Time and Distance problems
- 1. The ratio between the speeds of two cares is 7 : 8. If the 2nd car runs 200 km in 5 h, then find the speed of the 1st car.?
Options- A. 25 km/h
- B. 28 km/h
- C. 40 km/h
- D. 35 km/h Discuss
Correct Answer: 35 km/h
Explanation:
Let speed of the 1st car = 7k
and speed of the 2nd car = 8k
According to the question,
8k = 200/5 = 40 [ using, speed = Distance/ Time ]
? k = 40/8 = 5
? Speed of the 1st car = 7k
= 7 x 5 = 35 km/h
- 2. The ratio between the speeds of two buses is 5 : 3. If the 1st bus runs 400 km in 8 h, then find the speed of the 2nd bus.?
Options- A. 30 km/h
- B. 15 km/h
- C. 27 km/h
- D. 37 km/h Discuss
Correct Answer: 30 km/h
Explanation:
Let speed of 1st bus = 5k
and speed of 2nd bus = 3k
According to the question,
5k = 400/8 = 50
? k = 50/5 = 10
? Speed of 2nd bus = 3k = 3 x 10 = 30 km/h
- 3. The speeds of three cars are in the ratio of 2 : 3 : 5 find the ratio of the time taken by the above cars to travel the same distance.?
Options- A. 15 : 10 : 6
- B. 6 : 10 : 15
- C. 10 : 15 : 6
- D. 10 : 6 : 15 Discuss
Correct Answer: 15 : 10 : 6
Explanation:
We know that speed and time are inversely proportional.
? Ratio of time taken = 1/2 : 1/3 : 1/5
= 30/2 : 30/3 : 30/5 [ LCM of 2, 3, 5 = 30 ]
= 15 : 10 : 6
- 4. Nilu covers a distance by walking for 6 h. While returning, his speed decreases by 2km/h and he takes 9 h to cover the same distance. What was her speed while returning?
Options- A. 2 km/h
- B. 5 km/h
- C. 4 km/h
- D. 7 km/h Discuss
Correct Answer: 4 km/h
Explanation:
Let the speed in return journey = x
According to the question,
6( x + 2 ) = 9x
? 6x + 12 = 9x
? 9x - 6x = 12
? 3x = 12
? x = 12/3 = 4km/h
- 5. A takes 4 h more than the time taken by B to walk D km. If A doubles his speed, he can make it in 2 h less than that of B. How much time does B require for walking D km?
Options- A. 8 h
- B. 4 h
- C. 6 h
- D. 9 h Discuss
Correct Answer: 8 h
Explanation:
Let B takes x h to walk D km.
Then, A takes ( x + 4 ) h to walk D km.
With doube of the speed,
A will take ( x+ 4)/2 h.
According to the question,
x - (x + 4)/2 = 2
? 2x - (x + 4) = 4
? 2x - x - 4 = 4
? x = 4 + 4 = 8 h
- 6. If Sohail walks from his home to office at 16 km/h, he is late by 5 min. If he walks at 20 km/h, he reaches 10 min before the office time. Find the distance of his office from his house.
Options- A. 22 km
- B. 20 km
- C. 18 km
- D. 16 km Discuss
Correct Answer: 20 km
Explanation:
Let required distance = L
According to the question,
L/16 - L/20 = 15/20
? (5L - 4L)/80 = 1/4
? L = (1/4) x 80 = 20 km
- 7. Walking with 3/4 of his usual speed, Sachin covers a certain distance in 2 h more than the time he takes to cover the distance at his usual speed. Find the time taken by him to cover this distance with usual speed.
Options- A. 5 h
- B. 6 h
- C. 9 h
- D. 4 h Discuss
Correct Answer: 6 h
Explanation:
Let th distance = D
and usual speed = V
According to the question,
D/(3V/4) - D/V = 2
? D/V = 3 x 2 = 6
Time taken to cover the distance with usual speed = 6 h
- 8. A car covers a distance of 200 km in 2 h 40 min whereas a jeep covers the same distance in 2 h. What is the ratio of their speeds?
Options- A. 3 : 4
- B. 4 : 3
- C. 4 : 5
- D. 5 : 4 Discuss
Correct Answer: 3 : 4
Explanation:
Speed of car = Distance/Time = 200/240/60
= 600/8 = 75 km/h
Speed of jeep = 200/2 = 100 km/h
? Required ratio = 75/100 = 3/4 3 : 4
- 9. Amit walks at a uniform speed of 4 km/h and 4 h after his start, Brijesh cycles after him at the uniform rate of 20 km/h. How far from the starting point will Brijesh catch Amit?
Options- A. 15 km
- B. 18 km
- C. 13d km
- D. 20 km Discuss
Correct Answer: 20 km
Explanation:
Let Brijesh Catches Amit after x h.
Then, distance travelled by Amit in (x + 4) h = Distance travelled by Brijesh in x h.
According to the question,
4(x + 4) = 20 x
? 4x + 16 = 20x
? 16x = 16
? x = 16/16 = 1
Distance travelled by Brijesh in1h = 1 x 20 = 20 km
- 10. A train travel at the rate of 50 km/h without stoppages and it travels at 40 km/h with stoppages. How many minutes does the train stop on an average per hour?
Options- A. 6 min
- B. 12 min
- C. 18 min
- D. 14 min Discuss
Correct Answer: 12 min
Explanation:
Due to stoppages, it covers 10 km less per hour.
Time taken to cover 10 km = (10/50) x 60 = 12 min
Hence, the train stops on an average 12 min per hour.
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