Time and Distance problems
- 1. A car reached Raipur from sonagarh in 35 min with an average speed of 69 km/h. If the average speed is increased by 36 km/h, how long will it take to cover the same distance?
Options- A. 24 min
- B. 27 min
- C. 23 min
- D. 29 min Discuss
Correct Answer: 23 min
Explanation:
Distance between Sonagarh and Raipur = Average speed x time
= 69 x (35/60) km = 161/4 km
New speed = (69 + 36) km/h = 105 km/h
? Required time = Distance/speed
= 161/(4 x 105) h
= (161 x 60)/(4 x 105) min
= 23 min
- 2. A student walks from his house at 2 1/ 2 km/h and reaches his school late by 6 min. Next day, he increase his speed by 1 km/h and reaches 6 min before school time. How far is the school form his house?
Options- A. 5/4 km
- B. 7/4 km
- C. 9/4 km
- D. 11/4 km Discuss
Correct Answer: 7/4 km
Explanation:
Let the required distance = L
According to the question,
L/(5/2) - L/(7/2) = 12/60 (difference between two times = 6 + 6 =12 min)
? 2L/5 - 2L/7 = 1/5
? 14L - 10L = 7
? 4L = 7
? L = 7/4 km
- 3. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman, chases him. The thief and the policeman run at rate of 10 km/h and 11 km/h, respectively. The distance between them after 6 min will be?
Options- A. 100 m
- B. 180 m
- C. 150 m
- D. 125 m Discuss
Correct Answer: 100 m
Explanation:
Relative speed of policeman with respect to thief = ( 11 - 10 ) = 1 km/h.
Now, relative distance covered by policeman in 6 min = Speed x Time
= (1 x 6)/60 = 1/10 km = 100 m
The distance between the policeman and thief after 6 min = (200 - 100) = 100 m
- 4. A truck covers a distance of 368 km at a certain speed in 8 h. How much time would a car take at an average speed which is 18 km/h more than that of the speed of the truck to cover a distance which is 16 km more than that travelled by the truck?
Options- A. 7 h
- B. 5 h
- C. 6 h
- D. 8 h Discuss
Correct Answer: 6 h
Explanation:
Speed of truck = Distance/time = 368/8 = 46 km/h
Now, speed of car = (speed of truck + 18) km/h = (46 + 18) = 64 km/h and
Distance travelled by car = 368 + 16 = 384 km
? Time taken by car = Distance/Speed = 384/64 h = 6 h
- 5. Shantanu drives a motorcycle and covers a distance of 715 km at a constant speed.
If the speed of the motorcycle had been 10 km/h more, he would have taken 2 h less to cover the same distance. What is the original speed of the motorcycle?
Options- A. 65 km/h
- B. 55 km/h
- C. 60 km/h
- D. 36 km/h Discuss
Correct Answer: 55 km/h
Explanation:
Let the constant speed = V
According to the question,
715/V - 715/(V + 10) = 2
? 1/V - 1/(V + 10) = 2/715
? [(V + 10) - V] / [V(V + 10)] = 2/715
? V2 + 10V = 10 x 715/2
? V2 + 10V - 3575 = 0
? V2 + 65V - 55V - 3575 = 0
? V(V + 65) - 55(V + 65) = 0
? (V - 55) (V + 65) = 0
? V = 55 or V = - 65
Ignoring the negative value, we get V = 55
? Original speed of the motorcycle = 55 km/h
- 6. The ratio of speeds of a train and a car is 16 : 15 , respectively and a bus covered a distance of 480 km in 8h. The speed of the bus is 3/4th of the speed of train. What will be covered by car in 6 h?
Options- A. 450 km/h
- B. 480 km/h
- C. 360 km/h
- D. Couldn't be determined Discuss
Correct Answer: 450 km/h
Explanation:
Let speed of train = 16k
Speed of car = 15k
Speed of bus = 480/8 = 60 km/h
According to the question,
16k = 60 x 4/3 = 80
? k = 5
? Speed of car = 15k = 15 x 5 = 75 km/h
? Required distance = Speed x Time
= 75 x 6 = 450 km
- 7. Sumit drove at the speed of 45 km/h from home to a resort, returning over the same route, he got stuck in traffic and took an hour longer. Also, he could drive only at the speed of 40 km/h. How many kilometers did he drive each way?
Options- A. 250 km
- B. 360 km
- C. 375 km
- D. None of these Discuss
Correct Answer: 360 km
Explanation:
Let distance he drove be L.
Using Time = Distance/speed
From given condition. L/40 - L/45 = 1
? (45L - 40L)/(40 x 45) = 1
? 5L = 40 x 45
? L = 360 km
- 8. A car runs at the speed of 40 km/h when not serviced and runs at 65 km/h when serviced. After servicing, the car covers a certain distance in 5 h. How much approximate time will the car take to cover the same distance when not serviced?
Options- A. 10 h
- B. 7 h
- C. 12 h
- D. 8 h Discuss
Correct Answer: 8 h
Explanation:
When serviced, the distance covered by the car = 65 x 5 = 325 km.
When not serviced, the time taken by the car to cover 325 km at 40 km/h
= 325/40 = 8.125 = 8 h (approx)
- 9. The ratio between the rates of travelling of A and B is 2 : 3 and therefore A takes 20 min more than time taken by B to reach a destination. If A had walked at double the speed, how long would he have taken to cover the distance?
Options- A. 30 min
- B. 35 min
- C. 20 min
- D. 45 min Discuss
Correct Answer: 30 min
Explanation:
We know that speed is inversely proportional to time.
Therefore, Time taken by A : Time taken by B = 1/2 : 1/3
Let B takes T min. Then, A takes (T + 20) min.
? (T + 20) : T = 1/2 : 1/3 = 3 : 2
? (T + 20)/T = 3/2
? 2T + 40 = 3T
? T = 40
? A takes (T + 20) = (40 + 20) = 60 min.
? At double the speed, A would have covered it in 30 min.
- 10. A car travels a distance of 75 km at the speed of 25 km/h. It covers the next 25 km of its journey at the speed of 5 km/h and the last 50 km of its journey at the speed of 25 km/h. What is the average speed of the car?
Options- A. 40 km/h
- B. 25 km/h
- C. 15 km/h
- D. 12.5 km/h Discuss
Correct Answer: 15 km/h
Explanation:
Time taken to cover first 75 km = 75/25 = 3 h
Time taken to cover next 25 km = 25/5 = 5 h
Time taken to cover last 50 km of its journey = 50/25 = 2 h
Total distance = 75 + 25 + 50 = 150 km
Total time taken = 3 + 5 + 2 = 10 h
? Required average speed = Total distance / Total time taken
= 150/10 = 15 km/h
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