Time and Distance problems
- 1. Two cars A and B are running towards each other from two different place 88 km apart. If the ratio of the speeds of the cars A and B is 5:6 and the speeds of the cars B is 90 km/h, after what time will they meet each other?
Options- A. 38 min
- B. 39 min
- C. 45 min
- D. 32 min Discuss
Correct Answer: 32 min
Explanation:
Let speed of A = 5x
Then, spend of B = 6x
Given that,speed of B = 6x = 90
? x = 90/6 = 15
? Speed of A = 5x = 5x = 5 x 15 = 75 km/h
Let A and B meet after T h. Then,
75 x T + 90 x T =88
? T = 88/165 h = (88 x 60)/165 = 32 min
- 2. A car starts running with the initial speed of 40 km/h with its speed increasing every hour by 5 km/h. How many hours will it taken to cover a distance of 385 km?
Options- A. 81/2 h
- B. 91/2 h
- C. 9 h
- D. 7 h Discuss
Correct Answer: 7 h
Explanation:
Required number of hours is the number of terms of the series 40 + 45 + 50 +... as speed increases every hour.
Given, sum of the series is 385
? a = 40, d=5, s = 385 and n= ?
Using S = n/2[2a + (n - 1)d]
? 385 = n/2[80 + 5n - 5]
? 770 = 5n2 + 75n
? n2 + 15n - 154 = 0
? n2 + 22n - 7n - 154 = 0
? n(n + 22) - 7(n + 22) = 0
? (n + 22) (n - 7) = 0
? n = 7
Remaining part = 1/12 - 1/20 = (5 - 3)/60 = 2/60 = 1/30 i.e., 1/30 th part is filled by B in 1 min
Hence, required time to fill the whole tank = (165 + 1 + 1) min = 167 min
- 3. An express train travelled at an average speed of 100 km/h, stopping for 3 min after every 75 km. A local train travelled at a speed of 50 km/h, stopping for 1 min after every 25 km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time in which the express train travel 600 km?
Options- A. 400 km
- B. 405 km
- C. 307.25 km
- D. 415.5 km Discuss
Correct Answer: 307.25 km
Explanation:
Time taken by express train to cover 75 km including stoppage
= (60 / 100 x 75) min + = 48 min
Time taken by express train to cover 600 km.
= Time taken by it to cover 75 km
= (48 / 75 x 525 ) min + (60 / 100 x 75 ) min
= (336 + 45) min = 381
Time taken by local train to9 cover 25 km including stoppage
= (60 / 50 x 25) min + 1 min = 31 min
In 31 min, distance covered = 25 km
In(31 x 12) min. distance covered
= (25 / 31 x 31 x 12 ) = 300 km
In last 9 min, distance covered
= (25 / 31 x 9 ) = 7.25 km
? Required total distance
= 300 + 7.25 = 307.25 km
- 4. A student goes to his school from his house walking at 4 km/h and reaches his school 10 min late. Next day, starting at the same time he walks as 6 km/h and reaches his school 5 min earlier than the scheduled time. Find the distance between school and home?
Options- A. 2 km
- B. 3 km
- C. 4 km
- D. 5 km Discuss
Correct Answer: 3 km
Explanation:
Let the distance be x km.
? Time = Distance/speed
1st day time taken = x/4 h
2nd day time taken = x/6 h
Difference in time = (x/4 - x/6) h
Actual difference between these two times = 15 min = 1/4 h
? x/4 - x/6 = 1/4 ? (3x - 2x)/12 = 1/4
? x = 3 km
- 5. Two train of length 250 m and 140 m are running on parallel lines in the same direction at 58 km/h and 32 km/h, respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options- A. 58 s
- B. 54 s
- C. 52 s
- D. 48 s Discuss
Correct Answer: 54 s
Explanation:
Relative speed = (58 - 32) = 26 km/h
= (26 x 5/18) m/s = 65/9 m/s
Time taken to cross each other = (250 + 140)/(65/9)
= (390 x 9)/65 = 54 s
- 6. A person travelled a distance of 50 km in 8 h. He covered a part of the distance on foot at the rate of 4 km/h and a part on a bicycle at the rate of 10 km/h. How much distance did he travel on foot?
