CBSE Class 10 Mathematics Time, Speed and Distance MCQs Set 20

Mathematics Objective Questions and Answers: Time, Speed and Distance

Access targeted multiple-choice questions for Time, Speed and Distance designed to align with the latest CBSE academic syllabus for Class 10 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

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Multiple Choice Questions

Question 1: A clerk walks from his house at 4 km/hr and reaches his office 5 minutes late. If his speed is 5 km/hr, he will reach his office 10 minutes early. How far is his office from home?
(a) 5 km
(b) 5/12 km
(c) 5/2 km
(d) 15 km
Show Answer & Explanation

Answer: (a) 5 km

Explanation:
1. d/4 − d/5 = 15/60
2. d/20 = 1/4, so d = 5 km.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 2: A train running at a speed of 54 km/hour passes a signal post in 8 seconds. The length of the train is
(a) 432 m
(b) 150 m
(c) 120 m
(d) Data inadequate
Show Answer & Explanation

Answer: (c) 120 m

Explanation:
1. Speed = 54 × 5/18 = 15 m/s
2. Length = 15 × 8 = 120 m.

Teacher's Note:
1. Convert all speeds to the same units; 1 km/h = 5/18 m/s.
2. When two trains cross, add their lengths for the distance to be covered.

Question 3: Hari Singh can cover a circular path of radius 21 m in 44 sec. He will cover a distance of 3 km in
(a) 16 min 20 secs
(b) 16 min 40 secs
(c) 18 min 00 secs
(d) 18 min 30 secs
Show Answer & Explanation

Answer: (b) 16 min 40 secs

Explanation:
1. Circumference = 2 × 22/7 × 21 = 132 m, so speed = 132/44 = 3 m/s
2. Time for 3000 m = 1000 s = 16 min 40 s.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 4: Rohit can row 18 km in 4 hrs downstream but while returning he takes 12 hours. The speed of the water current is
(a) 1.5 km/hr
(b) 4 km/hr
(c) 2 km/hr
(d) 3 km/hr
Show Answer & Explanation

Answer: (a) 1.5 km/hr

Explanation:
1. Downstream speed = 18/4 = 4.5 km/hr and upstream speed = 18/12 = 1.5 km/hr
2. Current = (4.5 − 1.5)/2 = 1.5 km/hr.

Teacher's Note:
1. Downstream speed = b + s and upstream speed = b − s.
2. Speed in still water = half the sum of the two speeds.

Question 5: Two persons move towards each other from two places 55 km apart. One moves at a speed of 12 km/hr and the other at 10 km/hr. They will be first 11 km apart after moving for
(a) 3 hrs
(b) 2 hrs
(c) 6 hrs
(d) 4 hrs
Show Answer & Explanation

Answer: (b) 2 hrs

Explanation:
1. Distance to be closed = 55 − 11 = 44 km at 22 km/hr
2. Time = 2 hrs.

Teacher's Note:
1. Use relative speed: add the speeds for opposite directions and subtract for the same direction.
2. Time = distance/relative speed.

Question 6: Kishan cycles at a speed of 8 km/hr. After every 10 km, he rests for 20 minutes. How long will he take to travel a distance of 40 km?
(a) 6 hrs 20 min
(b) 8 hrs
(c) 6 hrs
(d) 5 hrs
Show Answer & Explanation

Answer: (c) 6 hrs

Explanation:
1. Cycling time = 40/8 = 5 hrs
2. He rests after 10, 20 and 30 km, i.e. 3 times = 60 min, with no rest at the end
3. Total time = 6 hrs.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 7: What is the speed of a 75 m long train which passes a 150 m long platform in 10 seconds?
(a) 63 km/hr
(b) 72 km/hr
(c) 76.75 km/hr
(d) 81 km/hr
Show Answer & Explanation

Answer: (d) 81 km/hr

Explanation:
1. Distance = 75 + 150 = 225 m
2. Speed = 22.5 m/s = 22.5 × 18/5 = 81 km/hr.

Teacher's Note:
1. Convert all speeds to the same units; 1 km/h = 5/18 m/s.
2. When two trains cross, add their lengths for the distance to be covered.

