The ratio between the rates of walking of A and B is 2:3 and therefore A takes 10 minute more than the time taken by B to reach the destination.

If A had walked at double the speed, how much time he would have taken to reach the destination.

15 min i.e assume the same distance, d; then d/tA : d/tB =2:3

d/tA * tB/d =2/3 tB/tA = 2/3 tA = 3/2tB................1 but tA = tB +10min tB = 20min and tA = 30min at double speed, eqn 1 becomes tA = 3/4tB. but tB is unchanged, which is 20min tA = 15min

d/tA * tB/d =2/3 tB/tA = 2/3 tA = 3/2tB................1 but tA = tB +10min

tB = 20min and tA = 30min at double speed, eqn 1 becomes tA = 3/4tB. but tB is unchanged, which is 20min tA = 15min

tB = 20min and tA = 30min at double speed, eqn 1 becomes tA = 3/4tB. but tB is unchanged, which is 20min

tA = 15min

probably 4:3

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