In a kilometre race, A beats B by 100 m and B beats C by 150 m. In the same race, by how many metres does A beat C ?

Answer: Option B

A : B = 1000 : 900 and
B : C = 1000 : 850
$$\begin{array}{rl}& \therefore \frac{A}{C}=\frac{A}{B}\times \frac{B}{C}\\ & =\frac{1000}{900}\times \frac{1000}{850}\\ & =\frac{1000}{765}\end{array}$$
A : C = 1000 : 765
∴ A beats C by (1000 - 765) m = 235 m