Question

The ratio of speed of A and B is 2:3 and A takes 10 minutes more than the time taken by B to reach a destination. If A had walked at triple the
speed, and B at half the speed, the difference between time taken by A and B will be:
a) 15 minutes
b) 20 minutes
c) 25 minutes
d) 30 minutes
e) Cannot be determined

Answer 1

speed of A --- 2x units/min
speed of B --- 3x

time for trip for A = trip/2x = t/2x, where t is the trip
time for trip for B = trip/3x = t/3x

t/2x = t/ 3x + 10
t/(2x) - t(3x) = 10
times 6x
3t - 2t = 60x
t = 60x

case2:
speed of A = 6x
speed of B = 3x/2
time for A = t/(6x)
time for B = t/(3x/2)) = 2t/(3x)

difference in time
= 2t/(3x) - t/(6x)
= 4t/6x - t/6x = 3t/6x = t/2x
= (60x/(2x)) = 30 minutes