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Question 1 of 5
1. Question
A man started from home at 16:10 hours and drove to a village, arriving there when the village clock indicated 16:40 hours. After staying for 5 minutes, he drove back by a different route of length 1.5 times the first route at a rate three times as fast, reaching home at 17:15 hours. As compared to the clock at home, the village clock is
Correct
Answer: (a)
Given that,
He started at 16:10 and reached home at 17:15. He stayed in the village for 5 minutes. The return route is 1.5 times the onward route, and the return speed is three times the onward speed.
Now,
Let onward speed be S km/h and onward distance be D km.
Total time taken = 17:15 − 16:10 = 1 h 5 min = 65 min.
Total travelling time = 65 − 5 = 60 min.
Return time = (1.5D)/(3S) = 0.5 × (D/S).
So, total travelling time = (D/S) + 0.5(D/S) = 1.5(D/S) = 60 min ⇒ D/S = 40 min.
Exact arrival time on home clock = 16:10 + 40 min = 16:50.
Village clock showed 16:40, i.e., 10 minutes slow.
Hence option (a) is correct.
Incorrect
Answer: (a)
Given that,
He started at 16:10 and reached home at 17:15. He stayed in the village for 5 minutes. The return route is 1.5 times the onward route, and the return speed is three times the onward speed.
Now,
Let onward speed be S km/h and onward distance be D km.
Total time taken = 17:15 − 16:10 = 1 h 5 min = 65 min.
Total travelling time = 65 − 5 = 60 min.
Return time = (1.5D)/(3S) = 0.5 × (D/S).
So, total travelling time = (D/S) + 0.5(D/S) = 1.5(D/S) = 60 min ⇒ D/S = 40 min.
Exact arrival time on home clock = 16:10 + 40 min = 16:50.
Village clock showed 16:40, i.e., 10 minutes slow.
Hence option (a) is correct.
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Question 2 of 5
2. Question
The monthly income of Anita and Beena are in the ratio 4 : 5.
Question: What is the ratio of their monthly savings?
Statement I: Beena saves 20% of her income.
Statement II: The expenditures of Anita and Beena are in the ratio 6 : 7.
Statement III: The difference in their monthly savings is ₹4,000.Which one of the following is correct?
Correct
Answer: (a)
Explanation:
Let incomes be:
Anita : Beena = 4x : 5xStatement I:
Beena saves 20% of income ⇒ Expenditure = 80% of 5x = 4x
⇒ Beena’s savings = 5x − 4x = 1xStatement II:
Expenditure ratio Anita : Beena = 6 : 7
Beena’s expenditure = 4x
⇒ Anita’s expenditure = (6/7) × 4x = 24x / 7Anita’s income = 4x
⇒ Anita’s savings = 4x − (24x/7) = (4x*7 − 24x)/7 = (28x − 24x)/7 = 4x / 7Now:
Savings ratio = Anita : Beena = (4x/7) : x = 4 : 7Thus, I and II together are sufficient
Statement III is not required to compute ratio.
Incorrect
Answer: (a)
Explanation:
Let incomes be:
Anita : Beena = 4x : 5xStatement I:
Beena saves 20% of income ⇒ Expenditure = 80% of 5x = 4x
⇒ Beena’s savings = 5x − 4x = 1xStatement II:
Expenditure ratio Anita : Beena = 6 : 7
Beena’s expenditure = 4x
⇒ Anita’s expenditure = (6/7) × 4x = 24x / 7Anita’s income = 4x
⇒ Anita’s savings = 4x − (24x/7) = (4x*7 − 24x)/7 = (28x − 24x)/7 = 4x / 7Now:
Savings ratio = Anita : Beena = (4x/7) : x = 4 : 7Thus, I and II together are sufficient
Statement III is not required to compute ratio.
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Question 3 of 5
3. Question
Two statements are given below followed by a question:
S1: The number is greater than one.
S2: The number has 3 factors.
Question: What is the number if it is a positive integer < 11?
Which one of the following is correct with respect to above?
Correct
Answer: D
Solution
The number is greater than one. So, possible numbers will be: 2, 3……10
Thus, there is no unique solution. Therefore, S1 alone is not sufficient to answer the question.
