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 ?
Correct Answer: 235 m
A : B = 1000 : 900 and
B : C = 1000 : 850
$$\eqalign{ & \therefore \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} \cr & \,\,\,\,\,\,\,\, = \frac{{1000}}{{900}} \times \frac{{1000}}{{850}} \cr & \,\,\,\,\,\,\,\, = \frac{{1000}}{{765}} \cr} $$
A : C = 1000 : 765
∴ A beats C by (1000 - 765) m = 235 m
B : C = 1000 : 850
$$\eqalign{ & \therefore \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} \cr & \,\,\,\,\,\,\,\, = \frac{{1000}}{{900}} \times \frac{{1000}}{{850}} \cr & \,\,\,\,\,\,\,\, = \frac{{1000}}{{765}} \cr} $$
A : C = 1000 : 765
∴ A beats C by (1000 - 765) m = 235 m