In a 500 m race, the ratio of speeds of two participants, A and B, is 4:5 respectively. If A has a start of 180 m, then the distance by which A wins is

100 m

The correct answer is Option (1) → 100 m

Given race length =$ 500\ \text{m}, speed ratio A:B = 4:5, head start for A = 180\ \text{m}$

Distance A must run = $500 - 180 = 320\ \text{m}$

$\text{Time for A to finish} = \frac{320}{v_A}$

$\text{Distance covered by B in this time} = v_B \cdot \frac{320}{v_A} = \frac{5}{4} \cdot 320 = 400\ \text{m}$

$\text{Distance by which A wins} = 500 - 400 = 100\ \text{m}$