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

Speed ratio $A:B = 4:5$. With a $180$ m start, $A$ runs $500 - 180 = 320$ m.

Let common speed unit be $k$. Time for $A$ to finish $= \frac{320}{4k} = \frac{80}{k}$.

Distance covered by $B$ in this time $= 5k \cdot \frac{80}{k} = 400$ m.

$A$ finishes $500$ m while $B$ is at $400$ m $\Rightarrow$ win by $500 - 400 = \mathbf{100}$ m.