ÷ 2 = 5.5 km/h

⇒ Upstream Speed (v) = 11 ÷ 4 = 2.75 km/h

⇒ Speed of boat (x) = (5.5 + 2.75) ÷ 2

⇒ x = 8.25 ÷ 2 = 4.125 km/h

⇒ Speed of current (y) = (5.5 − 2.75) ÷ 2

⇒ y = 2.75 ÷ 2 = 1.375 km/h

∴ The correct answer is 4.125 km/h and 1.375 km/h.

Additional Information

Relative Speed in Water

When moving with the flow, the speeds add up (x + y). When moving against the flow, the stream speed is subtracted from the boat speed (x − y).

Average Speed of Boat

If the boat covers equal distance upstream and downstream, Average Speed = (u × v) / x = (x² − y²) / x km/h.

Time Ratio Property

The ratio of Speed of Boat to Speed of Current is given by (t_up + t_down) : (t_up − t_down).

Shortcut Trick

Use the Alligation Method to find the ratio of quantities.

Profit 1: 11%, Profit 2: 18%, Mean Profit: 14%.

Ratio = (18 − 14) : (14 − 11) = 4 : 3.

Total units = 4 + 3 = 7 units.

7 units = 980 kg ⇒ 1 unit = 140 kg.

Quantity at 18% profit = 3 × 140 = 420 kg.

∴ The correct answer is 420 kg.

Alternate Method

Given: Total quantity = 980 kg, Part 1 profit = 11%, Part 2 profit = 18%, Overall profit = 14%.

Formulas: Profit = SP − CP | Weighted Average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂)

⇒ Let quantity at 18% be x kg, then quantity at 11% is (980 − x) kg.

⇒ 11(980 − x) + 18x = 14 × 980

⇒ 10780 − 11x + 18x = 13720

⇒ 7x = 13720 − 10780

⇒ 7x = 2940

⇒ x = 420 kg.

∴ The correct answer is 420 kg.

Additional Information

Alligation Rule

It is used to find the ratio in which two ingredients at given prices/profits are mixed to produce a mixture of a mean price/profit.

Profit and Loss on Quantities

When overall profit % is given for two parts of a total quantity, the ratio of quantities is inversely proportional to the deviation of their profit % from the mean profit %.

The pattern of the given series is a Fibonacci series. Every number from third number is a sum of the previous two numbers.

⇒ 17 = 5 + 12

⇒ 29 = 17 + 12

⇒ 46 = 29 + 17

⇒ 75 = 46 + 29

⇒ 121 = 75 + 46

⇒ 196 = 121 + 75

The series is formed by the following logic

⇒ 3 + 1² = 4

⇒ 4 + 3² = 13

⇒ 13 + 5² = 38

⇒ 38 + 7² = 87

⇒ 87 + 9² = 168

∴ the answer is 38

The pattern of the number series is as follows:

17 × 2 + 4 = 38

38 × 2 + 4 = 80

80 × 2 + 4 = 164

164 × 2 + 4 = 332

332 × 2 + 4 = 668

668 × 2 + 4 = 1340

∴ The required next number is 1340.

Given:

Population of town is 63400

In the first year 15% and second year decreases by 20%

Calculation:

According to question,

⇒ {63400 × (115/100) × (80/100)}

⇒ 58328

∴ After 2 year later population of town is 58328

Formula used:

[X + Y + {(XY)/100}%]

⇒ X = 15%, and Y = - 20%

Applying the net% effect formula

⇒ [(+15 - 20) - {15 × 20}/100]

⇒ - 5 - 3 

⇒ - 8

So, (100 - 8)% of 63400

⇒ 92% of 63400

⇒ 58328

∴ After 2 year later population of town is 58328

1^st year 15% increase(3/20) , 2^nd year 20% decrease(1/5)

   year  =           Present pop.                last pop.

1^st year =          20                                     23

2^nd yrs =            5                                      4

After 2 yrs present pop. 100  and last pop. 92 

Given to 100 unit = 63400

⇒ 1 unit = 634

⇒ last population = 634 × 92

⇒ 58328

∴ After 2 year later population of town is 58328

Shortcut Trick

Total Time taken from 9 a.m. to 2 p.m. = 5 hours.

