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

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

(a) -1
(b) 0
(c) 1
(d) 2

Correct Answer: (d) 2

Solution:x + 1/x = 2 ⇒ x² -2x +1

(x - 1)² = 0 ⇒ x = 1

Now ,

(x)³² + 1/(x)³² = (1)³² + 1/(1)³² = 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?

(a) ₹375
(b) ₹400
(c) ₹425
(d) ₹450

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?

(a) 9 8/15 days
(b) 10 1/15 days
(c) 10 14/25 days
(d) 11 1/10 days

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?

(a) 10 1/3 minutes
(b) 10 2/5 minutes
(c) 10 4/5 minutes
(d) 11 2/3 minutes

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?

(a) 4 hours 40 minutes
(b) 4 hours 55 minutes
(c) 5 hours 5 minutes
(d) 5 hours 15 minutes

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?

(a) 8.6%
(b) 9.8%
(c) 10.7%
(d) 12%

Correct Answer: (c) 10.7%

Solution:

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

(a) 6.33
(b) 7.66
(c) 9.33
(d) 11.55

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?

(a) 6
(b) 15
(c) 30
(d) 40

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 in12 seconds. What is the length of the train and that of the platform, respectively?

(a) 160 m and 153.33 m
(b) 170 m and 166.66 m
(c) 180 m and 153.33m
(d) 180 m and 170 m

Correct Answer: (c) 180 m and 153.33m

10. In a partnership firm, A invests 1/6th of the total investment for 1/6th of the tenure. B invests 1/3rd of the total investment for 1/3rd 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?

(a) ₹30,00,000
(b) ₹32,00,000
(c) ₹34,00,000
(d) ₹36,00,000

Correct Answer: (d) ₹36,00,000

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

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

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?

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?

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?

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?

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

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?

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 in12 seconds. What is the length of the train and that of the platform, respectively?

10. In a partnership firm, A invests 1/6th of the total investment for 1/6th of the tenure. B invests 1/3rd of the total investment for 1/3rd 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?

Related Posts