A puts Rs. 600 more in a business than B, but B has invested his capital for 5 months,while A has invested for 4 months. if the share of A in profit in Rs. 48 more that that of B out of the total profit of Rs. 528, Then find the capital contributed by A (in Rs.)?
Question
A puts Rs. 600 more in a business than B, but B has invested his capital for 5 months,while A has invested for 4 months. if the share of A in profit in Rs. 48 more that that of B out of the total profit of Rs. 528, Then find the capital contributed by A (in Rs.)?
Solution
Let's denote the capital contributed by B as x (in Rs.). Therefore, the capital contributed by A would be x + 600 (in Rs.).
According to the problem, the ratio of their profits is equal to the ratio of the products of their capitals and the time they invested for. So, we can write the equation as follows:
(A's capital * A's time) / (B's capital * B's time) = (A's profit) / (B's profit)
Substituting the given values into the equation, we get:
((x + 600) * 4) / (x * 5) = (A's profit) / (B's profit)
We also know that the total profit is Rs. 528 and A's profit is Rs. 48 more than B's profit. So, we can write:
A's profit = B's profit + 48 B's profit + A's profit = 528
Substituting A's profit from the first equation into the second equation, we get:
2 * B's profit + 48 = 528 B's profit = (528 - 48) / 2 = 240
Substituting B's profit into the first equation, we get:
A's profit = 240 + 48 = 288
Now, substituting A's profit and B's profit into the ratio equation, we get:
((x + 600) * 4) / (x * 5) = 288 / 240 (x + 600) / x = 6 / 5
Solving this equation for x, we get:
x = 600 * 5 = 3000
Therefore, the capital contributed by A is x + 600 = 3000 + 600 = Rs. 3600.
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