Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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Question 1 of 5
1. Question
Raj is rowing upstream from point A to point B, a distance of 40 km. He starts at a constant speed. Ten minutes later, a rescue boat leaves point A and overtakes him in 50 minutes.
Question: What is Raj’s rowing speed in still water?
Statement I: The speed of the current is 2 km/h.
Statement II: The rescue boat’s speed in still water is 10 km/h.Which one of the following is correct in respect of the Statements and the Question?
Correct
Answer: (c)
Explanation:
Let Raj’s still-water speed = km/h, and current speed = km/h.
Hence his upstream speed = .He starts from A; 10 minutes = 1/6 hour later, the rescue boat starts from A and overtakes him in 50 minutes = 5/6 hour.
Thus, the rescue boat travels for 5/6 hour, and Raj travels for 1 hour in total until the meeting point.
Let the meeting point be at a distance km from A.Then for Raj:
For the boat: , where is the boat’s effective speed (depends on current direction).Without knowing the current’s direction for the rescue boat (upstream or downstream) or its relation to Raj, we can’t solve for unless both the current speed (c) and rescue boat speed (v_b) are known.
- Statement I alone: gives , but not . → Not sufficient.
- Statement II alone: gives , but not . → Not sufficient.
- Together: and . Substituting, we can find using the ratio of times and distances. → Sufficient.
Incorrect
Answer: (c)
Explanation:
Let Raj’s still-water speed = km/h, and current speed = km/h.
Hence his upstream speed = .He starts from A; 10 minutes = 1/6 hour later, the rescue boat starts from A and overtakes him in 50 minutes = 5/6 hour.
Thus, the rescue boat travels for 5/6 hour, and Raj travels for 1 hour in total until the meeting point.
Let the meeting point be at a distance km from A.Then for Raj:
For the boat: , where is the boat’s effective speed (depends on current direction).Without knowing the current’s direction for the rescue boat (upstream or downstream) or its relation to Raj, we can’t solve for unless both the current speed (c) and rescue boat speed (v_b) are known.
- Statement I alone: gives , but not . → Not sufficient.
- Statement II alone: gives , but not . → Not sufficient.
- Together: and . Substituting, we can find using the ratio of times and distances. → Sufficient.
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Question 2 of 5
2. Question
In a conference, 50% of attendees are women. If 75% of total attendees are married couples, then which of the following statements is/are correct?
- All men are married.
- 25% of women are unmarried.
Correct
Answer: (b)
Explanation:
Let total attendees = 100.
→ Women = 50, Men = 50.
→ 75% (i.e., 75 people) are married ⇒ 37.5 couples.
So, 37.5 men and 37.5 women are married.
Unmarried: 12.5 men and 12.5 women.- All men married → False (only 75% married).
- 25% women unmarried → True (12.5 of 50).
Incorrect
Answer: (b)
Explanation:
Let total attendees = 100.
→ Women = 50, Men = 50.
→ 75% (i.e., 75 people) are married ⇒ 37.5 couples.
So, 37.5 men and 37.5 women are married.
Unmarried: 12.5 men and 12.5 women.- All men married → False (only 75% married).
- 25% women unmarried → True (12.5 of 50).
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Question 3 of 5
3. Question
A café sells n cups of coffee at ₹p each. To boost sales, the price was cut by 25%, and the number sold rose by 40%. What is the total revenue on that day?
Correct
Answer: (c)
Explanation:
Reduced price = 0.75 p; new quantity = 1.4 n.
Revenue = 1.4 n × 0.75 p = 1.05 np.
Hence, revenue increased by 5%. Option (c) is correct.Incorrect
Answer: (c)
Explanation:
Reduced price = 0.75 p; new quantity = 1.4 n.
Revenue = 1.4 n × 0.75 p = 1.05 np.
Hence, revenue increased by 5%. Option (c) is correct. -
Question 4 of 5
4. Question
The average weight of three friends A, B, and C is 53 kg. Another friend D joins them, and the new average becomes 55 kg. If another person E, whose weight is 2 kg more than D, replaces A, then the average weight of B, C, D, and E becomes 58 kg. What is the weight of A?
Correct
Answer: (a)
Solution:
Average of A, B, C = 53 → A + B + C = 159
With D, average = 55 → A + B + C + D = 220 → D = 220 – 159 = 61
E = D + 2 = 63
Now, B + C + D + E = 58 × 4 = 232
So, B + C + 61 + 63 = 232 → B + C = 108
From A + B + C = 159 → A = 159 – 108 = 51Incorrect
Answer: (a)
Solution:
Average of A, B, C = 53 → A + B + C = 159
With D, average = 55 → A + B + C + D = 220 → D = 220 – 159 = 61
E = D + 2 = 63
Now, B + C + D + E = 58 × 4 = 232
So, B + C + 61 + 63 = 232 → B + C = 108
From A + B + C = 159 → A = 159 – 108 = 51 -
Question 5 of 5
5. Question
Classes A and B have 28 and 32 students respectively. In Class-A, scores range from 40 to 72. In Class-B, scores range from 55 to 70. Three students are shifted from Class-A to Class-B.
Consider the following statements:
- The average score of Class-B will definitely increase.
- The average score of Class-A will definitely decrease.
Which of the following is correct with respect to above?
Correct
Answer: (d)
Solution:
The ranges overlap (A has some scores below 55 and some above 70; B is 55–70). If the three shifted from A happen to be high (e.g., 70–72), B’s average may increase; if they are low (e.g., near 40), B’s average may decrease. So Statement 1 is not definite.
For Class-A, removing high scorers would decrease A’s average, but removing low scorers would increase it. So Statement 2 is also not definite.Hence, option (d) is correct.
Incorrect
Answer: (d)
Solution:
The ranges overlap (A has some scores below 55 and some above 70; B is 55–70). If the three shifted from A happen to be high (e.g., 70–72), B’s average may increase; if they are low (e.g., near 40), B’s average may decrease. So Statement 1 is not definite.
For Class-A, removing high scorers would decrease A’s average, but removing low scorers would increase it. So Statement 2 is also not definite.Hence, option (d) is correct.
