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

šŸ“† April 30, 2025

Total Questions: 32

1. Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C is [2014-II]

Correct Answer: (b) 13
Solution:

Shortest Distance, BC = āˆš5Ā² + 12Ā² = 13 km

2. Two cars start towards each other, from two places A and B which are at a distance of 160 km. They start at the same time 08:10 AM. If the speeds of the cars are 50 km and 30 km per hour respectively, they will meet each other at [2014-II]

Correct Answer: (a) 10:10 AM
Solution:

Suppose the cars meet at point C after 't' hrs.
āˆ“ AC = 50 t and BC = 30 t
āˆ“ 50 t + 30 t = 160
t = 160 / 80 = 2 hrs.

So, the cars will meet at 10:10 AM

3. A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the second point and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points? [2014-II]

Correct Answer: (b) 12
Solution:

Here 1st point = 1 cm
2nd point = 2 cm
3rd point = 3 cm
4th point = 4 cm
5th point = 5 cm
6th point = 6 cm
7th point = 7 cm
8th point = 8 cm

Sum of distances = 1 + 2 + 2 + 3 + ..... + 8 = 36 km
Thus, total points from both ends = 8 + 8 = 16
When two ends point omitted,
total number of points = 16 - 2 = 14
Again, 5th and 6th points are common points, so omitted.
Hence, total required points = 14 - 2 = 12 points.

4. A and B decide to travel from place X to place Y by bus. A has ā‚¹ 10 with him and he finds that it is 80% of the bus fare for two persons. B finds that he has ā‚¹ 3 with him and hands it over to A. In this context, which one of the following statements is correct? [2014-II]

Correct Answer: (c) After buying the two tickets A will be left with 50 paise.
Solution:Let cost of 1 ticket is ā‚¹ x.
āˆ“ for A, 10 = (80 / 100) Ɨ 2x

= 50 / 8 = 25 / 4 = 6.25

Now B gives ā‚¹ 3 to A.
So, A has ā‚¹ 13.
Cost of 2 tickets = ā‚¹ 12.50, which is more than enough to buy 2 tickets.
āˆ“ (a) Rules out
(b) is clearly ruled out
(c) is true, because after buying 2 tickets.
A is left with ā‚¹ 13 - 12.50 = 50 paise

5. A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr, if he walks at a speed of 6 km/hr then he reaches the factory 7 minutes early. The distance of the factory from his house is [2014-II]

Correct Answer: (c) 5 km
Solution:Let the distance is x km
ATQ,
x / 5 āˆ’ 3 / 60 + x / 6 + 7 / 60 ā‡’ x/5 - x/6 = 10/60 = 1/6 ā‡’ x/30 = 1/6

āˆ“ x = 5 km

6. In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speeds of A to B assuming that both start at the same time? [2015-II]

Correct Answer: (a) 25:21
Solution:Total distance = 500m
Distance covered by A = 500m
Distance covered by B = 500 - 45 - 35
= 500 - 80 = 420

speed of A/speed of B = (distance of A /Time)/(distance of B /Time) = 500/time Ɨ time/420 = 500/420 = 25/21 = 25 : 21

7. Two cities A and B are 360 km apart. A car goes from A to B with a speed of 40 km/hr and returns to A with a speed of 60 km/hr. What is the average speed of the car? [2015-II]

Correct Answer: (b) 48 km/hr
Solution:Average speed of two cars at a speed Vā‚ and Vā‚‚ km/hr

= 2Vā‚Vā‚‚ / (Vā‚ + Vā‚‚)
= 2 Ɨ 40 Ɨ 60 / 60 + 40
= 2 Ɨ 40 Ɨ 60 / 100
= 48 km/hr

8. Two pipes A and B can independently fill a tank completely in 20 and 30 minutes respectively. If both the pipes are opened simultaneously, how much time will they take to fill the tank completely? [2015-II]

Correct Answer: (b) 12 minutes
Solution:Time taken by both tanks = 30 Ɨ 20 / 30 + 20
= 30 Ɨ 20 / 50
= 12 min

9. A and B walk around a circular park. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other after 8:00 a.m. and before 9:30 a.m.? [2016-II]

Correct Answer: (a) 7
Solution:Here, A and B are moving in opposite directions. So,
Relative speed = 2 + 3 = 5 rounds/hour
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 7 times before 9:30 a.m.

10. Four friends A, B, C and D need to cross a bridge. A maximum of two persons can cross it at a time. It is night and they just have one lamp. Persons that cross the bridge must carry the lamp to find the way. A pair must walk together at the speed of slower person. After crossing the bridge, the person having faster speed in the pair will return with the lamp each time to accompany another person in the group. Finally, the lamp has to be returned at the original place and the person who returns the lamp has to cross the bridge again without lamp. To cross the bridge, the time taken by them is as follows : [2016-II]

A: 1 minute, B: 2 minutes, C: 7 minutes and D: 10 minutes. What is the total minimum time required by all the friends to cross the bridge?

Correct Answer: (a) 23 minutes
Solution:

Here, A takes the shortest time to cross the bridge i.e. 1 min. And, D takes 10 min, C takes 7 min and B takes 2 min to cross the bridge.
So, 4 friends can cross the bridge in minimum time in the following ways.

  1. A + B crossing and A returning : (2 + 1) min
  2. A + C crossing and A returning : (7 + 1) min
  3. A + D crossing and A returning : (10 + 1) min
  4. A crossing the bridge for the last time : 1 min

Hence, total minimum time = 3 + 8 + 11 + 1 = 23 min.

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