Question

Three runners A, B, C run a race, A finishes 12 m ahead of B and 18 m ahead of C, while B finishes 8 m ahead of C. All run entire distance at constant speed. What was the length of the race?

• A. 36 m
• B. 48 m
• C. 60 m
• D. 72 m

Hint:

Race problems with finish-ahead info are solved by converting to speed ratios and chaining them.

Answer 1

The Correct Option is B

Let length of race = $d$. When A finishes $d$, B covers $d - 12$, C covers $d - 18$. Also, when B finishes $d$, C covers $d - 8$. Ratio speeds: A:B = $d : (d-12)$, B:C = $d : (d-8)$. From A:C ratio = $d : (d-18)$ = A:B × B:C = $\frac{d}{d-12} \times \frac{d}{d-8}$. Cross-multiply and solve: $(d-18)(d) = (d-12)(d-8) \Rightarrow d^2 - 18d = d^2 - 20d + 96 \Rightarrow 2d = 96 \Rightarrow d = 48$.