Time and Distance problems
- 1. A car is moving with the speed of 47.52km/hr and the radius of the wheel of car is 21 cm. Calculate the approximate number of revolutions made by the wheel in one minute.
Options- A. 250 rpm
- B. 200 rpm
- C. 600 rpm
- D. 300 rpm Discuss
Correct Answer: 600 rpm
Explanation:
Speed in cm/minute = (Speed in km/hr x 1000 x100 )/60
= 47.52x(50/3)
=79200 cm/min
And Circumference of circle = 2?r
=2 x ( 22 / 7 ) x 21
=132
No. of revolutions = ( Speed in cm/minute ) / circumference of circle in cm
=79200 / 132
=600 rpm
- 2. A man walking at 3km/hr crosses a square field diagonally in 2 min. The area of the field is?
Options- A. 25 acres
- B. 30 acres
- C. 50 acres
- D. 60 acres Discuss
Correct Answer: 50 acres
Explanation:
speed = 3 x ( 5/18 ) m/sec.
= 5 / 6 m/sec.
? Distance covered in 2 min. = ( 5 / 6) x 2 x 60 m
= 100 m.
? Length of diagonal = 100 m
Area of the field = 1/2 x diagonal2
=1/2 x 100 x 100 m2
= 5000 m2
= 50 acres.
- 3. A certain distance is covered at a certain speed. If half of this distance is covered in double the time, the ratio of the two speed is?
Options- A. 4:1
- B. 1.4
- C. 2:1
- D. 1:2 Discuss
Correct Answer: 4:1
Explanation:
Let x km . be covered in y hrs.
then, 1st speed = (x / y) km/hr.
2nd speed = [(x/2) / 2y)] km/hr.
= (x/4y) km/hr.
? Ratio of speed = x/y : x/4y = 1 :1/4 = 4: 1
- 4. A is twice as fast as B and B is thrice as fact as C is . The journey covered by C in 42 minute, will be covered by A in?
Options- A. 14 min
- B. 28 min
- C. 63 min
- D. 7 min Discuss
Correct Answer: 7 min
Explanation:
Let C' s speed = x km/hr.
Then, B's speed = 3x km/hr.
and A's speed = 6x km/hr.
? Ratio of speed of A, B, C
= 6x : 3x : x = 6 : 3 : 1
Ratio of times taken = 1/6 : 1/3 : 1 or 1 : 2 : 6
? 6 : 1 : : 42 : t
? 6t = 42
? t = 7 min.
- 5. Ram travels a certain distance at 3 km/hr and reaches 15 min late. If he travels at 4 km/hr he reaches 15 min earlier. The distance he has to travel is?
Options- A. 4.5 km.
- B. 6 km.
- C. 7.2 km.
- D. 12 km. Discuss
Correct Answer: 6 km.
Explanation:
Let the distance be x km.
Then, x/3 - x/4 = 30/60
? (4x - 3x ) / 12 = 1/2
? x = 6 km.
- 6. A thief steals a car at 1:30 p.m. and drives it at 45 km an hour. The theft is discovered at 2 p.m. and the owner sets off in another car at 50 km an hour. He will overtake the thief at?
Options- A. 3:30 p.m.
- B. 4 p.m.
- C. 4:30 p.m.
- D. 6 p.m. Discuss
Correct Answer: 4 p.m.
Explanation:
Distance covered by thief in (1/2 ) hour = 20 km.
Now , 20 km is compensated by the owner at a relative speed of 10 km/hr in 2 hours so, he overtake the thief at 4 p.m.
- 7. Two train start at the same time Aligarh and Delhi and processed toward each other at 16 km/hr and 21 km/hr respectively when they meet, it is found that one train has travelled 60 km more than the other. The distance between two station is?
Options- A. 445 km.
- B. 444 km.
- C. 440 km.
- D. 450 km. Discuss
Correct Answer: 444 km.
Explanation:
Suppose they meet after y hours .
Then, 21y - 16y = 60
? y = 12
?required distance = (16 x 12 + 21 x 12) km.
= 444 km.
- 8. A car travels a distance of 840 km at uniform speed. If the speed of the car is 10 km/hr more. It takes two hours less to cover the same distance. The original speed of the car was?
Options- A. 45 km/hr.
- B. 50 km/hr.
- C. 60 km/hr .
- D. 75 km/hr. Discuss
Correct Answer: 60 km/hr .
Explanation:
Let the original speed be x km/hr.
Then, [ 840/x - 840/( x + 10) ] = 2
? 840 (x + 10) - 840x = 2x (x+10)
? x2 + 10x - 4200 = 0
? (x + 70) (x - 60 ) = 0
? x = 60 km/hr.
- 9. A dog starts chasing to a cat 2 hours later. It takes 2 hours to dog to catch the cat. If the speed of the dog is 30 Km/h. What is the speed of the cat?
Options- A. 10 km/h
- B. 15 km/h
- C. 20 km/h
- D. can't be determined Discuss
Correct Answer: 15 km/h
Explanation:
Time = Distance advanced / Relative speed
2 = 2x / (30 - x)
? x = 15 km/h
- 10. A train 350 m long is moving at the speed of 20 km/h. It will cross a man coming from the opposite direction at the speed of 1 km/h in?
Options- A. 27 sec
- B. 35 sec
- C. 45 sec
- D. 60 sec Discuss
Correct Answer: 60 sec
Explanation:
Relative speed = 20 + 1 = 21 km/h = 21 x 5/18 = 35/6 m/s
Time = Length of train / Relative speed = (350/35) x 6 = 60 s
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