A and B run a kilometre and A wins by 25 sec. A and C run a kilometre and A wins by 275 m. When B and C run the same distance, B wins by 30 sec. The time taken by A to run a kilometre is :

Answer: Option A

Let the time taken by A to cover 1 km = x sec
Time taken by B and C to cover the same distance = (x + 25) sec and (x + 55) sec

$$\begin{array}{rl}& \frac{\text{A}}{\text{C}}=\frac{29}{40}=\frac{x}{x+55}\\ & \Rightarrow 29x+1595=40x\\ & \Rightarrow x=\frac{1595}{11}\\ & \Rightarrow x=145\end{array}$$
∴ Time taken by A
= 145 sec
= 2 minutes 25 seconds