Question

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:

• A. 22.75 m
• B. 25 m
• C. 19.5 m
• D. $7\frac{4}{7}$ m

Answer 1

The correct option is B 25 m

A : B = 200 : 169.
A : C = 200 : 182.
$\therefore \frac{C}{B}=\left(\begin{array}{c}\frac{C}{A}\times \frac{A}{B}\end{array}\right)=\left(\begin{array}{c}\frac{182}{200}\times \frac{200}{169}\end{array}\right)=\frac{182}{169}=182:169.$
When C covers 182 m, B covers 169 m.
When C covers 350 m, B covers $\left(\begin{array}{c}\frac{169}{182}\times 350\end{array}\right)m=325m$
Therefore, C beats B by (350-325) m = 25 m.