In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

Answer: Option D

$$\begin{array}{rl}& A:B=100:90\\ & A:C=100:87\\ & \frac{B}{C}=\frac{B}{A}\times \frac{A}{C}\\ & =\frac{90}{100}\times \frac{100}{87}\\ & =\frac{30}{29}\end{array}$$
When B runs180m, C runs $$\left(\frac{29}{30}\times 180\right)\text{m}=174\text{m}$$
∴ B beats C by (180 - 174) m = 6 m