CAPF (AC) 2024 (Paper-1) (Questions 51-100)

Total Questions: 50

1. If x + ¹⁄ₓ = 2, then which one of the following is the value of x³² + ¹⁄ₓ³² ?

Correct Answer: (d) 2
Solution:

x + ¹⁄ₓ = 2 ⇒ x² -2x +1
(x - 1)² = 0 ⇒ x = 1
Now ,
(x)³² + 1/x³² = 1³² + 1/1³² = 2

2. A Shopkeeper sold a product at 30% loss. Had his selling price been ₹150 more, he would have made a profit of 10%. What was the cost price?

Correct Answer: (a) ₹ 375
Solution:

Let C .P. = x.
S.P. = x × (100 - 30)/100) = 0.7x.
ATQ, x × (100 + 10)/100) - 0.7x = 150
1.1x - 0.7x = 150
x = 150/0.4 = ₹ 375

3. A, B and C can finish a work in 20, 25 and 30 days, respectively. They start working together but B quits after working for 3 days. In how many days from the start shall the work be completed?

Correct Answer: (c) 10 ¹⁴⁄₂₅ days
Solution:

L.C.M. of 20, 25 and 30
= 5 × 5 × 12 = 300 units
A's efficiency = 300/200 = 15 units.
B's efficiency = 300/25 = 12 units
C's efficiency = 300/30= 10 units.
Work finished in 3 days = 3 × (15 + 12 + 10) = 111
Remaining units = 300 - 111 = 189 units
Time taken by (A + C) to complete
remaining work = 189/(15+10) = 7 ¹⁴⁄₂₅
∴ Total time required = 3 + 7 ¹⁴⁄₂₅ = 10 ¹⁴⁄₂₅

4. Two taps A and B can fill a tank with water in 20 minutes and 15 minutes, respectively. A third tap C can empty the full tank in 6 minutes. After the taps A and B fill the tank for 5 minutes, the tap C is opened to empty while A and B continue to fill it. In how many minutes after the start shall the tank get empty?

Correct Answer: (d) 11 ²⁄₃ minutes
Solution:

5. A and B start at the same time to reach the same destination. B travelled at 5/7 of A's speed and reached the destination 1 hour 20 minutes after A. What was the time taken by B to reach the destination?

Correct Answer: (a) 4 hours 40 minutes
Solution:

6. There was a hike in petrol price by 12%. By how much percentage should a person decrease his petrol consumption such that there is no change in his expenditure on petrol?

Correct Answer: (c) 10.7%
Solution:

7. If 19a + 19b + 19c = 437, then what is the mean of a, b and c?

Correct Answer: (b) 7.66
Solution:

8. Out of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers can be formed without repetition of digits?

Correct Answer: (c) 30
Solution:

Total number of digits = 6
Number of digits selected at a time = 2
∴  Total number of number = ⁶P₂ = 6 × 5 = 30

9. A train travelling at a speed of 60 km/hr crosses a platform in 20 seconds. The same train crosses a person who is walking at a speed of 6 km/hr in the same direction as that of the train in 12 seconds. What is the length of the train and that of the platform, respectively?

Correct Answer: (c) 180 m and 153.33m
Solution:

10. In a partnership firm, A invests ⅙ th of the total investment for ⅙ th of the tenure. B invests ⅓ rd of the total investment for ⅓ rd of the tenure while C invests the remaining part for the full duration. Out of total profit of ₹46,00,000, what shall be C's share?

Correct Answer: (d) ₹36,00,000
Solution: