Question 1

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

Accepted Answer

Let the speed of two trains be 7x and 8x km/hr. Then, 8x = ❨ 400 ❩ = 100 4 ⟹ x = ❨ 100 ❩ = 12.5 8 ∴ Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

Question 2

A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

Accepted Answer

(1/2)x + (1/2)x = 10 21 24 ⟹ x + x = 20 21 24 ⟹ 15x = 168 x 20 ⟹ x = ❨ 168 x 20 ❩ = 224 km. 15

Question 3

If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:

Accepted Answer

Let the actual distance travelled be x km. Then, x = x + 20 10 14 ⟹ 14x = 10x + 200 ⟹ 4x = 200 ⟹ x = 50 km.

Question 4

In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

Accepted Answer

Let the duration of the flight be x hours. Then, 600 - 600 = 200 x x + (1/2) ⟹ 600 - 1200 = 200 x 2x + 1 ⟹ x(2x + 1) = 3 ⟹ 2x2 + x - 3 = 0 ⟹ (2x + 3)(x - 1) = 0 ⟹ x = 1 hr. [neglecting the -ve value of x]

Question 5

A car travelling with 5⁄7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

Accepted Answer

Time taken = 1 hr 40 min 48 sec = 1 hr 40 4 min = 1 51 hrs = 126 hrs. 5 75 75 Let the actual speed be x km/hr. Then, 5 x x 126 = 42 7 75 ⟹ x = ❨ 42 x 7 x 75 ❩ = 35 km/hr. 5 x 126

Question 6

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

Accepted Answer

Let speed of the car be x kmph. Then, speed of the train = 150 x = ❨ 3 x ❩kmph. 100 2 ∴ 75 - 75 = 125 x (3/2)x 10 x 60 ⟹ 75 - 50 = 5 x x 24 ⟹ x = ❨ 25 x24 ❩ = 120 kmph. 5

Question 7

An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1⅔ hours, it must travel at a speed of:

Accepted Answer

Distance = (240 x 5) = 1200 km. Speed = Distance/Time Speed = 1200/(5/3) km/hr. [We can write 1⅔ hours as 5/3 hours] ∴ Required speed = ❨ 1200 x 3 ❩km/hr = 720 km/hr. 5

Question 8

A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:

Accepted Answer

Let the distance travelled on foot be x km. Then, distance travelled on bicycle = (61 -x) km. So, x + (61 -x) = 9 4 9 ⟹ 9x + 4(61 -x) = 9 x 36 ⟹ 5x = 80 ⟹ x = 16 km.

Question 9

A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

Accepted Answer

Speed = ❨ 600 ❩m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = ❨ 2 x 18 ❩ km/hr 5 = 7.2 km/hr.

Question 10

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:

Accepted Answer

Total time taken = ❨ 160 + 160 ❩hrs. = 9 hrs. 64 80 2 ∴ Average speed = ❨ 320 x 2 ❩km/hr = 71.11 km/hr. 9

Question 11

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

Accepted Answer

Due to stoppages, it covers 9 km less. Time taken to cover 9 km = ❨ 9 x 60 ❩min = 10 min. 54

Question 12

In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:

Accepted Answer

Let Abhay's speed be x km/hr. Then, 30 - 30 = 3 x 2x ⟹ 6x = 30 ⟹ x = 5 km/hr.

Question 13

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:

Accepted Answer

Let the speed of the train be x km/hr and that of the car be y km/hr. Then, 120 + 480 = 8 ⟹ 1 + 4 = 1 ....(i) x y x y 15 And, 200 + 400 = 25 ⟹ 1 + 2 = 1 ....(ii) x y 3 x y 24 Solving (i) and (ii), we get: x = 60 and y = 80. ∴ Ratio of speeds = 60 : 80 = 3 : 4.

Question 14

A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:

Accepted Answer

Let distance = x km and usual rate = y kmph. Then, x - x = 40 ⟹ 2y(y + 3) = 9x ....(i) y y + 3 60 And, x - x = 40 ⟹ y(y - 2) = 3x ....(ii) y -2 y 60 On dividing (i) by (ii), we get: x = 40.

Question 15

Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

Accepted Answer

Let the distance travelled by x km. Then, x - x = 2 10 15 ⟹ 3x - 2x = 60 ⟹ x = 60 km. Time taken to travel 60 km at 10 km/hr = ❨ 60 ❩hrs = 6 hrs. 10 So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M. ∴ Required speed = ❨ 60 ❩kmph. = 12 kmph. 5

Question 16

A and B are 20 km apart. A can walk at an average speed of 4 km/hr and B at 6 km/h. If they start walking towards each other at 7:000 am, when they will meet?

Accepted Answer

Suppose they will meet after T hours. Distance = Speed x Time Sum of distance traveled by them after T hours 6T + 4T = 20 km T = 2 hours. So they will meet at 7:00 AM + 2 hours = 9:00 AM

Question 17

Arjun runs a distance of 1500 m in 5 minutes. What is his speed in Km/hr?

Accepted Answer

Speed = (1500/300 ) m/sec = 5 m/sec = (5 x 18/5 ) km/hr = 18 km/hr

Question 18

In how many minutes will Rohit cover a distance of 800 m, if he runs at speed of 10 km/hr?

Accepted Answer

Rohit's speed = 10 Km/hr = (10 x 5/18) m/sec = 50/18 m/sec Time taken to cover 800 m = (800 / (50/18) ) sec = (800 x 18/50) sec = 288 sec = 4 min 48 sec

Question 19

A plane flies along the four sides of a square field at a speed of 200, 400, 600 and 800 km/hr. Then find the average speed of plane around the square field.

Accepted Answer

Let the side of the square field be x and the average speed of plane be y x/200 + x/400 + x/600 + x/800 = 4x/y ⇒ 25x/2400 = 4x/y ⇒ y =384 ∴ Average speed is 384 km/hr

Time and Distance Questions