In a 100 metre race, A beats B by 10 metres and C by 13 metres. By how many meters will B beat C in a 180 metre race ?

6 metres

The correct answer is Option (2) → 6 metres

Let speeds of A, B & C be $V_A,V_B,V_C$ respectively

A beats B by 10m:

$\frac{100}{V_A}=\frac{90}{V_B}⇒V_B=\frac{90}{100}V_A=0.9V_A$

A beats C by 13m:

$\frac{100}{V_A}=\frac{87}{V_C}⇒V_C=\frac{87}{100}V_C=0.87V_A$

$\frac{V_C}{V_B}=\frac{0.87V_A}{0.9V_A}=\frac{87}{90}=\frac{29}{30}$

When B runs 180m, time taken:

$t_B=\frac{180}{V_B}$

Distance by C in same time:

$=V_C×t_B=V_C×\frac{180}{V_B}=180×\frac{V_C}{V_B}$

$=180×\frac{29}{30}=6×29=174$ meters

∴ B beats C in a 180m race by

$180-174=6$ meters