A runs 1 3⁄ 8 times as fast as B. If A gives B a start of 120 m and they reach the goal at the same time, the goal is at a distance of:

The speed of A and B are in the ratio 11 : 8.
Let, speeds be 11s and 8s (in m/sec).
Let, race be of P meter.
Then, time taken by A to run P meter is same as that of B to run (P - 120) meter.
∴ P / 11 = (P - 120) / 8
∴ P / 11 = (P - 120 / 8
∴ 8P = 11 x (P - 120 )
∴ 8P = 11P - 120 x 11
∴ 11P - 8P = 120 x 11
∴ 3P = 11 × 120
∴ P = 440.