Question 8: A man rows upstream for 13 km and downstream for a distance of 28 km in 5 hrs each time. The speed of the water current is
(a) 2 km/hr
(b) 1.5 km/hr
(c) 2.5 km/hr
(d) 3 km/hr
Show Answer & Explanation

Answer: (b) 1.5 km/hr

Explanation:
1. Upstream speed = 13/5 = 2.6 km/hr and downstream speed = 28/5 = 5.6 km/hr
2. Current = (5.6 − 2.6)/2 = 1.5 km/hr.

Teacher's Note:
1. Downstream speed = b + s and upstream speed = b − s.
2. Speed in still water = half the sum of the two speeds.

Question 9: A train with stoppages covers a distance at 60 km/hr and without stoppages at 90 km/hr. The train stops for ... minutes per hour.
(a) 20
(b) 15
(c) 30
(d) 25
Show Answer & Explanation

Answer: (a) 20

Explanation:
1. In one hour with stoppages it covers 60 km, which takes 60/90 hr = 40 min of running
2. It stops for 60 − 40 = 20 minutes per hour.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 10: A boat takes 20 minutes and 30 minutes to cover a particular distance downstream and upstream respectively. If the speed of the boat in still water is 20 m/s, find the speed of the stream.
(a) 6 m/s
(b) 8 m/s
(c) 12 m/s
(d) 4 m/s
Show Answer & Explanation

Answer: (d) 4 m/s

Explanation:
1. Speeds are in the inverse ratio of times: (20 + s) : (20 − s) = 30 : 20 = 3 : 2
2. 40 + 2s = 60 − 3s, so s = 4 m/s.

Teacher's Note:
1. Downstream speed = b + s and upstream speed = b − s.
2. Speed in still water = half the sum of the two speeds.

Question 11: A 100 m long train crosses a stationary man in 10 seconds. What is the speed of the train?
(a) 18 km/h
(b) 27 km/h
(c) 36 km/h
(d) 45 km/h
Show Answer & Explanation

Answer: (c) 36 km/h

Explanation:
1. Speed = 100/10 = 10 m/s = 36 km/h.

Teacher's Note:
1. Convert all speeds to the same units; 1 km/h = 5/18 m/s.
2. When two trains cross, add their lengths for the distance to be covered.

Question 12: What is the speed of a train which overtakes a man walking at a speed of 5 km/h in 30 seconds, if the train is 274 metres long?
(a) 51.88 km/h
(b) 47.88 km/h
(c) 37.88 km/h
(d) 21.67 km/h
Show Answer & Explanation

Answer: (c) 37.88 km/h

Explanation:
1. Relative speed = 274/30 m/s = 32.88 km/h
2. Train speed = 32.88 + 5 = 37.88 km/h.

Teacher's Note:
1. Convert all speeds to the same units; 1 km/h = 5/18 m/s.
2. When two trains cross, add their lengths for the distance to be covered.

Question 13: In one hour a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/h) is
(a) 5
(b) 6
(c) 8
(d) 9
Show Answer & Explanation

Answer: (c) 8

Explanation:
1. Downstream speed = 11 and upstream speed = 5
2. Speed in still water = (11 + 5)/2 = 8 km/h.

Teacher's Note:
1. Downstream speed = b + s and upstream speed = b − s.
2. Speed in still water = half the sum of the two speeds.

Question 14: A motorboat whose speed in still water is 15 km/h goes 30 km downstream and comes back in a total of 4 hours 30 minutes. Determine the speed of the stream.
(a) 2 km/h
(b) 3 km/h
(c) 4 km/h
(d) 5 km/h
Show Answer & Explanation

Answer: (d) 5 km/h

Explanation:
1. 30/(15 + s) + 30/(15 − s) = 4.5
2. 900/(225 − s²) = 4.5, so 225 − s² = 200 and s = 5 km/h.

Teacher's Note:
1. Downstream speed = b + s and upstream speed = b − s.
2. Speed in still water = half the sum of the two speeds.

