In a 700 m race, the ratio of speeds of two participants A and B is 5 : 6. If A has a start of 150 m, then the distance by which A wins the race is:

40 m

The correct answer is Option (2) → 40 m

Given: Race distance = 700 m, speed ratio A:B = 5:6, A has a start of 150 m

Let speeds: $v_A : v_B = 5 : 6$ → $v_A = 5k$, $v_B = 6k$

Distance remaining for A: $700 - 150 = 550$ m

Time for A to finish: $t = \frac{550}{5k} = \frac{110}{k}$

Distance covered by B in this time: $s_B = v_B * t = 6k * \frac{110}{k} = 660$ m

Total race distance = 700 m → A wins by: $700 - 660 = 40$ m

Distance by which A wins = 40 m