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, 1/12 mile
• B. Chinmay, 1/32 mile
• C. Akshay, 1/24 mile
• D. Chinmay, 1/16 mile

Hint:

Use speed ratio logic from relative leads and scale them to find outcomes for new race lengths.

Answer 1

The Correct Option is B

Step 1: Convert race data into ratios:
Bhairav beats Akshay by 128 m in 1,600 m ⇒ Akshay runs 1,472 m when Bhairav runs 1,600 m.
So: Speed ratio of Akshay to Bhairav = $1472:1600$
Step 2: Bhairav beats Chinmay by 4 m in 100 m ⇒ Chinmay runs 96 m when Bhairav runs 100 m.
Speed ratio of Chinmay to Bhairav = $96:100$
Step 3: Now find ratio of Akshay to Chinmay:
Akshay / Chinmay = (Akshay / Bhairav) ÷ (Chinmay / Bhairav) = $(1472/1600) ÷ (96/100) = \frac{1472 \cdot 100}{1600 \cdot 96}$
Simplify: $\frac{147200}{153600} = \frac{23}{24}$
Step 4: In a 1.5-mile race = 2,400 m: Akshay runs 2,400 m, Chinmay runs $(24/23) \cdot 2400 = 2,504.35$ m
So Chinmay wins by $\approx 104.35$ m
Convert to miles: $104.35 / 1600 \approx 1/15.3$ mile ≈ 1/16 mile
So Chinmay wins, lead ≈ 1/16 mile ⇒ Option (d)