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# Time Speed and Distance Questions for SSC CPO PDF

Download Top-15 SSC CPO Time Speed and Distance Questions and Answers PDF, based on asked questions in previous CPO & other SSC exam papers.

Question 1: A man travels 420 kilometres in, partly by rail and partly by steamer. He spends 8 hours more time on steamer. If the velocity of the steamer is 35 km/hr and the velocity of rail is 65 km/hr, how much distance does he cover by steamer?

a) 395 km

b) 329 km

c) 494 km

d) 592 km

Question 2: Manoj can do a piece of work in 42 hours. If he is joined by Jayashree who is 100% more efficient, in what time they will finish the work together?

a) 7 hours

b) 3.5 hours

c) 14 hours

d) 2.5 hours

Question 3: A man travels 404 kilometres in partly by rail and steamer. He spends 10 hours more time on steamer. If the speed of the steamer is 30 km/hr and the velocity of rail is 50 km/hr, how much distance does he cover by steamer?

a) 407 km

b) 509 km

c) 610 km

d) 339 km

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Question 4: What should be the average speed of a car to cover a distance of 189 km in 3.5 hours?

a) 15 m/s

b) 54 m/s

c) 27 m/s

d) 30 m/s

Question 5: To cover a distance of 252 km in 2.5 hours what should be the average speed of the car in meters/second?

a) 100.8 m/s

b) 50.4 m/s

c) 28 m/s

d) 56 m/s

Question 6: A thief is stopped by a policeman from a distance of 350 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 7 km/h and that of police man as 12 km/h, how far the thief would have run, before he is overtaken?

a) 490 metres

b) 392 metres

c) 588 metres

d) 294 metres

Question 7: A thief is stopped by a policeman from a distance of 200 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 8 km/hr and that of police man as 10 km/hr. How far the thief would have run, before he is over­taken?

a) 640 metres

b) 800 metres

c) 960 metres

d) 480 metres

Question 8: 4 hrs after a goods train passed a station, another train travelling at a speed of 60 km/hr following that goods train passed through that station. If after passing the station the train overtakes the goods train in 8 hours. What is the speed of the goods train?

a) 40 km/hr

b) 48 km/hr

c) 60 km/hr

d) 32 km/hr

Question 9: To travel 648 km, an Express train takes 12 hours more than Rajdhani. If however, the speed of the Express train is doubled, it takes 6 hours less than Rajdhani. The speed of Rajdhani is _____.

a) 36 km/hr

b) 18 km/hr

c) 45 km/hr

d) 27 km/hr

Question 10: 9 hrs after a goods train passed a station, another train travelling at a speed of 72 km/hr following that goods train passed through that station. If after passing the station the train overtakes the goods train in 3 hours. What is the speed of the goods train?

a) 21.6 km/hr

b) 27 km/hr

c) 18 km/hr

d) 14.4 km/hr

Question 11: A car travels a certain distance at 34 km/h and comes back at 66 km/h. What is the average speed for total journey?

a) 50 km/hr

b) 39.76 km/hr

c) 55.12 km/hr

d) 44.88 km/hr

Question 12: Rizvan walks at 15 km/hr and Ruchitha cycles at 20 km/hr towards each other. What was the distance between them when they started if they meet after 42 minutes?

a) 36.8 kms

b) 30.6 kms

c) 24.5 kms

d) 18.4 kms

Question 13: To cover a distance of 315 km in 2.8 hours what should be the average speed of the car in meters/second?

a) 112.5 m/s

b) 56.25 m/s

c) 62.5 m/s

d) 31.25 m/s

Question 14: To travel 612 km, an Express train takes 9 hours more than Rajdhani. If the speed of the Express train is doubled, it takes 3 hours less than Rajdhani. The speed (in km/hr) of Rajdhani is

a) 40.8

b) 51

c) 30.6

d) 61

Question 15: To travel 732 km, an Express train takes 6 hours more than Rajdhani. If the speed of the Express train is doubled, it takes 3 hours less than Rajdhani. The speed of Rajdhani is

a) 81.3 km/hr

b) 61 km/hr

c) 40.7 km/hr

d) 101.7 km/hr

Question 16: Ruchir walks at 20 km/hr and Rukma cycles at 25 km/hr towards each other. What was the distance between them when they started if they meet after 48 minutes?

a) 54 km

b) 45 km

c) 36 km

d) 27 km

Let distance covered by steamer = $d$ km

=> Distance covered by rail = $(420 – d)$ km

Let time taken on rail = $t$ hours and time taken on steamer = $(t + 8)$ hours

Speed of rail = 65 km/hr and speed of steamer = 35 km/hr

Using, speed = distance/time

For steamer, $\frac{d}{t + 8} = 35$

=> $d = 35t + 280$ ————–(i)

