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, the equation becomes (60/(60/(2x) - 1)) = Rohit's speed. Solving gives x = 10 km/h, which is Arjun's original speed.

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) and 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 cover this in 6 hours, 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 takes 3/2 hours to cover 12 km (8 km/h). For the return, he covers 11 km in the same time minus 0.5 hours of rest. To find the new speed, use the formula: speed = distance/time. The required speed is 11 km/(3/2 - 0.5) = 11 km/1 hour = 11 km/h. The percentage increase is ((11-8)/8) * 100 = 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 takes 50/x hours to reach Kalka and meets Sachin 20 km from Kalka. The time taken by Anil to return is equal to the time taken by Sachin to walk 30 km. Solving gives Sachin's speed as 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, and he covers 30(14/15) = 28x/15 km. The difference is 10 km: 30x - 28x/15 = 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, totaling 72 km. A travels 48 km to meet B. Setting the time equations equal gives x = 12, so 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 70 km back when they meet. 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.