Question

If in a race over a distance of $d$ meters at uniform speed, A can beat B by 20 meters, B can beat C by 10 meters and A can beat C by 28 meters, then $d$, in meters, is equal to

• A. 100
• B. 150
• C. 300
• D. 500

Answer 1

The correct option is A 100

According to the given information the ratio of speeds of A and B can be given as $\frac{A}{B}=\frac{d}{d-20}$.....(1)

Similarly,

$\frac{B}{C}=\frac{d}{d-10}$.....(2)

$\frac{A}{C}=\frac{d}{d-28}$.....(3)

From eqn (1) & (2):
$\frac{A}{C}=\frac{d}{d-20}\times \frac{d}{d-10}$.....(4)

From eqn (3) & (4)
$\frac{d}{d-28}=\frac{d}{d-20}\times \frac{d}{d-10}$

$\Rightarrow (d-10)(d-20)=d(d-28)$

$\Rightarrow d^2-30d+200=d^2-28d$

$\Rightarrow -2d=-200$

$\Rightarrow d=100$