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

Total Questions: 33

11. A bus is moving at a speed of 30 km/hr ahead of a car with a speed of 50 km/hr. How many kilometers apart are they if it takes 15 minutes for the car to catch up the bus? [2002]

(a) 5 km
(b) 7.5 km
(c) 12.5 km
(d) 15 km

Correct Answer: (a) 5 km

Solution:

12. A train of length 150 metres, moving at a speed of 90 km/hr can cross a 200 metres bridge in [2002]

(a) 8 seconds
(b) 14 seconds
(c) 6 seconds
(d) 15 seconds

Correct Answer: (b) 14 seconds

Solution:

13. A car travels the first one-third of a certain distance with a speed of 10 km/hr. The next one-third of distance with a speed of 20 km/hr, and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is: [2003]

(a) 18 km/hr
(b) 24 km/hr
(c) 30 km/hr
(d) 36 km/hr

Correct Answer: (a) 18 km/hr

Solution:

14. Total time taken by a person in going to a place by walking and returning on cycle is 5 hours 45 minutes. He would have gained 2 hours by cycling both ways. The time taken by him to walk both ways, is [2003]

(a) 6 hours 45 minutes
(b) 7 hours 45 minutes
(c) 8 hours 15 minutes
(d) 8 hours 30 minutes

Correct Answer: (b) 7 hours 45 minutes

Solution:Walking time + cycling time
= 5 Hours 45 minutes = 345 min. .....(i)

15. Two cars X and Y starts from two places A and B respectively which are 700 km apart at 9 a.m. Both the cars run at an average speed of 60 km/hr. Car X stops at 10 a.m. and again starts at 11 a.m., while the other car Y continues to run without stopping. When do the two cars cross each other? [2004]

(a) 2:40 p.m.
(b) 3:20 p.m.
(c) 4:10 p.m.
(d) 4:20 p.m.

Correct Answer: (b) 3:20 p.m.

Solution:Distance travelled by

X

upto 11 a.m. = Distance travelled by

X

upto 10 a.m.

= 60 \times 1 = 60

km.

Distance travelled by $Y$ upto 11 a.m. $= 2 \times 60 = 120$

Now, at 11 a.m., distance between $X$ and $Y$ $= 700 - (120 + 60) = 520$ km.hr. Relative speed of $X$ with respect to $Y$

$= 60 - (- 60) = 120$ km/hr.

Now, they will cross each other, when they cover a distance of 520 km with a relative speed of 120 km/hr after 11 a.m.

Time taken after 11 a.m. = $520 = 13 \times 60$ min $= 13 \times 20 = 260$ min $= 4$ hr. 20 min.

$∴$ Time $= 11 + 4$ hr. 20 min $= 3 : 20$ p.m.

16. A and B start from the same point and in the same direction at 7 a.m. to walk around a rectangular field 400 m × 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively. How many times shall they cross each other, if they continue to walk till 12:30 p.m.? [2004]

(a) Not even once
(b) Once
(c) Twice
(d) Thrice

Correct Answer: (b) Once

Solution:

17. 50 men or 80 women can finish a job in 50 days. A contractor employs 40 men and 48 women for this work, but after every duration of 10 days, 5 completed. The work is completed in [2004]

(a) 45 days
(b) 50 days
(c) 54 days
(d) 62 days

Correct Answer: (b) 50 days

Solution:

18. Aryan runs at a speed of 40 metres/minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 metres/minute. Rahul's dog runs at a speed of 60 metres/minute and starts along with Rahul. The dog reaches Aryan and then comes back to Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered by the dog? [2005]

(a) 600 metres
(b) 750 metres
(c) 980 metres
(d) 1200 metres

Correct Answer: (d) 1200 metres

Solution:

19. There are eight equidistant points 'A', 'B', 'C', 'D', 'E', 'F', 'G', and 'H' in the clockwise direction on the periphery of a circle. In a time interval t, a person reaches from 'A' to 'C' with uniform motion while another person reaches the point 'E' from the point 'B' during the same time interval with uniform motion. Both the persons move in the same direction along the circumference of the circle and start at the same instant. How much time after the start, will the two persons meet each other? [2006]

(a) 4t
(b) 7t
(c) 9t
(d) Never

Correct Answer: (b) 7t

Solution:

20. Amit starts from a point A and walks to another point B, and then returns from B to A by his car and thus takes a total time of 6 hours and 45 minutes. If he had driven both ways in his car, he would have taken 2 hours less. How long would it take for him to walk both ways? [2007]

(a) 7 hours 45 minutes
(b) 8 hours 15 minutes
(c) 8 hours 30 minutes
(d) 8 hours 45 minutes

Correct Answer: (d) 8 hours 45 minutes

Solution:

Let the time taken by car = C

and the time taken by walking = W

C + W = 6 hrs 45 minutes = $6 \times 3/4$ or $27$ hrs

C + C = 6 hrs 45 minutes - 2 hrs = 4 hr 45 minutes

or $6 \times 3/4 - 2$ hr $= 43/4$ hrs

W + W = $2 \times 27/4 - 43/4$ hrs

$= 54/4 - 19/4 = 35/4 = 8 \times3/4$

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

11. A bus is moving at a speed of 30 km/hr ahead of a car with a speed of 50 km/hr. How many kilometers apart are they if it takes 15 minutes for the car to catch up the bus? [2002]

12. A train of length 150 metres, moving at a speed of 90 km/hr can cross a 200 metres bridge in [2002]

13. A car travels the first one-third of a certain distance with a speed of 10 km/hr. The next one-third of distance with a speed of 20 km/hr, and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is: [2003]

14. Total time taken by a person in going to a place by walking and returning on cycle is 5 hours 45 minutes. He would have gained 2 hours by cycling both ways. The time taken by him to walk both ways, is [2003]

16. A and B start from the same point and in the same direction at 7 a.m. to walk around a rectangular field 400 m × 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively. How many times shall they cross each other, if they continue to walk till 12:30 p.m.? [2004]

17. 50 men or 80 women can finish a job in 50 days. A contractor employs 40 men and 48 women for this work, but after every duration of 10 days, 5 completed. The work is completed in [2004]

20. Amit starts from a point A and walks to another point B, and then returns from B to A by his car and thus takes a total time of 6 hours and 45 minutes. If he had driven both ways in his car, he would have taken 2 hours less. How long would it take for him to walk both ways? [2007]

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