Question
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.)Solution
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
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