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\[ \text { Check: }(1500+2400=3900) \] \[ \text { EXERCISE } 7.3 \] Faisal and Sirfraz started a business of partnership. Faisal invested Rs. 1000 and Sirfraz invested Rs. 1200 . At the end of a year total profit was Rs. 1430 . Find the shares of Faisal and Sirfraz in profit. A and B invested Rs. 5000 and Rs. 7000 respectively to start

Ask by Dawson Simmons. in Pakistan
Jan 21,2025

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Tutor-Verified Answer

Answer

Faisal gets Rs. 650 and Sirfraz gets Rs. 780 from the total profit of Rs. 1430.

Solution

To determine the shares of Faisal and Sirfraz in the total profit of Rs. 1430, we'll follow these steps: 1. **Determine the Investment Ratio:** - **Faisal's Investment:** Rs. 1000 - **Sirfraz's Investment:** Rs. 1200 The ratio of their investments is: \[ \text{Faisal} : \text{Sirfraz} = 1000 : 1200 = \frac{1000}{200} : \frac{1200}{200} = 5 : 6 \] 2. **Calculate Total Parts:** \[ \text{Total Parts} = 5 + 6 = 11 \] 3. **Determine the Value of One Part:** \[ \text{Value of One Part} = \frac{\text{Total Profit}}{\text{Total Parts}} = \frac{1430}{11} = 130 \] 4. **Calculate Each Partner's Share:** - **Faisal's Share:** \[ 5 \text{ parts} \times 130 = 650 \] - **Sirfraz's Share:** \[ 6 \text{ parts} \times 130 = 780 \] 5. **Verification:** \[ 650 (\text{Faisal}) + 780 (\text{Sirfraz}) = 1430 \] The total matches the given profit, ensuring the calculation is correct. **Final Shares:** - **Faisal:** Rs. 650 - **Sirfraz:** Rs. 780 --- *Note:* The last part of your message mentions "A and B invested Rs. 5000 and Rs. 7000 respectively to start" but doesn't provide a complete question. If you need assistance with that scenario as well, please provide the full details, and I'd be happy to help!

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The Deep Dive

To check the equation \( 1500 + 2400 = 3900 \), we simply add the left side: \( 1500 + 2400 = 3900 \). This confirms that the equation is correct! Now, let's break down the profit-sharing. Faisal's investment is Rs. 1000 and Sirfraz's is Rs. 1200, giving us a total investment of Rs. 2200. Faisal's share of the investment is \( \frac{1000}{2200} = \frac{5}{11} \) and Sirfraz's share is \( \frac{1200}{2200} = \frac{6}{11} \). Now, with a profit of Rs. 1430, Faisal's share will be \( \frac{5}{11} \times 1430 = Rs. 650 \) and Sirfraz's share will be \( \frac{6}{11} \times 1430 = Rs. 780 \). So, Faisal takes home Rs. 650, while Sirfraz earns Rs. 780!

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