Find their speeds

Let X and Y be the speeds of Ajeet and Amit respectively.

time = distance/speed

30/X = 30/Y + 2   .. (1)

Hence Ajeet takes 30/X, hrs while Amit takes 30/Y.

If 2X, then 30/(2X) = 30/Y - 1

15/X - 30/Y = - 1  .... (2)

Put 1/X = x and 1/Y = y in (1) and (2).

30x - 30y = 2

15x - 30y = - 1

Solving these simultaneously we find,

x = 1/5 i.e. X = speed of Ajeet = 1/x = 5 km/hr.

y = 2/15 i.e. Y = speed of Amit = 1/y = 15/2 = 7.5 km/hr.

regards,

Team,

TopperLearning.