Distance = Speed × Time

Distance = 37 × 5 = 185 km.

∴ The correct answer is 185 km.

Alternate Method

Given:

Starting time = 9 a.m.

Arrival time = 2 p.m.

Speed of Train A = 37 km/h

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Time duration = 2 p.m. − 9 a.m.

⇒ Time duration = (12 − 9) + 2 = 5 hours

⇒ Distance = 37 km/h × 5 hours

⇒ Distance = 185 km

∴ The correct answer is 185 km.

Additional Information

Speed-Distance Relation

The fundamental relation is Distance = Speed × Time. If Speed is in km/h and Time is in hours, Distance will be in km.

Unit Conversion

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

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal distances with speeds x and y, Average Speed = 2xy ÷ (x + y).

Given expression:

⇒ 48% of 250 + 1050 ÷ 3 – √(?) = 423

⇒ (48/100) × 250 + 1050 ÷ 3 – √(?) = 423

⇒ (48/100) × 250 + 350 – √(?) = 423

⇒ 120 + 350 – √(?) = 423

⇒ 470 – √(?) = 423

⇒ √(?) = 470 – 423

⇒ √(?) = 47

⇒ ? = 2209

Given, 139% of 459 + $5\frac{1}{2}$ of 384

Approximating terms to the closest values, we get

⇒ 140% of 460 + 11/2 × 384

⇒ (140 × 460)/100 + 11/2 × 384

⇒ 644 + 2112 = 2756 ≈ 2760

∴ Approx value of the expression is 2760

⇒ 150 + 45 × 2(36 – 16) ÷ 18 = ?

⇒ 150 + 45 × 2(20) ÷ 18

⇒ 150 + 100 = 250

To solve questions of this type, follow the laws of “Surds and indices’’ given below -

Laws of Indices:

1. a^m × aⁿ = a^{{m + n}}
2. a^m ÷ aⁿ = a^{{m - n}}
3. (a^m)ⁿ = a^mn
4. (a)^-m = 1/a^m
5. (a)^m/n = ⁿ√a^m
6. (a)⁰ = 1

By using this laws:

⇒ (216)^7/3 × 64² × 81^5/4 = 3^-7 × 6^?

⇒ (6³)^7/3 × (2⁶)² × (3⁴)^5/4 = 3^-7 × 6^?

⇒ 6⁷ × 2¹² × 3⁵ = 3^-7 × 6^?

⇒ 6⁷ × 2¹² × 3⁵ = 3^-7 × 6^?

⇒ 6⁷ × 2¹² × 3⁵ ÷ 3^-7 = 6^?

⇒ 6⁷ × 2¹² × 3¹² = 6⁷

⇒ 6⁷ × 6¹² = 6^?

⇒ ? = 19

[3132 ÷ 29 × 48] ÷ 18 = 12 × ?

⇒ (3132/29) × 48 × ( 1/18) = 12 × ?

⇒ (108 × 48)/18 = 12 × ?

⇒ 12 × ? = 6 × 48

⇒ ? = 24

∴ ? = 24.

⇒ 76% of 395 + 48% of 135 =?

⇒ ? = 76/100 × 395 + 48/100 × 135

⇒ ? = 300.2 + 64.8

⇒ ? = 365

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

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

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

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

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

Given expression is,

⇒ 3 + {3 + (4 - 1 × 2)} × 4 = 759 ÷ ?

⇒ 3 + {3 + (4 - 2)} × 4 = 759 ÷ ?

⇒ 3 + {3 + 2} × 4 = 759 ÷ ?

⇒ 3 + 5 × 4 = 759 ÷ ?

⇒ 3 + 20 = 759 ÷ ?

⇒ 23 = 759 ÷ ?

⇒ ? = 759/23 = 33

⇒ ? = 33

Given expression is,

⇒ 12% of (75% of (25% of (8% of 4800))) = ?

