Nabiha, Warda and Ayesha have started a business. They invested some money that their shares were not equal. The condition was fixed that the profit will be distributed as directly proportional to their investment. After one year they found a profit of 720000 taka, Ayesha receives \( 20 \% \) of the profit and this amount is \( 20 \% \) of that she had invested. (a) Find the total amount of money invested to their business.

To solve the problem, we need to extract the known conditions and then proceed step by step. ### Known Conditions: 1. The total profit is 720,000 Taka. 2. Ayesha receives 20% of the profit. 3. The amount Ayesha receives is also 20% of her investment. ### Step 1: Calculate Ayesha's Profit Ayesha receives 20% of the total profit: \[ \text{Ayesha's Profit} = 0.20 \times 720000 \] ### Step 2: Calculate Ayesha's Investment Let \( A \) be Ayesha's investment. According to the problem, Ayesha's profit is also 20% of her investment: \[ \text{Ayesha's Profit} = 0.20 \times A \] ### Step 3: Set Up the Equation From the above two equations, we can set them equal to each other: \[ 0.20 \times 720000 = 0.20 \times A \] ### Step 4: Solve for Ayesha's Investment Now we can solve for \( A \): \[ 720000 = A \] ### Step 5: Calculate Total Investment Since Ayesha's profit is 20% of her investment, we can find Ayesha's investment: \[ A = 720000 \] Now, since Ayesha's profit is 144000 Taka (which is 20% of 720000), we can find the total investment. Let \( T \) be the total investment of all three partners. Since the profit is distributed in proportion to their investments, we can express the total investment as: \[ T = A + W + N \] where \( W \) is Warda's investment and \( N \) is Nabiha's investment. ### Step 6: Find Total Investment Since we know Ayesha's investment is 720000 Taka, we can express the total investment in terms of Ayesha's investment and the ratios of Warda's and Nabiha's investments. However, we need more information about Warda's and Nabiha's investments to find the exact total. Since we don't have the exact amounts for Warda and Nabiha, we can only conclude that Ayesha's investment is 720000 Taka, and we need additional information to find the total investment. ### Conclusion The total amount of money invested in the business cannot be determined without knowing the investments of Warda and Nabiha. However, Ayesha's investment is 720000 Taka. If you have more information about Warda's and Nabiha's investments, please provide it to find the total investment.