Question 1

A man covered a distance of 12 km in 90 min by cycle. How much distance will he cover in 3 h, if he rides the cycle at a uniform speed?

Accepted Answer

We know that, speed = Distance / Time Speed = 12/90 km/min ∴ Distance covered in 3 h = Speed x Time = (12/90) x (3 x 60) = 24km

Question 2

Two trains A and B travel from points X to Y and the ratio of the speeds of A to that of B is 2 : 7. Find the ratio of time taken by A and B to reach From X to Y.

Accepted Answer

We know that speed is inversely proportional to time. Given that, (Speed of A ) : (speed of B ) = 2 : 7 ∴(Time taken by A ) : (Time taken by B ) = 1/2 : 1/7 = 7 : 2

Question 3

A man completes 30 km of a journey at 6 km/h and the remaining 40 km of the journey in 5 h. Find the average speed for the whole journey.

Accepted Answer

Total distance = 30 + 40 = 70 km Total time taken = (30/6) + 5 = 10 h ∴ Required average speed = 70/10 = 7 km/h

Question 4

A certain distance is covered at a certain speed. If half of the distance is covered in double time, the ratio of the two speeds is .

Accepted Answer

Let L km distance be covered in T h. So, speed in first case = L/T km/h. And speed in second case = (L/2)/2T = L/4T km/h ∴ Required ratio = L/T : L/4T =1 : 1/4 = 4 : 1

Question 5

Moving 6/7 of its usual speed a train is 10 min late. Find its usual time to cover the journey.

Accepted Answer

New speed = 6/7 of usual speed Now, time taken = 7/6 of usual time (7/6 of the usual time) - (usual time) = 10 min ⇒ 1/6 of the usual time = 10 min ∴ Usual time = 60 min

Question 6

John started from A to B and Vinod from B to A. If the distance betweeen A and B is 125 km and they meet at 75 km from A, what is the ratio of John's speed to that of Vinod's speed?

Accepted Answer

John's speed : Vinod's speed = 75 : ( 125 - 75 ) = 75 : 50 = 3 : 2

Question 7

A person goes from one point to another point with a speed of 5 km/h and comes back to starting point with a speed of 3 km/h. Find the average speed for the whole journey.?

Accepted Answer

Average speed = 2AB/(A + B) = 2 x 5 x 3/(5 + 3) = 30/8 = 3.75 km/h

Question 8

A train covers a distance in 1 h 40 min, if it runs at a speed of 96 km/h on an average. Find the speed at which the train must run reduce the time of journey to 1 h 20 min.

Accepted Answer

Distance= Speed x Time = 96 x (100/60) = 160 km New time = 80/60 h = 4/3 h New speed = 160 x 3/4 = 40 x 3 =120 km/h

Question 9

The average speed of a car is 75 km/h. The driver first decrease its average speed by 40% and then increase it by 50%. What is the new average speed now?

Accepted Answer

Required average speed = 75 x {(100 - 40)/100} x {(100 + 50)/100} = 75 x 3/5 x 3/2 = 67.5 km/h

Question 10

If a train runs at 5/6 of its original speed, then it reaches the station 10 min late. Then find out the usual time taken by train to cover the distance.

Accepted Answer

Let the actual speed of train be x and actual time taken be y Then new speed of train = 5x/6 Therefore, new time taken = 6y/5 (as distance is same in both case) Given, 6y/5 - y = 1/6 hr , therefore actual time = 50 min

Question 11

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.

Accepted Answer

Speed in cm/minute = (Speed in km/hr x 1000 x100 )/60 = 47.52x(50/3) =79200 cm/min And Circumference of circle = 2πr =2 x ( 22 / 7 ) x 21 =132 No. of revolutions = ( Speed in cm/minute ) / circumference of circle in cm =79200 / 132 =600 rpm

Question 12

A man walking at 3km/hr crosses a square field diagonally in 2 min. The area of the field is?

Accepted Answer

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.

Question 13

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?

Accepted Answer

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

Question 14

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?

Accepted Answer

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.

Question 15

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?

Accepted Answer

Let the distance be x km. Then, x/3 - x/4 = 30/60 ⇒ (4x - 3x ) / 12 = 1/2 ∴ x = 6 km.

Question 16

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?

Accepted Answer

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.

Question 17

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?

Accepted Answer

Suppose they meet after y hours . Then, 21y - 16y = 60 ⇒ y = 12 ∴required distance = (16 x 12 + 21 x 12) km. = 444 km.

Question 18

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?

Accepted Answer

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.

Question 19

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?

Accepted Answer

Time = Distance advanced / Relative speed 2 = 2x / (30 - x) ⇒ x = 15 km/h

Question 20

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?

Accepted Answer

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

Time and Distance Questions