Sita and Gita enter into a partnership. Sita contributes Rs 5,000 while gita contributes Rs 4,000. After 1 monts, Gita Withdraws 1/4th part of her conntribution and after 3 months from the starting Sita puts Rs 2,000 more. When Gita widhdraws her money at the same time, Rita alos joins them with Rs 7,000. If at the end of 1 year there is a profit of Rs 1,218, What will be share of Rita in the profit?

Answer

To solve the problem step by step, we will calculate the effective capital contribution of each partner based on the time their money was invested in the partnership.

### Step 1: Determine the initial contributions and their time periods
- **Sita's Contribution**: Rs 5,000 for 12 months.
- **Gita's Contribution**: Rs 4,000 for 1 month, then she withdraws 1/4th of her contribution (Rs 1,000), leaving her with Rs 3,000 for the remaining 11 months.
- **Rita's Contribution**: Rs 7,000 for 9 months (since she joins after Gita withdraws).

### Step 2: Calculate the effective capital for each partner
To find the effective capital, we multiply the amount contributed by the time period (in months).

- **Sita's Effective Capital**:
\[ 5000 \times 12 = 60000 \]

- **Gita's Effective Capital**:
- For the first month:
\[ 4000 \times 1 = 4000 \]
- For the next 11 months (after withdrawing Rs 1,000):
\[ 3000 \times 11 = 33000 \]
- Total for Gita:
\[ 4000 + 33000 = 37000 \]

- **Rita's Effective Capital**:
\[ 7000 \times 9 = 63000 \]

### Step 3: Calculate the total effective capital
Now we sum up the effective capitals of all partners:
\[ 60000 + 37000 + 63000 = 160000 \]

### Step 4: Determine the profit-sharing ratio
Now we find the ratio of their effective capitals:
- Sita: 60000
- Gita: 37000
- Rita: 63000

The ratio is:
\[ 60000 : 37000 : 63000 \]

To simplify this ratio, we can divide each term by 1000:
\[ 60 : 37 : 63 \]

### Step 5: Calculate the total parts in the ratio
Now, we add the parts of the ratio:
\[ 60 + 37 + 63 = 160 \]

### Step 6: Determine Rita's share of the profit
Given that the total profit is Rs 1,218, we can find Rita's share:
- Rita's part in the ratio is 63.
- To find Rita's share of the profit:
\[ \text{Rita's Share} = \left(\frac{63}{160}\right) \times 1218 \]

Calculating this gives:
\[ \text{Rita's Share} = \frac{63 \times 1218}{160} = \frac{76614}{160} = 478.84 \]

### Final Answer
Rita's share in the profit is approximately Rs 478.84.

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