Question
Harish decided to distribute Rs.16,250 among his three
sons Rohit, Ashish and Dinesh such that Ashish would get 1/4th of what Rohit and Dinesh would together get, while Dinesh would get 1/12th of what Rohit and Ashish would together get. What is the difference between Ashish and Rohit's share?Solution
Let the amount received (in Rs.) by Ashish, Rohit and Dinesh be x, y and z respectively.
∴ x = (y + z)/4
∴ 4x = y + z ... (i)
Similarly, z = (x + y)/12
∴ 12z = x + y ... (ii)
Solving (i) and (ii); 4x − 12z = z − x
∴ 5x = 13z i.e. z = 5x/13
Putting the value of z in (i), y = 47x/13
∴ x : y : z = x : 47x/13 : 5x/13 = 13 : 47 : 5
∴ Difference between the share of Rohit and Ashish = [(47 − 13)/(13 + 47 + 5)] X 16250
= (34/65) X 16250 = Rs. 8,500
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