In a 800 m race. A beats B by 74 m and in a 600 m race, B beats C by 50 m. By how many metres will A beat C in a race of 800 m ?

134.5 m

The correct answer is Option (3) → 134.5 m

$\frac{Speed\,of\,A}{Speed\,of\,B}=\frac{800}{726}$

$\frac{Speed\,of\,B}{Speed\,of\,C}=\frac{600}{550}$

$∴\frac{Speed\,of\,A}{Speed\,of\,C}=\frac{800}{726}×\frac{600}{550}$

$=\frac{9600}{7986}≃1.201$

∴ Distance covered = $\frac{800}{1.201}≃666.94m$

∴ A beats C by,

$800-666.94≃134.5m$