From S2: The number has 3 Factors. 4 and 9 are such numbers, which have only 3 factors. Thus, there is no unique solution.
Therefore, S2 alone is not sufficient to answer the question.
From S1 and S2: Even on combining S1 and S2, we are not able to find a unique solution.
Therefore, S1 and S2 together are not sufficient to answer the question
Incorrect
Answer: D
Solution
The number is greater than one. So, possible numbers will be: 2, 3……10
Thus, there is no unique solution. Therefore, S1 alone is not sufficient to answer the question.
From S2: The number has 3 Factors. 4 and 9 are such numbers, which have only 3 factors. Thus, there is no unique solution.
Therefore, S2 alone is not sufficient to answer the question.
From S1 and S2: Even on combining S1 and S2, we are not able to find a unique solution.
Therefore, S1 and S2 together are not sufficient to answer the question
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Question 4 of 5
4. Question
A father said to his son, “8 years ago, I was 4 times as old as you were. 8 years from now, I will be twice your age.”
What is the difference in their present ages?Correct
Answer: C
Let son’s present age = x
Father = x + d8 years ago:
x + d − 8 = 4(x − 8)
→ x + d − 8 = 4x − 32
→ d = 3x − 24 … (1)8 years ahead:
x + d + 8 = 2(x + 8)
→ x + d + 8 = 2x + 16
→ d = x + 8 … (2)Equating (1) and (2):
3x − 24 = x + 8 ⇒ 2x = 32 ⇒ x = 16
Then d = x + 8 = 24Incorrect
Answer: C
Let son’s present age = x
Father = x + d8 years ago:
x + d − 8 = 4(x − 8)
→ x + d − 8 = 4x − 32
→ d = 3x − 24 … (1)8 years ahead:
x + d + 8 = 2(x + 8)
→ x + d + 8 = 2x + 16
→ d = x + 8 … (2)Equating (1) and (2):
3x − 24 = x + 8 ⇒ 2x = 32 ⇒ x = 16
Then d = x + 8 = 24 -
Question 5 of 5
5. Question
Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Rivers are often viewed only as sources of water for irrigation, drinking, or hydropower, but their geographical role extends far beyond this. A river sustains entire ecosystems, recharges groundwater, transports fertile silt that renews floodplains, and shapes human settlements through centuries of interaction. However, excessive damming, pollution, and sand mining disrupt these natural processes. When a river’s flow is artificially altered, it affects not only aquatic biodiversity but also agriculture, soil fertility, and the livelihoods that depend on periodic flooding and silt deposition. Sustainable river management, therefore, requires recognising rivers as living systems that maintain a delicate balance between ecological function and human need.
Which one of the following statements best reflects the critical message conveyed by the author of the passage?
Correct
Answer: (b)
Explanation:
Option (a) is incorrect: The passage explicitly criticises viewing rivers merely as utilitarian sources of water or energy, warning that such a narrow view disrupts natural processes.
Option (b) is correct: The author’s main argument is that sustainable management “requires recognising rivers as living systems” and maintaining “a balance between ecological function and human need.” This captures both environmental and economic dimensions, reflecting a pragmatic and balanced message.
Option (c) is incorrect: The author does not advocate an absolute ban but calls for moderation and sustainability in human intervention.
Option (d) is incorrect: Although agriculture benefits from natural river processes, the passage does not claim exclusivity. Other factors like rainfall, soil type, and human management also matter.
Hence, option (b) best summarises the critical message.Incorrect
Answer: (b)
Explanation:
Option (a) is incorrect: The passage explicitly criticises viewing rivers merely as utilitarian sources of water or energy, warning that such a narrow view disrupts natural processes.
Option (b) is correct: The author’s main argument is that sustainable management “requires recognising rivers as living systems” and maintaining “a balance between ecological function and human need.” This captures both environmental and economic dimensions, reflecting a pragmatic and balanced message.
Option (c) is incorrect: The author does not advocate an absolute ban but calls for moderation and sustainability in human intervention.
Option (d) is incorrect: Although agriculture benefits from natural river processes, the passage does not claim exclusivity. Other factors like rainfall, soil type, and human management also matter.
Hence, option (b) best summarises the critical message.