For rail, $\frac{420 – d}{t} = 65$

Substituting value of $d$ from equation (i), we get :

=> $420 – (35t + 280) = 65t$

=> $420 – 280 = 65t + 35t = 100t$

=> $t = \frac{140}{100} = 1.4$ hours

Substituting value of $t$ in equation (i), => $d = (35 \times 1.4) + 280$

= $49 + 280 = 329$ km

Let total work to be done = 42 units

Manoj’s efficiency = $\frac{42}{42} = 1$ unit/hr

Jayashree is 100% more efficient, => Jayashree’s efficiency = $1 + \frac{100}{100} \times 1 = 2$ units/hr

(Manoj + Jayashree)’s 1 day’s work together = 1 + 2 = 3 units/hr

$\therefore$ Time taken by Manoj and Jayashree together to finish the work = $\frac{42}{3} = 14$ hours

=> Ans – (C)

Let distance covered by steamer = $d$ km

=> Distance covered by rail = $(404 – d)$ km

Let time taken on rail = $t$ hours and time taken on steamer = $(t + 10)$ hours

Speed of rail = 50 km/hr and speed of steamer = 30 km/hr

Using, speed = distance/time

For steamer, $\frac{d}{t + 10} = 30$

=> $d = 30t + 300$ ————–(i)

For rail, $\frac{404 – d}{t} = 50$

Substituting value of $d$ from equation (i), we get :

=> $404 – (30t + 300) = 50t$

=> $404 – 300 = 50t + 30t = 80t$

=> $t = \frac{104}{80} = 1.3$ hours

Substituting value of $t$ in equation (i), => $d = (30 \times 1.3) + 300$

= $39 + 300 = 339$ km

The car covers 189 km in 3.5 hours

Speed of car (in km/h) = $\frac{189}{3.5} = 54$ km/hr

=> Speed of car (in m/s) = $54 \times \frac{5}{18}$

= $3 \times 5 = 15$ m/s

=> Ans – (A)

The car covers 252 km in 2.5 hours

Speed of car (in km/h) = $\frac{252}{2.5} = 100.8$ km/hr

=> Speed of car (in m/s) = $100.8 \times \frac{5}{18}$

= $5.6 \times 5 = 28$ m/s

=> Ans – (C)

Since the thief is escaping from the police man, thus they both are running in same direction.

Speed of thief = 7 km/hr and speed of policeman = 12 km/hr

=> Relative speed = 12 – 7 = 5 km/hr

Distance between them = 350 metres = 0.35 km

=> Time taken = $\frac{distance}{speed}$

= $\frac{0.35}{5} = \frac{7}{100}$ hr

$\therefore$ Distance covered by thief before he was caught = $7 \times \frac{7}{100}$

= 0.49 km = 490 metres

=> Ans – (A)

Since the thief is escaping from the police man, thus they both are running in same direction.

Speed of thief = 8 km/hr and speed of policeman = 10 km/hr

=> Relative speed = 10 – 8 = 2 km/hr

Distance between them = 200 metres = 0.2 km

=> Time taken = $\frac{distance}{speed}$

= $\frac{0.2}{2} = \frac{1}{10}$ hr

$\therefore$ Distance covered by thief before he was caught = $8 \times \frac{1}{10}$

= 0.8 km = 800 metres

Let the speed of goods train = $x$ km/hr

Speed of another train = 60 km/hr

Distance between the two trains = $60 \times 4 = 240$ km

The trains are moving in same direction, => Relative speed = $(60 – x)$ km/hr

Time = 4 + 8 = 12 hours

=> speed = distance/time

=> $60 – x = \frac{240}{12} = 20$

=> $x = 60 – 20 = 40$ km/hr

=> Ans – (A)

Let speed of Rajdhani train = $x$ km/hr and Express train = $y$ km/hr

Using, time = distance/speed

Acc. to ques, => $\frac{648}{y} – \frac{648}{x} = 12$

=> $\frac{1}{y} – \frac{1}{x} = \frac{12}{648} = \frac{1}{54}$ —————-(i)

If speed of express train is doubled = $2y$ km/hr

=> $\frac{648}{x} – \frac{648}{2y} = 6$

=> $\frac{1}{x} – \frac{1}{2y} = \frac{6}{648} = \frac{1}{108}$ —————-(ii)

Adding equations (i) and (ii), we get :

