Practice | Hashtable

1. 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:

A. 5.4 m

B. 4.5 m

C. 5 m

D. 6 m

Solution:

\begin{aligned} A : B = 100 : 90 \\ A : C = 100 : 87 \\ \frac{B}{C} = \frac{B}{A} \times \frac{A}{C} \\ = \frac{90}{100} \times \frac{100}{87} \\ = \frac{30}{29} \end{aligned}

When B runs180m, C runs

(\frac{29}{30} \times 180) m = 174 m

∴ B beats C by (180 - 174) m = 6 m

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