The ratio between the rates of travelling of A and B is 2 : 3 and therefore A takes 20 min more than time taken by B to reach a destination. If A had walked at double the speed, how long would he have taken to cover the distance?

We know that speed is inversely proportional to time.
Therefore, Time taken by A : Time taken by B = 1/2 : 1/3
Let B takes T min. Then, A takes (T + 20) min.
∴ (T + 20) : T = 1/2 : 1/3 = 3 : 2
⇒ (T + 20)/T = 3/2
⇒ 2T + 40 = 3T
∴ T = 40
∴ A takes (T + 20) = (40 + 20) = 60 min.
∴ At double the speed, A would have covered it in 30 min.