Let the total profit be Rs. 100.
After paying to charity, A's share = (95*3/5) = Rs. 57.
If A's share is Rs. 57, total profit = Rs. 100.
If A's share is Rs. 855, total profit = (100/57*855) = 1500.
Let their initial investments be x, 3x and 5x respectively. Then,
A:B:C = (x*4+2x*8) : (3x*4+(3x/2)*8) : (5x*4+(5x/2)*8)
20x : 24x : 40x = 5 : 6 : 10
Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
B's share = Rs. (378 * 8/21) = Rs. 144.
Let the total profit be Rs. z. Then,
B's share = Rs. 2z/3, A's share = Rs. ( z - 2z/3 ) = Rs. z/3.
A : B = z/3 : 2z/3 = 1:2
Let the total capital be Rs, X and suppose B's money was used for x months. Then.
(1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3) = 10 .
Thus, B's money was used for 10 months.
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