A certain amount was divided among four people P, Q, R and S such that the amount obtained by S is 12.5% more than the amount obtained by Q. The amount obtained by P is one third of the amount obtained by S. The average of the amount obtained by R and Q is Rs. 27000. If the difference between the amount obtained by R and S is Rs. 7200, then find out the amount obtained by Q. (It is assumed that the amount is not in fractions or decimals.)

The amount obtained by P is one third of the amount obtained by S.

Let’s assume the amount obtained by S is ‘9a’.

amount obtained by P = (1/3) of 9a = 3a

The amount obtained by S is 12.5% more than the amount obtained by Q.

9a = (100+12.5)% of the amount obtained by Q

9a = 112.5% of the amount obtained by Q

amount obtained by Q = 8a

The average of the amount obtained by R and Q is Rs. 27000.

Total amount obtained by R and Q = 27000x2 = 54000

amount obtained by R + 8a = 54000

amount obtained by R = (54000-8a)

If the difference between the amount obtained by R and S is Rs. 7200.

9a - (54000-8a) = 7200

9a - 54000 + 8a = 7200

9a + 8a = 7200+54000

17a = 61200

a = 3600

(54000-8a) - 9a = 7200

54000-7200 = 8a+9a

17a = 46800 [This value of ‘a’ is not possible. Because it will give values in decimals.]

So the amount obtained by Q = 8a = 8x3600 = Rs. 28800