Question

Rutu, Rushin and Nistha invested Rs. 8000, Rs. 4000 and Rs.8000 respectively in a business. Rutu left after six months. If after eighth month, there was gain of Rs.4005, then what will be the share of Rushin?

• A. 890
• B. 550
• C. 980
• D. 850

Hint:

In partnership problems, always multiply the investment amount by the duration of the investment.
Simplifying the ratio of these products at the beginning prevents calculations with large numbers.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In a partnership, the profit is distributed among partners in proportion to the product of their capital investment and the duration of their investment.
Key Formula or Approach:
The ratio of profit sharing is calculated as:
\[ \text{Profit Ratio} = (C_1 \times T_1) : (C_2 \times T_2) : (C_3 \times T_3) \]
Where \(C\) represents the capital invested and \(T\) represents the time period of investment.

Step 2: Detailed Explanation:
Let us identify the investment parameters for each partner:
1. Rutu:
- Capital invested (\(C_{\text{Rutu}}\)) = \(\text{Rs. } 8000\)
- Time period (\(T_{\text{Rutu}}\)) = \(6\text{ months}\) (since she left after six months)
\[ \text{Equivalent investment} = 8000 \times 6 = 48000 \]
2. Rushin:
- Capital invested (\(C_{\text{Rushin}}\)) = \(\text{Rs. } 4000\)
- Time period (\(T_{\text{Rushin}}\)) = \(8\text{ months}\) (since the total business duration is eight months)
\[ \text{Equivalent investment} = 4000 \times 8 = 32000 \]
3. Nistha:
- Capital invested (\(C_{\text{Nistha}}\)) = \(\text{Rs. } 8000\)
- Time period (\(T_{\text{Nistha}}\)) = \(8\text{ months}\)
\[ \text{Equivalent investment} = 8000 \times 8 = 64000 \]
4. Find the ratio of profit sharing:
\[ \text{Ratio} = 48000 : 32000 : 64000 \]
Simplify by dividing all terms by 16000:
\[ \text{Ratio} = 3 : 2 : 4 \]
5. Calculate Rushin's share of the profit:
- Total profit = \(\text{Rs. } 4005\)
- Total ratio units = \(3 + 2 + 4 = 9\text{ units}\)
- Rushin's share corresponds to 2 units of the total 9 units:
\[ \text{Rushin's Share} = \frac{2}{9} \times 4005 \]
\[ \text{Rushin's Share} = 2 \times 445 = 890 \]
This matches Option A.

Step 3: Final Answer:
The share of profit for Rushin is Rs. 890.