Question

In a kilometre race, $A$ beats $B$ by $30$ seconds and $B$ beats $C$ by $15$ seconds. If $A$ beats $C$ by 180 metres, the time taken by $A$ to run $1$ kilometre is

• A. $250$ seconds
• B. $205$ seconds
• C. $200$ seconds
• D. $210$ seconds

Answer 1

Answer: (B)

$205$ seconds

A beats B by $30$ seconds, B beats C by $15$ seconds
$\therefore$ A beats C by $(30+15)$ seconds = $45$ seconds
$\Rightarrow$ Time taken by C to travel $180$ m = $45$ seconds
$\Rightarrow$ Time taken by C to cover the distance of
$1km\left(1000m\right)=\frac{45}{180}\times 1000=250seconds$
$\therefore$ Required time taken by A to cover the distance of 1 km $=(250-45)sec=205sec.$