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 :
Correct Answer: 2 min 25 sec
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
$$\eqalign{ & \frac{{\text{A}}}{{\text{C}}} = \frac{{29}}{{40}} = \frac{x}{{x + 55}} \cr & \Rightarrow 29x + 1595 = 40x \cr & \Rightarrow x = \frac{{1595}}{{11}} \cr & \Rightarrow x = 145 \cr} $$
∴ Time taken by A
= 145 sec
= 2 minutes 25 seconds
Time taken by B and C to cover the same distance = (x + 25) sec and (x + 55) sec
$$\eqalign{ & \frac{{\text{A}}}{{\text{C}}} = \frac{{29}}{{40}} = \frac{x}{{x + 55}} \cr & \Rightarrow 29x + 1595 = 40x \cr & \Rightarrow x = \frac{{1595}}{{11}} \cr & \Rightarrow x = 145 \cr} $$
∴ Time taken by A
= 145 sec
= 2 minutes 25 seconds