Question 15: Sujit covers a distance in 40 minutes if he drives at a speed of 60 km/h on an average. Find the speed at which he must drive to reduce the time of the journey by 25%.
(a) 60 km/h
(b) 70 km/h
(c) 75 km/h
(d) 80 km/h
Show Answer & Explanation

Answer: (d) 80 km/h

Explanation:
1. New time = 30 min, so speed is multiplied by 40/30
2. New speed = 60 × 4/3 = 80 km/h.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 16: Rakesh travelled from Hyderabad to Mumbai in his car at a certain speed. He would have reached Mumbai 2 1/2 hours early if he had driven his car at 75 km/h. If the distance between Hyderabad and Mumbai is 750 km, then the speed at which Rakesh travelled is
(a) 60 km/h
(b) 50 km/h
(c) 80 km/h
(d) 90 km/h
Show Answer & Explanation

Answer: (a) 60 km/h

Explanation:
1. Time at 75 km/h = 10 hrs, so his actual time = 12.5 hrs
2. Speed = 750/12.5 = 60 km/h.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 17: If a 300 m long train is travelling at a constant speed, find the ratio of the time it takes to cross a pole and a 500 m long bridge.
(a) 3 : 8
(b) 3 : 5
(c) 5 : 6
(d) 5 : 12
Show Answer & Explanation

Answer: (a) 3 : 8

Explanation:
1. Distance for the pole = 300 m and for the bridge = 800 m
2. Ratio of times = 300 : 800 = 3 : 8.

Teacher's Note:
1. Convert all speeds to the same units; 1 km/h = 5/18 m/s.
2. When two trains cross, add their lengths for the distance to be covered.

Question 18: A man can swim downstream at 10 km/h and upstream at 4 km/h. Find the speed of the man in still water and the speed of the current respectively.
(a) 7 kmph; 2 kmph
(b) 7.5 kmph; 2.5 kmph
(c) 7 kmph; 3 kmph
(d) 8 kmph; 2 kmph
Show Answer & Explanation

Answer: (c) 7 kmph; 3 kmph

Explanation:
1. Still water = (10 + 4)/2 = 7 km/h
2. Current = (10 − 4)/2 = 3 km/h.

Teacher's Note:
1. Downstream speed = b + s and upstream speed = b − s.
2. Speed in still water = half the sum of the two speeds.

Question 19: A car covers 300 km at a constant speed. If its speed was 10 kmph more, it would have taken one hour less to travel the same distance. Find the speed of the car.
(a) 60 kmph
(b) 50 kmph
(c) 40 kmph
(d) 75 kmph
Show Answer & Explanation

Answer: (b) 50 kmph

Explanation:
1. 300/s − 300/(s + 10) = 1
2. 3000 = s² + 10s, so s² + 10s − 3000 = 0 and s = 50 kmph.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 20: A person saves 5 minutes in covering a certain distance by increasing his speed by 20%. What is the time taken to cover the distance at his usual speed?
(a) 25 minutes
(b) 30 minutes
(c) 45 minutes
(d) 50 minutes
Show Answer & Explanation

Answer: (b) 30 minutes

Explanation:
1. New time = t/1.2, so t − t/1.2 = 5
2. t/6 = 5, so t = 30 minutes.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 21: Shiva walks at 3 km/h from his house and reaches his office 17 minutes late. If he walks at 5 km/h he is early to the office by 15 minutes. Find the distance between his office and house.
(a) 3 km
(b) 5 km
(c) 4 km
(d) 2 km
Show Answer & Explanation

Answer: (c) 4 km

Explanation:
1. d/3 − d/5 = 32/60
2. 2d/15 = 8/15, so d = 4 km.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 22: Ravi is 1 1/3 times as fast as Pradeep. If Pradeep has a head start of 50 meters, what should be the length of the racecourse such that both of them reach the finishing point at the same time?
(a) 250 m
(b) 100 m
(c) 150 m
(d) 200 m
Show Answer & Explanation

Answer: (d) 200 m

Explanation:
1. Speeds Ravi : Pradeep = 4 : 3
2. L/4 = (L − 50)/3, so 3L = 4L − 200 and L = 200 m.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

Question 23: A man misses a train by 1 hour if he travels at a speed of 4 km/h. If he increases his speed to 5 km/h he still misses it by 24 minutes. At what speed should he travel so that he reaches the station exactly on time?
(a) 12 kmph
(b) 8 kmph
(c) 6 kmph
(d) 10 kmph
Show Answer & Explanation

Answer: (c) 6 kmph

Explanation:
1. d/4 − d/5 = 36/60, so d = 12 km
2. Time at 4 km/h = 3 h, which is 1 h late, so the right time = 2 h
3. Speed = 12/2 = 6 kmph.

Teacher's Note:
1. Use distance = speed × time carefully with consistent units.
2. Average speed = total distance/total time, not the average of the speeds.

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Practice MCQs for Class 10 Mathematics Time, Speed and Distance

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FAQs

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