Question

In a 500 m race, P and Q have speeds in the ratio of 3 : 4. Q starts the race when P has already covered 140 m. What is the distance between P and Q (in m) when P wins the race?

• A. 20
• B. 40
• C. 60
• D. 140

Hint:

When two people are running a race at different speeds, you can use the ratio of their speeds to find how much distance one covers when the other reaches the finish line.

Answer 1

The Correct Option is A

Let the speeds of P and Q be \( 3x \) and \( 4x \) respectively. The total distance of the race is 500 m. P has already covered 140 m, so the remaining distance for P to cover is: \[ 500 - 140 = 360 \text{ m}. \] Since P takes time to cover 360 m, the time taken by P is: \[ \text{Time taken by P} = \frac{360}{3x} = \frac{120}{x}. \] Now, Q starts the race when P has covered 140 m. In the same time, the distance covered by Q is: \[ \text{Distance covered by Q} = \text{Speed of Q} \times \text{Time} = 4x \times \frac{120}{x} = 480 \text{ m}. \] Since the total length of the race is 500 m, the remaining distance between P and Q when P finishes the race is: \[ 500 - 480 = 20 \text{ m}. \] Thus, the distance between P and Q when P wins the race is 20 meters.