A and B started together to cover a certain distance, at a speed of 8 km/h and 10 km/h, respectively. If A arrives 15 minutes after B, then find the distance.

10 km

The correct answer is Option (4) → 10 km

Let the distance be D km.

• Speed of A = 8 km/h
• Speed of B = 10 km/h
• Time taken by A = $\frac{D}{8}$​ hours
• Time taken by B = $\frac{D}{10}$​ hours

Given: A arrives 15 minutes (¼ hour) after B

$\frac{D}{8} - \frac{D}{10} = \frac{1}{4}$

$D\left(\frac{1}{8} - \frac{1}{10}\right) = \frac{1}{4}$

$D\left(\frac{5 - 4}{40}\right) = \frac{1}{4}$

$\frac{D}{40} = \frac{1}{4}$

$D = 10$