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- Question
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
- Correct Answer
- 120 kmph
ExplanationLet 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
Time and Distance problems
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- 1. 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 - 2. 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]
- 3. 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.
- 4. 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 - 5. 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.
- 6. 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 - 7. 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.
- 8. 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.
- 9. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Options- A. 35.55 km/hr
- B. 36 km/hr
- C. 71.11 km/hr
- D. 71 km/hr Discuss
Correct Answer: 71.11 km/hr
Explanation:
Total time taken = ❨ 160 + 160 ❩hrs. = 9 hrs. 64 80 2 ∴ Average speed = ❨ 320 x 2 ❩km/hr = 71.11 km/hr. 9 - 10. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options- A. 9
- B. 10
- C. 12
- D. 20 Discuss
Correct Answer: 10
Explanation:
Due to stoppages, it covers 9 km less.Time taken to cover 9 km = ❨ 9 x 60 ❩min = 10 min. 54
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