The problem involves calculating a partner's profit share based on their investment and the duration of their involvement in a business. We are given information about the investments of A, B, and C, the time periods, and a portion of the total profit. We need to find B's share of the profit.
1. Calculate the Total Profit
We are told that 15% of the total profit amounts to ₹6,600. Let the total profit be '\(P\)'.
\( 0.15 \times P = ₹6,600 \)
To find the total profit \(P\), we rearrange the equation:
\( P = \frac{₹6,600}{0.15} \)
\( P = ₹44,000 \)
So, the total profit for the year is ₹44,000.
2. Determine Profit Sharing Ratio
The profit sharing ratio depends on the product of the investment amount and the duration (in months). The business runs for a year (12 months).
- A invested ₹29,000 for 12 months.
- B invested ₹95,000 for 6 months.
- C invested ₹67,000 for the remaining 6 months (since B withdrew after 6 months).
Calculate the ratio product for each partner:
| Partner | Investment (₹) | Time (Months) | Ratio Product (Investment × Time) |
|---|---|---|---|
| A | 29,000 | 12 | \(29,000 \times 12 = 348,000\) |
| B | 95,000 | 6 | \(95,000 \times 6 = 570,000\) |
| C | 67,000 | 6 | \(67,000 \times 6 = 402,000\) |
The ratio of their profits is the ratio of these products: A : B : C = 348,000 : 570,000 : 402,000.
Simplify the ratio by dividing by common factors. First, divide by 1,000:
A : B : C = 348 : 570 : 402
Now, divide by 6 (a common factor):
A : B : C = \((348 \div 6)\) : \((570 \div 6)\) : \((402 \div 6)\)
A : B : C = 58 : 95 : 67
The sum of the ratio parts is \(58 + 95 + 67 = 220\).
3. Calculate B's Profit Share
B's share of the profit is calculated using his ratio part and the total profit.
B's Share = \( \left( \frac{\text{B's Ratio Part}}{\text{Total Ratio Parts}} \right) \times \text{Total Profit} \)
B's Share = \( \left( \frac{95}{220} \right) \times ₹44,000 \)
B's Share = \( 95 \times \left( \frac{44,000}{220} \right) \)
B's Share = \( 95 \times 200 \)
B's Share = ₹19,000
Therefore, B's share of the profit is ₹19,000.
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Important Questions from Partnership
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