$\begin{array}{l} \Rightarrow \frac{{12}}{{100}} \times \left( {\frac{{75}}{{100}} \times \left( {\frac{{25}}{{100}} \times \left( {\frac{8}{{100}} \times 4800} \right)} \right)} \right) = ;?\ \Rightarrow \frac{3}{{25}} \times \left( {\frac{3}{4} \times \left( {\frac{1}{4} \times \left( {48 \times 8} \right)} \right)} \right) = ;?\ \Rightarrow \frac{3}{{25}} \times \left( {\frac{3}{4} \times 96} \right) = ;?\ \Rightarrow \frac{3}{{25}} \times 3 \times 24 = ;? \end{array}$

⇒ ? = 216/25 = 8.64

⇒ ? = 8.64

Shortcut Trick

When Simple Interest is a fraction (1/n) of Principal and Time (T) equals Rate (R).

Formula: Rate (R) = √(Fraction × 100)

R = √(1/16 × 100) = √(100/16)

R = 10/4 = 2.5%

∴ The correct answer is 2.5%.

Alternate Method

Given:

Simple Interest (SI) = 1/16 × Principal (P)

Number of years (T) = Rate per annum (R)

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ P/16 = (P × R × R) ÷ 100

⇒ 1/16 = R² ÷ 100

⇒ R² = 100 ÷ 16

⇒ R = √(100/16)

⇒ R = 10/4

⇒ R = 2.5%

∴ The correct answer is 2.5%.

Additional Information

Simple Interest Formula

The basic formula is SI = (P × R × T) / 100, where P is Principal, R is Rate, and T is Time.

Case when R = T

If numerical values of Rate and Time are equal, then R = T = 10 × √(SI/P).

Amount Calculation

Total Amount (A) is the sum of Principal and Simple Interest: A = P + SI.

New mines in A = 150 + 20% of 150 = 150 + 30 = 180

New mines in D = 300 − 10% of 300 = 300 − 30 = 270

Ratio (A:D) = 180 : 270 = 2 : 3

Hence, the correct answer is 2 : 3.

Original mines in C = 200

If doubled ⇒ New mines in C = 200 × 2 = 400

New total mines = 150 + 250 + 400 + 300 = 1100

Required percentage = (400 ÷ 1100) × 100 = 36.36%

Hence, the correct answer is 36.36%.

Average number of mines in Place A and B = (150 + 250) ÷ 2 = 400 ÷ 2 = 200

Average number of mines in Place C and D = (200 + 300) ÷ 2 = 500 ÷ 2 = 250

Difference = 250 − 200 = 50

Hence, the correct answer is 50.

Mines in Place A = 150

Mines in Place B = 250

Difference = 250 − 150 = 100

Percentage increase = (Difference ÷ Place A) × 100

= (100 ÷ 150) × 100 = 66.67%

Hence, the correct answer is 66.67%.

Mines in Place A = 15 hundreds = 150

Mines in Place C = 20 hundreds = 200

Total (A + C) = 150 + 200 = 350

Mines in Place B = 250

Mines in Place D = 300

Total (B + D) = 250 + 300 = 550

Ratio (A + C) : (B + D) = 350 : 550 → 7 : 11

Hence, the correct answer is 7 : 11.

Shortcut Trick

Side of Square = √1764 = 42 cm.

Radius of Semicircle (r) = 42 ÷ 2 = 21 cm.

Perimeter of Semicircle = r × (36 ÷ 7).

Perimeter = 21 × (36 ÷ 7) = 3 × 36 = 108 cm.

∴ The correct answer is 108 cm.

Alternate Method

Given: Area of Square = 1764 cm²; Radius = Side / 2.

Formula Used: Area of Square = a²; Perimeter of Semicircle = πr + 2r.

⇒ Side of Square (a) = √1764

⇒ a = 42 cm

⇒ Radius of Semicircle (r) = 42 ÷ 2 = 21 cm

⇒ Perimeter = (π × r) + (2 × r)

⇒ Perimeter = (22/7 × 21) + (2 × 21)

⇒ Perimeter = 66 + 42 = 108 cm

∴ The correct answer is 108 cm.

Additional Information

Area of Semicircle

The Area is half of the circle's area, given by (πr²) ÷ 2.

Diagonal of a Square

The Diagonal of a square with side 'a' is calculated as a√2.

Simplified Perimeter Constant

The Perimeter of a semicircle can be expressed as r × (36/7) when using π = 22/7.

Shortcut Trick

Profit ratio = (Capital_A × Time_A) : (Capital_B × Time_B)

Ratio of Capitals A : B = 76,000 : 57,000 = 4 : 3

Let B joined for x months. A was there for 12 months.