Options- A. 10 km
- B. 20 km
- C. 30 km
- D. 40 km Discuss
Correct Answer: 20 km
Explanation:
Let T h, he travels on foot.
? 4T + 10(8 - T) = 50
? 80 - 6T = 50
? 6T = 30,
? T = 5 h
? The distance travelled on foot = 4 x 5 = 20 km
- 7. Total time taken by a person in going to a place by walking and returning on cycle is 5 h 45 min. He would have gained 2 h by cycling both ways. The time taken by him to walk both ways, is?
Options- A. 6 h 45 min
- B. 7 h 45 min
- C. 8 h 15 min
- D. 8 h 30 min Discuss
Correct Answer: 7 h 45 min
Explanation:
Walking time + Cycling time = 5 h 45 min = 345 min ....(i)
If he had cycled both way he would have gained 2 h (120 min).
? 2 x Cycling time = 345 - 120 = 225 min ...(ii)
Walking time = 2 x 345 - 225 = 690 - 225 = 465 min
Time taken by him to walk both ways = 7 h 45 min
- 8. Amit start from a point A and walks to another point B and then return from B to A by his car and thus takes a total time of 6 h 45 min. If he had driven both ways in his car, he would have taken 2 h less. How long would it take for him to walk both ways?
Options- A. 7 h 45 min
- B. 8 h 15 min
- C. 8 h 30 min
- D. 8 h 45 min Discuss
Correct Answer: 8 h 45 min
Explanation:
Let w be the time taken in one way by walking and c be the time taken in one way by car.
Now, according to the question,
In first case, w + c = 6 h 45 min
or
2w + 2c = 13 h 30 min ..(i)
In second case, 2c = 4 h 45 min ....(ii)
From Eqs. (i) and (ii), we get
2w + 2c = 13 h 30 min
? 2w + 4h 45 min = 13 h 30 min
? 2w = 13 h 30 min - 4 h 45 min
? 2w = 8 h 45 min
? If he walks both ways, then time taken = 8 h 45 min
- 9. Two cars X and Y starts from two places A and B respectively which are 700 km apart at 9 am. Both the cars run at an average speed of 60 km/h, Car X stops at 10 am and again starts at 11 am, while the other car Y continues to run without stopping. When do the two cars cross each other?
Options- A. 2 : 40 pm
- B. 3 : 20 pm
- C. 4 : 10 pm
- D. 4 : 20 pm Discuss
Correct Answer: 3 : 20 pm
Explanation:
Since, the speed of X and Y are 60 km/h each. The distance between A and B is 700 km. Distance traveled by X upto 11 am is 60 km. Since, X stops at 10 am and distance traveled by up to 11 am is 120 km.
Now, the distance between them = 700 - 180 = 520 km
Now, let they will meet at a distance of x km from X's position.
? Distance traveled by X = x km
and distance traveled by Y = (520 - x) km
? x/60 = (520 - x)/60
? 2x = 520
? x = 260
? T = 260/60 = 41/3 h
Thus, they will cross each other after, 41/3 h after 11 am i.e., at 3 : 20 pm.
- 10. A car covers a distance from town A to town B at the speed of 58 km/h and covers the distance from town B to town A at the speed of 52 km/ h. What is the Approximate average speed of the car?
Options- A. 55 km/h
- B. 52 km/h
- C. 48 km/h
- D. 60 km/h Discuss
Correct Answer: 55 km/h
Explanation:
We know that, if two equal distances are covered at two different speeds A and B, then
Average speed = 2AB/(A + B) = (2 x 58 x 52)/(58 + 52)
= 54.8 km/h
= 55 km/h (Approx)
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