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

1. A person travelled from one place to another at an average speed of 40 kilometres/hour and back to the original place at an average speed of 50 kilometres/hour. What is his average speed (in kilometres/hour) during the entire round-trip? [ 1995]

(a) 45
(b) 20/5
(c) 400 / 9
(d) impossible to find out

Correct Answer: (c) 400 / 9

Solution:

Let the distance covered by the person be x km in each lap.

Total time taken = x/40 + x/50 = 9x/200

Total distance covered = x + x = 2x Km

Average speed = Total distance covered / Total time taken

= 2x/(9x/200) = 400/9 km/h.

2. Distance time graph in respect of a race among four persons is shown in the given figure. Consider the following statements in this regard: [1996]

1. 'A' stood first in the race

2. 'C' led all the way

3. 'D' ran faster than others in the later part of the race Of these statements

(a) 1 and 3 are false and 2 is true
(b) 1 and 2 are false and 3 is true
(c) 1 and 3 are true and 2 is false
(d) 1 is true and 2 and 3 are false

Correct Answer: (b) 1 and 2 are false and 3 is true

Solution:'A' never stood

1ˢᵗ

in the race, it was 'D' who stood

1ˢᵗ

. From the graph, it can be seen that 'C' do not lead all the way. While 'D' after starting slower, ran faster than others in the later part of the race.

3. A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water (in km/hr) is [1997]

(a) 1
(b) 3
(c) 4
(d) √41

Correct Answer: (b) 3

Solution:The speed of the boat along the shortest possible path

AB = (1/15)/60 = 4km/h

Now the velocity of the riverwater

4. One local and another express train were proceeding in the same direction on parallel tracks at 29 km/hour and 65 km/hour respectively. The driver of the former noticed that it took exactly 16 seconds for the faster train to pass by him. What is the length of the faster train? [1999]

(a) 60m
(b) 120m
(c) 160m
(d) 240m

Correct Answer: (c) 160m

Solution:

5. The average speed of a train in the onward journey is 25% more than that of the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and fro journey is 17 hours covering a distance of 800 km. The speed of the train in the onward journey is [1999]

(a) 45 km per hour
(b) 47.06 per hour
(c) 50.00 km per hour
(d) 56.25 km per hour

Correct Answer: (d) 56.25 km per hour

Solution:

6. A person starts from a point A and travels 3 km eastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. The shortest distance between the starting point and destination is [2000]

(a) 18 km
(b) 16 km
(c) 15 km
(d) 12 km

Correct Answer: (c) 15 km

Solution:

7. A person travels from X to Y at a speed of 40 kmph and returns by increasing his speed 50%. What is his average speed for both the trips? [2001]

(a) 36 kmph
(b) 45 kmph
(c) 48 kmph
(d) 50 kmph

Correct Answer: (c) 48 kmph

Solution:

8. 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 [2001]

(a) 4 km
(b) 5 km
(c) 6 km
(d) 7 km

Correct Answer: (b) 5 km

Solution:

9. A conveyer belt delivers baggage at the rate of 3 tons in 5 minutes and a second conveyer belt delivers baggage at the rate of 1 ton in 2 minutes. How much time will it take to get 33 tons of baggage delivered using both the conveyer belts? [2001]

(a) 25 minutes and 30 seconds
(b) 30 minutes
(c) 35 minutes
(d) 40 minutes and 45 seconds

Correct Answer: (b) 30 minutes

Solution:

10. Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometers does each lady travel in one hour? [2002]

(a) 5 km, 3 km
(b) 7 km, 5 km
(c) 8 km, 6 km
(d) 16 km, 14 km

Correct Answer: (c) 8 km, 6 km

Solution:

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

1. A person travelled from one place to another at an average speed of 40 kilometres/hour and back to the original place at an average speed of 50 kilometres/hour. What is his average speed (in kilometres/hour) during the entire round-trip? [ 1995]

2. Distance time graph in respect of a race among four persons is shown in the given figure. Consider the following statements in this regard: [1996]

3. A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water (in km/hr) is [1997]

4. One local and another express train were proceeding in the same direction on parallel tracks at 29 km/hour and 65 km/hour respectively. The driver of the former noticed that it took exactly 16 seconds for the faster train to pass by him. What is the length of the faster train? [1999]

7. A person travels from X to Y at a speed of 40 kmph and returns by increasing his speed 50%. What is his average speed for both the trips? [2001]

8. 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 [2001]

9. A conveyer belt delivers baggage at the rate of 3 tons in 5 minutes and a second conveyer belt delivers baggage at the rate of 1 ton in 2 minutes. How much time will it take to get 33 tons of baggage delivered using both the conveyer belts? [2001]

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