TIME AND DISTANCE ONLINE TEST

1. Walking at the rate of 4kmph a man covers certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in.

A.12
B.30
C.40
D.60
E.64

2. 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?

A.4
B.6
C.8
D.10
E.12

3. 2 trains starting at the same time from 2 stations 200km apart and going in opposite direction cross each other at a distance of 110km from one of the stations. What is the ratio of their speeds?

A.11:9
B.19:11
C.1:2
D.2:1
E.10:11

4. A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey in not more than 40min will be.

A.45
B.50
C.54
D.60
E.75
F.80
G.90

5.Sachin can cover a distance in 1hr 24min by covering 2/3 of the distance at 4 kmph and the rest at 5kmph.the total distance is(Enter only the numeric value in kms)?

6.Walking at 3/4 of his usual pace, a man reaches his office 20 minute late. Find his usual time?

A.1hr
B.1.5hr
C.2hr
D.2.5hr
E.3hr

7. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:

A.2/5
B.3/4
C.4/9
D.5/11
E.6/13
F.8/15
G.9/17

8. A monkey tries to ascend a greased pole 14 m high. It ascends 2m in first two minutes and slips 1m in alternate minute. If it continues to ascend in this fashion, how long does it take to reach the top?

A.22
B.24
C.25
D.26
E.28

9. Two boys begin together to write out a booklet containing 535 lines. The first boy starts with the first line, writing at the rate of 100 lines an hour; and the second starts with the last line then writes line 534 and so on, backward proceeding at the rate of 50 lines an hour. At what line will they meet?

A.257
B. 277
C.327
D.357
E.377

10. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

A.7
B.8
C.9
D.10
E.12
F.15
G.17

11. A man and a woman 81 miles apart from each other, start travelling towards each other at the same time. If the man covers 5 miles per hour to the women's 4 miles per hour, how far will the woman have travelled when they meet?(Enter numeric value in kms)

12. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:

A. 2
B. 3
C. 4
D. 5
E. 6

13.A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?

A. 240
B. 360
C. 420
D. 600
E. 720

14.A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds. What is the length of the train in meters?

A. 200
B. 360
C. 400
D. 600
E. 720

15. Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph?

A. 25
B. 32.5
C. 37.5
D. 42.5
E. 47.5

16. A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?

A. 25
B. 30
C. 35
D. 45
E. 50

17.Jane covered a distance of 340 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?

A. 1hr
B. 2hr 30min
C. 3hr
D. 3hr 30min
E. 5hr

18. Steve traveled the first 2 hours of his journey at 40 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?

A. 54mph
B. 60mph
C. 64mph
D. 72mph
E. 75mph

19. John drove home to Jake’s house at 60 miles per hour. Returning over the same route, the traffic caused him to slow down to 40 miles per hour. If the return trip took 1 hour longer, how many miles did he drive each way?

A. 60
B. 80
C. 100
D. 120
E. 180

20.A car travels at one speed for 4 hours, and then at twice that speed for 6 hours. The average velocity for the whole 10 hour trip is 40 mph. Find the initial speed in mph.

A. 25
B. 30
C. 35
D. 40
E. 50

Explanation for Question1:Walking at the rate of 4kmph a man cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in.
Answer – (C) Solution: s₁t₁=s₂t₂
2hr45min=11/4hrs
4 X 11/4=16.5Xt==> t=2/3hr=40min.

Explanation for Question2: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? Answer – (D) Solution: Due to stoppages, it covers 9 km less. Time taken to cover 9 km =(9/54)×60 min = 10 min.

Explanation for Question3:2 trains starting at the same time from 2 stations 200km apart and going in opposite direction cross each other at a distance of 110km from one of the stations. What is the ratio of their speeds?
Answer – (A) Solution: In same time, they cover 110km and 90 km respectively. For the same time speed and distance is inversely proportional. so ratio of their speed =110:90= 11: 9

Explanation for Question 4: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey in not more than 40min will be. Answer-DEFG Solution:
To cover the distance in 40 min. it has to travel at speed 60KMPH.
Answers will be greater than or equalto 60.

Explanation for Question 5:Sachin can cover a distance in 1hr 24min by covering 2/3 of the distance at 4 kmph and the rest at 5kmph.the total distance is? Answer:6
Solution: Total time =(D₁/S₂)+ (D₂/S₂)
Asume total disrance is 3X.
D₁=2X,D₂X.Given S₁=4,S₂=5.
after simplification X=2 => 3X=6

Explanation for Question 6:Walking at 3/4 of his usual pace, a man reaches his office 20 minute late. Find his usual time?
Answer – (A)Solution:Let the original speed be S and time be T s₁t₁=s₂t₂
s₁=S,t₁=T
s₂=(3/4)S,t₂=(4/3)T.
given t₂=t₁+20.
i.e (4/3)T-T=20.
⇒T=60min=1hr.

