Question
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:
Answer: Option D
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A : B = 100 : 90.
A : C = 100 : 87.
\(\frac{B}{C}=\frac{B}{A}\times\frac{A}{C}=\frac{90}{100}\times\frac{100}{87}=\frac{30}{29}.\)
When B runs 30 m, C runs 29 m.
When B runs 180 m, C runs \(\left(\frac{29}{30}\times180\right)m. = 174m.\)
So, B beats C by (180 - 174) m = 6 m.
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