Question
Download Solution PDFA invests ₹2400 for 12 months. After 8 months, B joins with an investment of ₹x. After one year, the profit of B is 3/11 of the total profit. Find the value of x.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFA invests ₹2400 for 12 months.
B joins after 8 months, so B invests ₹x for 4 months.
The profit of B is 3/11 of the total profit.
The profit-sharing ratio in a partnership is calculated as:
Profit Ratio = Investment × Time
A's investment = ₹2400 × 12 months = ₹28,800
B's investment = ₹x × 4 months = ₹4x
The ratio of their investments is:
A : B = 28,800 : 4x
Simplify the ratio by dividing both sides by 4:
A : B = 7,200 : x
The profit of B is 3/11 of the total profit. This means:
Profit of B / Total Profit = 3 / 11
The profit-sharing ratio is:
B's Share / (A's Share + B's Share) = 3 / 11
Substitute the investment ratio:
x / (7,200 + x) = 3 / 11
11x = 3 (7,200 + x)
11x = 21,600 + 3x
8x = 21,600
x = 21,600 / 8 = 2,700
Thus, the value of x is ₹2,700.
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