(4 × 12) : (3 × x) = 2 : 1 ⇒ 48 : 3x = 2 : 1

3x × 2 = 48 × 1 ⇒ 6x = 48 ⇒ x = 8 months.

B joined after = 12 − 8 = 4 months.

∴ The correct answer is 4 months.

Alternate Method

Given → Investment of A = Rs. 76,000, Investment of B = Rs. 57,000, Profit Ratio = 2 : 1, Time for A = 12 months. Formulas: Profit = Investment × Time | Investment₁ × T₁ ÷ Investment₂ × T₂ = P₁ ÷ P₂

⇒ Let B invested for t months. ⇒ (76000 × 12) ÷ (57000 × t) = 2 ÷ 1 ⇒ (4 × 12) ÷ (3 × t) = 2 ÷ 1 ⇒ 48 ÷ 3t = 2 ÷ 1 ⇒ 16 ÷ t = 2 ⇒ t = 8 months. ⇒ Since the business ran for 12 months and B was in for 8 months, B joined after 12 − 8 = 4 months.

∴ The correct answer is 4 months.

Additional Information

Partnership Basics

In a partnership, the profit is distributed based on the weighted investment, which is the product of Capital and Time Period.

Time Calculation

Always distinguish between the duration of investment and the time after which a partner joins. Time joined after = Total time − Duration of investment.

General Solution:

Given:

Total visitors on Monday = 390

Females on Monday = 62.5% of Males on Monday

Males on Tuesday = Females on Monday + 35

Let MMon = males on Monday, FMon = females on Monday.

Calculations:

FMon = 62.5% of MMon = (5/8)·MMon

MMon + FMon = 390 ⇒ MMon + (5/8)MMon = 390

⇒ (13/8)MMon = 390 ⇒ MMon = 390 × 8 / 13 = 240

⇒ FMon = 390 − 240 = 150

Males on Tuesday = FMon + 35 = 150 + 35 = 185

Thus,

Males on Monday = 240

Females on Monday = 150

Males on Tuesday = 185

Calculations:

Original males on Monday = 240

Reduced by 20% ⇒ New males = 240 − 0.2 × 240 = 240 − 48 = 192

Females remain the same = 150

New total visitors = 192 + 150 = 342

Hence, the correct answer is 342.

General Solution:

Given:

Total visitors on Monday = 390

Females on Monday = 62.5% of Males on Monday

Males on Tuesday = Females on Monday + 35

Let MMon = males on Monday, FMon = females on Monday.

Calculations:

FMon = 62.5% of MMon = (5/8)·MMon

MMon + FMon = 390 ⇒ MMon + (5/8)MMon = 390

⇒ (13/8)MMon = 390 ⇒ MMon = 390 × 8 / 13 = 240

⇒ FMon = 390 − 240 = 150

Males on Tuesday = FMon + 35 = 150 + 35 = 185

Thus,

Males on Monday = 240

Females on Monday = 150

Males on Tuesday = 185

Calculations:

Males on Monday = 240

Males on Tuesday = 185

Ratio = Males(Monday) : Males(Tuesday) = 240 : 185 → 48 : 37

Hence, the correct answer is 48 : 37.

General Solution:

Given:

Total visitors on Monday = 390

Females on Monday = 62.5% of Males on Monday

Males on Tuesday = Females on Monday + 35

Let MMon = males on Monday, FMon = females on Monday.

Calculations:

FMon = 62.5% of MMon = (5/8)·MMon

MMon + FMon = 390 ⇒ MMon + (5/8)MMon = 390

⇒ (13/8)MMon = 390 ⇒ MMon = 390 × 8 / 13 = 240

⇒ FMon = 390 − 240 = 150

Males on Tuesday = FMon + 35 = 150 + 35 = 185

Thus,

Males on Monday = 240

Females on Monday = 150

Males on Tuesday = 185

Calculations:

Males on Tuesday = 185

Total visitors on Monday = 390

Percentage = (185 ÷ 390) × 100

= 47.44% (approx)

Hence, the correct answer is 47.44%.

General Solution:

Given:

Total visitors on Monday = 390

Females on Monday = 62.5% of Males on Monday

Males on Tuesday = Females on Monday + 35

Let M_Mon = males on Monday, F_Mon = females on Monday.

