Question

In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

• A. 500
• B. 475
• C. 550
• D. 450

Answer 1

Answer: (D)

450

Answer 2

The correct answer is (D): $450$

Let the length of the racetrack be $D$.

When $A$ covers $D$ km, $B$ covers $( D -45)$ km and $C$ covers $(D-90)$ km

When $B$ covers $D$ km, C covers $( D -50)$ km

The ratio of the speeds of the racers is same as the ratio of the distance travelled in a given time period.

Ratio of speed of $B$ and $C$ is $\frac{\text{speed of B}}{\text{speed of C}} = \frac{D-45}{D-90} = \frac{D}{D-50}$

$⇒ \frac{D}{D-50} = \frac{45}{40}$

$⇒ 40D = 45D-50×45$

$⇒ D = 450$