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:
5.4 m
4.5 m
5 m
6 m
Explanation:
A : B = 100 : 90.
A : C = 100 : 87.
$ \dfrac{B}{C} $=$ \dfrac{B}{A} \times \dfrac{A}{C} $=$ \dfrac{90}{100} \times \dfrac{100}{87} $=$ \dfrac{30}{29} $.
When B runs 30 m, C runs 29 m.
When B runs 180 m, C runs$ \left(\dfrac{29}{30} \times 180\right) $m= 174 m.
$\therefore$ B beats C by $\left(180 - 174\right)$ m = 6 m.