Calculations:

F_Mon = 62.5% of M_Mon = (5/8)·M_Mon

M_Mon + F_Mon = 390 ⇒ M_Mon + (5/8)M_Mon = 390

⇒ (13/8)M_Mon = 390 ⇒ M_Mon = 390 × 8 / 13 = 240

⇒ F_Mon = 390 − 240 = 150

Males on Tuesday = F_Mon + 35 = 150 + 35 = 185

Thus,

Males on Monday = 240

Females on Monday = 150

Males on Tuesday = 185

Calculations:

Total visitors on Monday = 390

Total visitors on Monday + Tuesday = 755

Males on Tuesday = 185 

Total visitors on Tuesday = 755 − 390 = 365

Females on Tuesday = Total visitors − Males on Tuesday = 365 − 185 = 180

Hence, the correct answer is 180.

Shortcut Trick

Efficiency ratio E : F = (1 + 1/4) : 1 = 5/4 : 1 = 5 : 4

Total Work = Efficiency of E × Days taken by E = 5 × 15 = 75 units

Combined efficiency of E + F = 5 + 4 = 9 units/day

Days taken together = 75 ÷ 9 = 25/3 days

∴ The correct answer is 25/3 days.

Alternate Method

Given:

Efficiency of E is 1/4 more than F.

Time taken by E = 15 days.

Calculations:

⇒ Let efficiency of F = 4 units/day

⇒ Efficiency of E = 4 + (1/4 × 4) = 5 units/day

⇒ Total Work = Efficiency × Time = 5 × 15 = 75 units

⇒ Time taken by E and F together = Total Work ÷ (Eff_E + Eff_F)

⇒ Time = 75 ÷ (5 + 4) = 75/9 days

⇒ Time = 25/3 days

∴ The correct answer is 25/3 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiency is x : y, the ratio of time taken is y : x.

Work Formula

Total Work = Efficiency × Time. Combined time for two people working together is (Total Work) ÷ (Sum of individual efficiencies).

Shortcut Trick

Combine the ratio of A : B : C : D using the common terms.

A : B = 3 : 4 | B : C = 1 : 2 (or 4 : 8) | C : D = 4 : 3 (or 8 : 6).

Combined ratio A : B : C : D = 3 : 4 : 8 : 6.

Given D = 6 units = 72 years → 1 unit = 12 years.

Oldest is C = 8 units = 8 × 12 = 96 years.

∴ The correct answer is 96 yrs.

Alternate Method

Given:

Ratio A : B = 3 : 4

Ratio B : C = 1 : 2

Ratio C : D = 4 : 3

Age of D = 72 years

Calculations:

⇒ To combine, make B same: A : B = 3 : 4, B : C = 4 : 8

⇒ Now make C same: C : D is 4 : 3, but in combined it is 8. So, C : D = 8 : 6

⇒ Combined Ratio A : B : C : D = 3 : 4 : 8 : 6

⇒ Value of D = 6x = 72

⇒ x = 72 ÷ 6 = 12

⇒ Oldest is C (highest ratio part)

⇒ Age of C = 8 × 12 = 96 years

∴ The correct answer is 96 yrs.

Additional Information

Combined Ratio Rule

To combine A:B and B:C, multiply the ratios so that the common term (B) has the same value in both sets.

Ratio & Proportion Basics

If a : b = c : d, then the product of extremes equals the product of means (a × d = b × c).

Age Related Problems

The difference between the ages of two persons remains constant throughout their lives regardless of the time elapsed.

Shortcut Trick

By Alligation Method, the ratio of Solution 1 to Solution 2 is calculated using the water concentrations.

Ratio = (35 − 23) : (23 − 15) = 12 : 8 = 3 : 2

Given: 2 units (Solution 2) = 40 L

⇒ 1 unit = 20 L

⇒ 3 units (Solution 1) = 3 × 20 L = 60 L

∴ The correct answer is 60 L.

Alternate Method

Given:

Water in Solution 1 = 15%

Water in Solution 2 = 35%

Target water concentration = 23%

Quantity of Solution 2 = 40 L

Calculations:

⇒ Let the quantity of Solution 1 be x L.

