Speed and Distance Problems

In covering a distance of 60 km. Arjun takes 2 hours more than Rohit. If Arjun doubles his speed, then he would take 1 hour less than Rohit. Arjun's original speed is :

• 15 km/h

• 25 km/h

• 5 km/h

• 10 km/h

Answer explanation

Let Arjun's speed be x km/h. Then, Rohit's speed is (60/(60/x - 2)) km/h. If Arjun doubles his speed, he takes 1 hour less than Rohit. Solving these equations gives Arjun's speed as 10 km/h.

The ratio of the speeds of a bus and a car is 7:11. If the car covers a distance of 396 km in 6 hours, what is the speed of the bus in km/h?

• 42

• 45.5

• 38.5

• 35

Answer explanation

The car's speed is 66 km/h (396 km / 6 h). The ratio of bus to car speeds is 7:11. Let the bus speed be 7x and car speed be 11x. Thus, 11x = 66, giving x = 6. Therefore, bus speed = 7x = 42 km/h.

A train covers a distance of 57.6 km in 48 minutes. What is its speed in m/s?

• 24

• 18

• 21

• 20

Answer explanation

To find speed, convert distance to meters: 57.6 km = 57600 m. Convert time to seconds: 48 min = 2880 s. Speed = distance/time = 57600 m / 2880 s = 20 m/s. Thus, the correct answer is 20.

A man covers a certain distance in 8 hours at the speed of 75 km/h. To cover the same distance in 6 hours, what should be his speed ?

• 150 km/h

• 100 km/h

• 300 km/h

• 200 km/h

Answer explanation

The distance covered is 75 km/h * 8 hours = 600 km. To find the speed for 6 hours, use the formula: Speed = Distance / Time = 600 km / 6 hours = 100 km/h. Thus, the required speed is 100 km/h.

Rashmika had to travel 612 km in a car travelling at a certain speed. If she reached her destination in 9 hours, find the speed of the car.

• 68 km/h

• 70 km/h

• 65 km/h

• 60 km/h

Answer explanation

To find the speed, divide the distance by time. Speed = Distance / Time = 612 km / 9 hours = 68 km/h. Thus, the speed of the car is 68 km/h.

A student reaches school on his bicycle in 3/2 hours at a speed of 8 km/h. On the return journey he rests for half an hour and takes a route which is 1 km shorter. What should be the percentage increase in the speed of the bicycle so that he reaches home in the same time?

• 37%

• 37.5%

• 30.5%

• 35%

Answer explanation

The student travels 12 km in 3/2 hours at 8 km/h. For the return, he covers 11 km (1 km shorter) in the same time minus 0.5 hours. To find the new speed, calculate: 11 km in 1 hour, which is 11 km/h. The increase is 3 km/h, or 37.5%.

Sachin and Anil started walking at the same time towards Kalka which is 50 km away from Chandigarh. The speed of Sachin is 6 km/h less than that of Anil. Anil reaches Kalka and immediately starts walking back to Chandigarh. On the way he meets Sachin at a distance of 20 km from Kalka. Find the speed of sachin :

• 4.5 km/h

• 5.1 km/h

• 4.9 km/h

• 5.0 km/h

Answer explanation

Let Anil's speed be x km/h. Then Sachin's speed is (x - 6) km/h. Anil travels 30 km to meet Sachin, taking 30/x hours. Sachin covers 20 km in the same time, so 20/(x - 6) = 30/x. Solving gives x = 10, Sachin's speed = 4.5 km/h.

Ramu can reach a certain distance to 30 hours. If he reduce his speed by 1/15th, he goes 10 km less in that time. Find his speed.

• 4 km/h

• 5 km/h

• 1 52 km

• 6 km/h

Answer explanation

Let Ramu's speed be x km/h. In 30 hours, he covers 30x km. Reducing speed by 1/15 gives (14/15)x km/h, covering 30(14/15) hours = 28x km. The difference is 10 km: 30x - 28x = 10, solving gives x = 5 km/h.

A and B start driving simultaneously from point X and go towards point Y. X and Y are 60 km apart. A's speed is 4 km/h less than that of B. B, after reaching Y, returns and meets A at a point 12 km away from Y. Find the speed of A.

• 16 km/h

• 12 km/h

• 8 km/h

• 20 km/h

Answer explanation

Let B's speed be x km/h, then A's speed is (x - 4) km/h. B travels 60 km to Y and 12 km back to meet A, covering 72 km. A travels 60 - 12 = 48 km. Setting up the equation: 72/x = 48/(x-4) leads to x = 12. Thus, A's speed is 8 km/h.

Two boys Rishi and Vamsi start at the same time to ride from Lucknow to Kanpur that is 95 km away. Rishi travels 5 km/h slower than Vamsi. Vamsi reaches Kanpur and immediately start to travel back. On his return journey he meets Rishi who is 25 km away from Kanpur. Find Rishi's speed.

• 8 km/h

• 5 km/h

• 7 km/h

• 6 km/h

Answer explanation

Let Vamsi's speed be x km/h. Then Rishi's speed is (x - 5) km/h. Vamsi travels 95 km to Kanpur and returns 70 km when he meets Rishi. The time taken by both is equal, leading to the equation: 95/x = 70/(x-5). Solving gives Rishi's speed as 7 km/h.