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- Question
A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Options- A. 220 km
- B. 224 km
- C. 230 km
- D. 234 km
- Correct Answer
- 224 km
Explanation(1/2)x + (1/2)x = 10 21 24 ⟹ x + x = 20 21 24 ⟹ 15x = 168 x 20
⟹ x = ❨ 168 x 20 ❩ = 224 km. 15
Time and Distance problems
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- 1. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
Options- A. 70 km/hr
- B. 75 km/hr
- C. 84 km/hr
- D. 87.5 km/hr Discuss
Correct Answer: 87.5 km/hr
Explanation:
Let the speed of two trains be 7x and 8x km/hr.Then, 8x = ❨ 400 ❩ = 100 4 ⟹ x = ❨ 100 ❩ = 12.5 8 ∴ Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
- 2. 3, 5, 7, 12, 17, 19
Options- A. 19
- B. 17
- C. 5
- D. 12 Discuss
Correct Answer: 12
Explanation:
Each of the numbers is a prime number except 12.- 3. 41, 43, 47, 53, 61, 71, 73, 81
Options- A. 61
- B. 71
- C. 73
- D. 81 Discuss
Correct Answer: 81
Explanation:
Each of the numbers except 81 is a prime number.- 4. 835, 734, 642, 751, 853, 981, 532
Options- A. 751
- B. 853
- C. 981
- D. 532 Discuss
Correct Answer: 751
Explanation:
In each number except 751, the difference of third and first digit is the middle one.- 5. 331, 482, 551, 263, 383, 362, 284
Options- A. 263
- B. 383
- C. 331
- D. 551 Discuss
Correct Answer: 383
Explanation:
In each number except 383, the product of first and third digits is the middle one.- 6. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
Options- A. 50 km
- B. 56 km
- C. 70 km
- D. 80 km Discuss
Correct Answer: 50 km
Explanation:
Let the actual distance travelled be x km.Then, x = x + 20 10 14 ⟹ 14x = 10x + 200
⟹ 4x = 200
⟹ x = 50 km.
- 7. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
Options- A. 1 hour
- B. 2 hours
- C. 3 hours
- D. 4 hours Discuss
Correct Answer: 1 hour
Explanation:
Let the duration of the flight be x hours.Then, 600 - 600 = 200 x x + (1/2) ⟹ 600 - 1200 = 200 x 2x + 1 ⟹ x(2x + 1) = 3
⟹ 2x2 + x - 3 = 0
⟹ (2x + 3)(x - 1) = 0
⟹ x = 1 hr. [neglecting the -ve value of x]
- 8. A car travelling with 5⁄7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.
Options- A.
17 6 km/hr 7 - B. 25 km/hr
- C. 30 km/hr
- D. 35 km/hr Discuss
Correct Answer: 35 km/hr
Explanation:
Time taken = 1 hr 40 min 48 sec = 1 hr 40 4 min = 1 51 hrs = 126 hrs. 5 75 75 Let the actual speed be x km/hr.
Then, 5 x x 126 = 42 7 75 ⟹ x = ❨ 42 x 7 x 75 ❩ = 35 km/hr. 5 x 126 - 9. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Options- A. 100 kmph
- B. 110 kmph
- C. 120 kmph
- D. 130 kmph Discuss
Correct Answer: 120 kmph
Explanation:
Let speed of the car be x kmph.Then, speed of the train = 150 x = ❨ 3 x ❩kmph. 100 2 ∴ 75 - 75 = 125 x (3/2)x 10 x 60 ⟹ 75 - 50 = 5 x x 24 ⟹ x = ❨ 25 x24 ❩ = 120 kmph. 5 - 10. An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1⅔ hours, it must travel at a speed of:
Options- A. 300 kmph
- B. 360 kmph
- C. 600 kmph
- D. 720 kmph Discuss
Correct Answer: 720 kmph
Explanation:
Distance = (240 x 5) = 1200 km.Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1⅔ hours as 5/3 hours]
∴ Required speed = ❨ 1200 x 3 ❩km/hr = 720 km/hr. 5
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