Time and Distance and Time and work (UPSC) Part-I

Total Questions: 33

21. A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete the job? [2007]

(a) 10
(b) 12
(c) 15
(d) 18

Correct Answer: (a) 10

Solution:Let alone time for A and B be x and y respectively.

22. A train completes a journey with a few stoppages in between at an average speed of 40 km per hour. If the train had not stopped anywhere, it would have completed the journey at an average speed of 60 km per hour. On an average, how many minutes per hour does the train stop during the journey? [2007]

(a) 20 minutes per hour
(b) 18 minutes per hour
(c) 15 minutes per hour
(d) 10 minutes per hour

Correct Answer: (a) 20 minutes per hour

Solution:Without stoppage, distance travelled per hour = 60 km

With stoppage, distance travelled per hour = 40 km.

$∴$ Stoppage distance per hour $= 60 - 40 = 20$ km.

Since, speed is 60 km per hour, i.e., in 60 min. (1 km - 1 min.)

Hence, stoppage time per hour = 20 min.

23. Carpenter A can make a chair in 6 hours, carpenter B in 7 hours and carpenter C in 8 hours. If each carpenter works for 8 hours per day, how many chairs will be made in 21 days? [2008]

(a) 61
(b) 67
(c) 73
(d) 79

Correct Answer: (c) 73

Solution:In 6 hours, number of chairs made by carpenter A = 1

24. Two trains leave New Delhi at the same time. One travels north at 60 kmph and the other travels south at 40 kmph. After how many hours will the trains be 150 km apart? [2010]

(a) 3/2
(b) 4/3
(c) 3/4
(d) 15/2

Correct Answer: (a) 3/2

Solution:Since, both trains are moving in opposite directions, so relative speed of one train with respect to the other

25. Running at a speed of 60 km per hour, a train passed through a 1.5 km long tunnel in two minutes. What is the length of the train? [2010]

(a) 250 m
(b) 500 m
(c) 1000 m
(d) 1500 m

Correct Answer: (b) 500 m

Solution:Let length of the train be

x

26. A person travelled a distance of 50 km in 8 hours. He covered a part of the distance, on foot at the rate of 4 km per hour and a part on a bicycle at the rate of 10 km per hour. How much distance did he travel on foot? [2010]

(a) 10 km
(b) 20 km
(c) 30 km
(d) 40 km

Correct Answer: (b) 20 km

Solution:Let the time taken to travel on foot and bicycle be

t_{1}

and

t_{2}

respectively Also, let distance travelled on foot be

x

27. Three men start together to travel the same way around a circular track of 11 km. Their speeds are 4, 5.5 and 8 kmph respectively. When will they meet at the starting point for the first time? [2010]

(a) After 11 hours
(b) After 21 hours
(c) After 22 hours
(d) After 33 hours

Correct Answer: (c) After 22 hours

Solution:Let the minimum time be

t

, when they meet at the starting point for the first time. So, the net distance covered must be a multiple of 11.

Now, $(4 + 5.5 + 8) t = 11 (n)$

where, $n$ is an integer. $t = 11 ( n )/17.5$

28. If a bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then what is the ratio of the distances travelled by them in one hour? [2011-II]

(a) 8 : 5
(b) 5 : 8
(c) 4 : 5
(d) 1 : 2

Correct Answer: (b) 5 : 8

Solution:Distance covered by a bus in 4 hours = 160 km.

$∴$ Distance covered by a bus in 1 hour = $160$ = 40 km

Further, Distance covered by a train in 5 hours = 320 km

$∴$ Distance covered by a train in 1 hour = $320$ = 64 km

Required ratio = $40$ = 5/8 = 5:8

29. Mr. Kumar drives to work at an average speed of 48 km per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office? [2012-II]

(a) 30 km
(b) 40 km
(c) 45 km
(d) 48 km

Correct Answer: (b) 40 km

Solution:

$0.6 d = 0.4 d/48 = 10/60 \Rightarrow 0.2 d = 10 \times 48/60$

$∴$ $d = 40$ km

30. A person can walk a certain distance and drive back in six hours. He can also walk both ways in 10 hours. How much time will he take to drive both ways? [2013-II]

(a) Two hours
(b) Two and a half hours
(c) Five hours
(d) Five and a half hours

Correct Answer: (a) Two hours

Solution:2 way walk = 10 hrs

$∴$ 1 way walk = 5 hrs

1 way walk + 1 way drive = 6 hrs

$∴$ 1 way drive = 6 - 5 = 1 hr

Hence, two way drive take 2 hrs.

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