⇒ By Alligation Rule: (Quantity of 1) / (Quantity of 2) = (35 − 23) / (23 − 15)

⇒ x / 40 = 12 / 8

⇒ x / 40 = 3 / 2

⇒ x = (3 × 40) ÷ 2

⇒ x = 120 ÷ 2 = 60 L

∴ The correct answer is 60 L.

Additional Information

Rule of Alligation

Used to find the ratio in which two ingredients at given prices or concentrations must be mixed to produce a mixture at a desired mean value.

Weighted Average Formula

Mean Concentration = (n₁c₁ + n₂c₂) ÷ (n₁ + n₂), where n is quantity and c is concentration.

Successive Dilution

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

Given: Eight persons, namely, E, F, G, H, I, J, K, L, bought different toys in an order, but not necessarily in the same order.

1. Only one person bought a toy after K.

2. There are three persons between G and K.

3. Only one person bought a toy between I and G.

Here, we have 2 Cases, i.e, Case 1 and Case 2.

4. Two people bought their toys between E and H; H bought their toy either just before or just after I.

5. F bought their toy before H.

Now, we can eliminate Case 1. (Because there is no vacant place before H)

6. Not more than three persons bought their toys between F and J.

This is our final arrangement,

Except for G - J, all others are adjacent to each other.

Hence, the correct answer is G - J.

Given: Eight persons, namely, E, F, G, H, I, J, K, L, bought different toys in an order, but not necessarily in the same order.

1. Only one person bought a toy after K.

2. There are three persons between G and K.

3. Only one person bought a toy between I and G.

Here, we have 2 Cases, i.e, Case 1 and Case 2.

4. Two people bought their toys between E and H; H bought their toy either just before or just after I.

5. F bought their toy before H.

Now, we can eliminate Case 1. (Because there is no vacant place before H)

6. Not more than three persons bought their toys between F and J.

This is our final arrangement,

Hence, the correct answer is I.

Given: Eight persons, namely, E, F, G, H, I, J, K, L, bought different toys in an order, but not necessarily in the same order.

1. Only one person bought a toy after K.

2. There are three persons between G and K.

3. Only one person bought a toy between I and G.

Here, we have 2 Cases, i.e, Case 1 and Case 2.

4. Two people bought their toys between E and H; H bought their toy either just before or just after I.

5. F bought their toy before H.

Now, we can eliminate Case 1. (Because there is no vacant place before H)

6. Not more than three persons bought their toys between F and J.

This is our final arrangement,

Hence, the correct answer is G bought the toy immediately after F.

Given: Eight persons, namely, E, F, G, H, I, J, K, L, bought different toys in an order, but not necessarily in the same order.

1. Only one person bought a toy after K.

2. There are three persons between G and K.

3. Only one person bought a toy between I and G.

Here, we have 2 Cases, i.e, Case 1 and Case 2.

4. Two people bought their toys between E and H; H bought their toy either just before or just after I.

5. F bought their toy before H.

Now, we can eliminate Case 1. (Because there is no vacant place before H)

6. Not more than three persons bought their toys between F and J.

This is our final arrangement,

Hence, the correct answer is Four.

Given: Eight persons, namely, E, F, G, H, I, J, K, L, bought different toys in an order, but not necessarily in the same order.

1. Only one person bought a toy after K.

2. There are three persons between G and K.

3. Only one person bought a toy between I and G.

Here, we have 2 Cases, i.e, Case 1 and Case 2.

4. Two people bought their toys between E and H; H bought their toy either just before or just after I.

5. F bought their toy before H.

Now, we can eliminate Case 1. (Because there is no vacant place before H)

6. Not more than three persons bought their toys between F and J.

This is our final arrangement,

Hence, the correct answer is I.

Given: A certain number of players are standing in a line facing north.

1. A stands third to the right of D.

2. The number of players standing between A and D is one more than the number of players standing between A and F.

Here, we have 2 Cases, i.e., Case 1 and Case 2.

3. L stands immediately to the right of F.

4. No player stands between L and K.

Now, we can eliminate Case 2.

5. B stands immediately to the left of D.

6. The number of players standing between F and K is the same as the number of players standing between Y and B.

7. Y stands to the left of B.

This is our final arrangement,

Hence, the correct answer is The one who stands fourth to the right of A.