Question
Download Solution PDFAanya started a business by investing some money, and Manya invested Rs. 3,500 more than Aanya did. Aanya remained in business for 6 months, and Manya remained in business for 2 months more than Aanya. Out of the total profit of Rs. 18,000, Manya got Rs. 3,000 more than Aanya. Find the capital invested by Aanya.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Manya invested Rs. 3,500 more than Aanya.
Aanya remained in business for 6 months.
Manya remained in business for 2 months more than Aanya, i.e., 8 months.
The total profit = Rs. 18,000.
Manya received Rs. 3,000 more than Aanya from the total profit.
Calculation:
Let the capital invested by Aanya be Rs. x.
Then, Manya’s capital = Rs. (x + 3500).
Aanya’s investment time = 6 months, and Manya’s investment time = 8 months.
The profit sharing ratio will be based on the product of capital invested and the time:
Aanya's share = x × 6
Manya's share = (x + 3500) × 8
Manya's share = Aanya's share + 3,000
Let Anaya's profit = y
The total profit is Rs. 18,000, and Manya received Rs. 3,000 more than Aanya:
y + y + 3000 = 18000
2y = 15000
y = 7500
Profit Ratio = \(\frac{7500}{7500 + 3000} = \frac{7500}{10500} = \frac{5}{7}\)
Investment ratio = Profit ratio
\(\frac{x\ ×\ 6}{(x\ +\ 3500) × 8} = \frac{5}{7}\)
⇒ 42x = 40(x + 3500)
⇒ 42x = 40x + 140000
⇒ 2x = 140000
⇒ x = 70000
∴ The capital invested by Aanya is Rs. 70000.
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