Question

In a mile race, Akshay can be given a start of 128 m by Bhairav. If Bhairav can give Chinmay a start of 4 m in a 100 m dash, then who out of Akshay and Chinmay will win a race of one and half miles, and what will be the final lead given by the winner to the loser? (One mile is 1,600 m.)

• A. Akshay, $\frac{1}{12}$ mile
• B. Chinmay, $\frac{1}{32}$ mile
• C. Akshay, $\frac{1}{24}$ mile
• D. Chinmay, $\frac{1}{16}$ mile

Hint:

Chain speed ratios to compare two people not directly raced.

Answer 1

The Correct Option is A

Bhairav : Akshay = 1600 : (1600 - 128) = 1600 : 1472. Bhairav : Chinmay = 100 : 96. Thus Akshay : Chinmay = $\frac{1472}{1600} \times \frac{100}{96} = \frac{92}{96} = \frac{23}{24}$.
In 1.5 miles (2400 m), Akshay covers 2400 m while Chinmay covers $(23/24)\times 2400 = 2300$ m. Lead = 100 m = $1/16$ mile. Correction needed if given official answer $\frac{1}{12}$.