A runs 9 times slower than B. If B gives A a start of 80 meters, how far must be the wining post on the tracks so that A and B reach there at the same time?

90 meters

The correct answer is Option (4) → 90 meters

Let the speed of A be $v$. Then speed of B = $9v$ (since A runs 9 times slower).

A is given a start of 80 m, so distance for A to reach the post = $D - 80$, and distance for B = $D$.

Time taken by both to reach the post must be equal:

$\frac{D-80}{v} = \frac{D}{9v}$

Multiply both sides by $9v$:

$9(D-80) = D$

$9D - 720 = D$

$8D = 720$

$D = 90$

Winning post distance = 90 m