Time and Distance problems
- 1. A man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km /hr. Find the distance travelled on foot?
Options- A. 32
- B. 36
- C. 48
- D. 44 Discuss
Correct Answer: 32
- 2. 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.
- 3. 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 Discuss
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 |
- 4. 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.
- 5. 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]
- 6. 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 |
- 7. 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 |
- 8. 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 |
- 9. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:
Options- A. 14 km
- B. 15 km
- C. 16 km
- D. 17 km Discuss
Correct Answer: 16 km
Explanation:
Let the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
| So, | x | + | (61 -x) | = 9 |
| 4 | 9 |
⟹ 9x + 4(61 -x) = 9 x 36
⟹ 5x = 80
⟹ x = 16 km.
- 10. A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Options- A. 3.6
- B. 7.2
- C. 8.4
- D. 10 Discuss
Correct Answer: 7.2
Explanation:
| Speed = | ❨ | 600 | ❩m/sec. |
| 5 x 60 |
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
| = | ❨ | 2 x | 18 | ❩ | km/hr |
| 5 |
= 7.2 km/hr.
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