In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:

Answer: Option B

$$\begin{array}{rl}& A:B=200:169\\ & A:C=200:182\\ & \frac{C}{B}=\frac{C}{A}\times \frac{A}{B}\\ & =\frac{182}{200}\times \frac{200}{169}\\ & =182:169\end{array}$$
When C covers 182 m, B covers 169 m
When C covers 350 m, B covers $$\left(\frac{169}{182}\times 350\right)\text{m}=325\text{m}$$
∴ C beats B by (350 - 325) m = 25 m