Explanation for Question 7:

7. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:

Answer: 3/4

Explanation for Question8:A monkey tries to ascend a greased pole 14 m high. He ascends 2 m in first two minutes and slips 1 m in alternate minute. If he continues to ascend in this fashion, how long does he take to reach the top?
Answer – C
Solution:In every two minutes itis able to ascend 1m. In this fashion he ascends up to 12m because when he reaches at the top he does not slip down. Thus, up to 12m it takes 12×2 = 24 min. and for the last 2m it takes 1min Therefore, total time taken by it is 24+1= 25 min to reach the top.

Explanation for Question9:Two boys begin together to write out a booklet containing 535 lines. The first boy starts with the first line, writing at the rate of 100 lines an hour; and the second starts with the last line then writes line 534 and so on, backward proceeding at the rate of 50 lines an hour. At what line will they meet? Answer-D
Solution:Writing ratio =100:50=2:1
Since equal quantities are taken,Therefore in a given time, first boy will be writing the line number (2/3)×535=356.66 ⇒ 357th line

Explanation for Question 10:Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15kmph. At what speed must he travel to reach A at 1 P.M.?
Answer is 12.
Solution:
He has to travel the distance with speed morethan 10kmph and less than 15kmph. There is only one option lies in between the given two speeds.

Explanation for Question 11:A man and a woman 81 miles apart from each other, start travelling towards each other at the same time. If the man covers 5 miles per hour to the women's 4 miles per hour, how far will the woman have travelled when they meet?
Answer – 36
Solution:Time taken to meet=(Distance between them)/(Relative speed)=81/(4+5)=9 hours
Therefore, woman travels =9×4=36 miles

Explanation for Question 12:
In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Answer:
SOLUTION: let Abhay's speed be "a", and Sameer's speed be "s". Then according to the given information 30/a-30/s=2--------->1
and 30/s-30/2a=1-------->2
add equations 1 and 2 we will get
30/a-30/2a=3==>a=5

Explanation for Question 13:A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
Explanatory Answer
the train covers platform in 30 s
the train covers its own length in 18 s
i.e the train covers only platform in 12 s
72kmph=20m/s
then the length of the platform is 20X12=240mts

Explanation for Question 14:A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds. What is the length of the train in meters?
Explanatory Answer
relative speed=100-64=36kmph=10m/sec.
length of the train = 10x40=400 meters.

Explanation for Question 15
Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph?
Explanatory Answer
Average speed = Total distance / Total Time Total distance traveled by Jim = Distance covered in the first 3 hours + Distance covered in the next 5 hours. Distance covered in the first 3 hours = 3 * 60 = 180 miles Distance covered in the next 5 hours = 5 * 24 = 120 miles Therefore, total distance traveled = 180 + 120 = 300 miles. Total time taken = 3 + 5 = 8 hours. Average speed =300/8 = 37.5 mph.

Explanation for Question 16:A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?
Explanatory Answer A runs 25% as fast as B. That is, if B runs 100m in a given time, then A will run 125m in the same time In other words, if A runs 5m in a given time, then B will run 4m in the same time. Therefore, if the length of a race is 5m, then A can give B a start of 1m so that they finish the race in a dead heat. Start : length of race :: 1 : 5 In this question, we know that the start is 7m. Hence, the length of the race will be 7 * 5 = 35m.

Explanation for Question 17:Jane covered a distance of 340 miles between city A and city taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour? Explanatory Answer Let 'x' hours be the time for which Jane traveled at 60 miles per hour. As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour. Distance covered at 60 miles per hour = Speed * time = 60 * x = 60x miles Distance covered at 80 miles per hour = Speed * time = 80 (5 - x) = 400 - 80x miles Total distance covered = Distance covered at 60 miles per hour + Distance covered at 80 miles per hour. Therefore, total distance = 60x + 400 - 80x. But, we know that the total distance = 340 miles. Therefore, 340 = 60x + 400 - 80x => 20x = 60 or x = 3 hours.

Explanation for Question 18: Steve traveled the first 2 hours of his journey at 40 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?
Average speed of travel = total distance travelled / total time taken Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours. Distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles Distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles Therefore, total distance covered = 80 + 240 = 320 miles Total time taken = 2 + 3 = 5 hours. Hence, average speed = 320/5 = 64 miles per hour. Note: If Steve had traveled equal amount of time at 40 mph and 80 mph, then his average speed will be the arithmetic mean (or simple average) of the two speeds.

Explanation for Question 19: John drove home to Jake’s house at 60 miles per hour. Returning over the same route, the traffic caused him to slow down to 40 miles per hour. If the return trip took 1 hour longer, how many miles did he drive each way?
60x = 40(x+1) ? 60x=40x+40 ? 20x = 40 ? x= 2
total distance =60(2)=120.

Explanation for Question 20:

A car travels at one speed for 4 hours, and then at twice that speed for 6 hours. The average velocity for the whole 10 hour trip is 40 mph. Find the initial speed in mph.

Total distance travelled=Average speed X total time=40X10=400
let intial speed be S.
4S+6(2S)=400
S=25.