Question

Vinay and Versha run a race with their speeds in the ration of 5:3. They prefer to run on a circular track of cricumference 1.5 km. What is the distance covered by Vinay when he passes Versha for the seventh time?

• A. 25.25 kms
• B. 26.25 kms
• C. 27 kms
• D. None of these

Answer 1

The correct option is B 26.25 kms

Since, the speeds of Vinay and Versha are in the ration of 5:3 i.e. when Vinay covers 5 rounds, then Versha covers 3 rounds, but first time Vinay and Versha meet when Vinay completes $2\frac{1}{2}$ round and Versha completes $1\frac{1}{2}$ round.
For Vinay to pass Versha $7^{th}$ time, Vinay would have completed $7\times 2\frac{1}{2}$ rounds. Since, each round is $1\frac{1}{2}$ km, the distance covered by Vinay is
$7\times 2\frac{1}{2}\times 1\frac{1}{2}=7\times \frac{5}{2}\times \frac{3}{2}=26\frac{1}{4}kms$