=> $\frac{1}{y} – \frac{1}{2y} = \frac{1}{54} + \frac{1}{108}$

=> $\frac{1}{2y} = \frac{3}{108}$

=> $y = \frac{108}{6} = 18$ km/hr

$\therefore$ Speed of Rajdhani = $\frac{1}{x} = \frac{1}{18} – \frac{1}{54}$

=> $\frac{1}{x} = \frac{2}{54} = \frac{1}{27}$

=> $x = 27$ km/hr

Let the speed of goods train = $x$ km/hr

Speed of another train = 72 km/hr

Distance between the two trains = $72 \times 9 = 648$ km

The trains are moving in same direction, => Relative speed = $(72 – x)$ km/hr

Time = 9 + 3 = 12 hours

=> speed = distance/time

=> $72 – x = \frac{648}{12} = 54$

=> $x = 72 – 54 = 18$ km/hr

Average speed of the journey is the harmonic mean of the speeds 34 and 66 km/hr

Harmonic mean of two numbers ‘x’ and ‘y’ = $\frac{2}{\frac{1}{x} + \frac{1}{y}}$

Average speed = $\frac{2}{\frac{1}{34} + \frac{1}{66}}$

= $2 \div {\frac{66 + 34}{66 \times 34}} = \frac{2 \times 66 \times 34}{100}$

= $\frac{4488}{100} = 44.88$ km/hr

=> Ans – (D)

Speed of Rizvan = 15 km/hr and Ruchitha = 20 km/hr

Since they are moving in opposite direction, => Relative speed = 20 + 15 = 35 km/hr

Let distance between them = $d$ km and time = $\frac{42}{60}$ hr

=> time = distance/speed

=> $\frac{d}{35} = \frac{42}{60}$

=> $d = \frac{42}{60} \times 35 = \frac{7 \times 7}{2}$

=> $d = \frac{49}{2} = 24.5$ km

Distance = 315 km and time = 2.8 hours

Speed = distance/time

=> Speed = $\frac{315}{2.8} = \frac{45}{0.4}$ km/hr

$\therefore$ Speed in meters/second = $\frac{45}{0.4} \times \frac{5}{18}$

= $\frac{25}{0.8} = 31.25$ m/s

Let speed of Rajdhani train = $x$ km/hr and Express train = $y$ km/hr

Using, time = distance/speed

Acc. to ques, => $\frac{612}{y} – \frac{612}{x} = 9$

=> $\frac{1}{y} – \frac{1}{x} = \frac{9}{612} = \frac{1}{68}$ —————-(i)

If speed of express train is doubled = $2y$ km/hr

=> $\frac{612}{x} – \frac{612}{2y} = 3$

=> $\frac{1}{x} – \frac{1}{2y} = \frac{3}{612} = \frac{1}{204}$ —————-(ii)

Adding equations (i) and (ii), we get :

=> $\frac{1}{y} – \frac{1}{2y} = \frac{1}{68} + \frac{1}{204}$

=> $\frac{1}{2y} = \frac{4}{204}$

=> $y = \frac{102}{4} = \frac{51}{2}$ km/hr

$\therefore$ Speed of Rajdhani = $\frac{1}{x} = \frac{2}{51} – \frac{1}{68}$

=> $\frac{1}{x} = \frac{1}{17} \times \frac{5}{12}$

=> $x = \frac{204}{5} = 40.8$ km/hr

Let speed of Rajdhani train = $x$ km/hr and Express train = $y$ km/hr

Using, time = distance/speed

Acc. to ques, => $\frac{732}{y} – \frac{732}{x} = 6$

=> $\frac{1}{y} – \frac{1}{x} = \frac{6}{732} = \frac{1}{122}$ —————-(i)

If speed of express train is doubled = $2y$ km/hr

=> $\frac{732}{x} – \frac{732}{2y} = 3$

=> $\frac{1}{x} – \frac{1}{2y} = \frac{3}{732} = \frac{1}{244}$ —————-(ii)

Adding equations (i) and (ii), we get :

=> $\frac{1}{y} – \frac{1}{2y} = \frac{1}{122} + \frac{1}{244}$

=> $\frac{1}{2y} = \frac{3}{244}$

=> $y = \frac{122}{3}$ km/hr

$\therefore$ Speed of Rajdhani = $\frac{1}{x} = \frac{3}{122} – \frac{1}{122}$

=> $\frac{1}{x} = \frac{2}{122} = \frac{1}{61}$

=> $x = 61$ km/hr

Speed of Rizvan = 20 km/hr and Ruchitha = 25 km/hr

Since they are moving in opposite direction, => Relative speed = 20 + 25 = 45 km/hr

Let distance between them = $d$ km and time = $\frac{48}{60} = \frac{4}{5}$ hr

=> time = distance/speed

=> $\frac{d}{45} = \frac{4}{5}$

=> $d = \frac{4}{5} \times 45 = 4 \times 9$

=> $d = 36$ km

We hope this Time Speed and Distance Questions PDF for SSC CPO Exam will be highly useful for your preparation.