Select the correct answerA,B and C are partners in a business. A, whose capital was used for 5 months, claims 17 part of the total profit. B, whose capital was used for 7 months, claims 15 part of the total profit. If C invested Rs. 4,600 for 9 months, then what is the amount invested by A?OptionsRs.1,650Rs.1,800Rs.1,600Rs.

Let's solve this step by step:

1. Let's assume the total profit is represented by 'P'.

2. According to the given information, A claims 17 parts of the total profit and B claims 15 parts of the total profit.

3. We can set up the following equation based on the given information: A's share of profit / B's share of profit = A's capital used / B's capital used

   Substituting the given values, we get: 17 / 15 = (A's capital used for 5 months) / (B's capital used for 7 months)

4. Simplifying the equation, we have: 17 / 15 = (A's capital used) / (B's capital used) * (7 months) / (5 months)

5. Cross-multiplying, we get: 17 * (B's capital used) * (7 months) = 15 * (A's capital used) * (5 months)

6. Now, let's consider C's investment. C invested Rs. 4,600 for 9 months.

7. We can set up another equation based on C's investment: C's capital used / B's capital used = C's investment / B's investment

   Substituting the given values, we get: (C's capital used for 9 months) / (B's capital used for 7 months) = Rs. 4,600 / (B's capital used for 7 months)

8. Simplifying the equation, we have: (C's capital used for 9 months) = Rs. 4,600

9. Now, we have two equations: 17 * (B's capital used) * (7 months) = 15 * (A's capital used) * (5 months) (C's capital used for 9 months) = Rs. 4,600

10. We can solve these equations simultaneously to find the values of A's and B's capital used.

11. Let's solve the second equation for C's capital used: (C's capital used for 9 months) = Rs. 4,600 C's capital used = Rs. 4,600 / 9

12. Now, substitute the value of C's capital used in the first equation: 17 * (B's capital used) * (7 months) = 15 * (A's capital used) * (5 months) 17 * (B's capital used) * (7) = 15 * (A's capital used) * (5) (B's capital used) = (15 * A's capital used * 5) / (17 * 7)

13. Substitute the value of B's capital used in the second equation: (C's capital used for 9 months) = Rs. 4,600 / 9 (15 * A's capital used * 5) / (17 * 7) = Rs. 4,600 / 9

14. Simplify the equation to find the value of A's capital used: A's capital used = (Rs. 4,600 / 9) * (17 * 7) / (15 * 5)

15. Calculate the value of A's capital used to find the answer.

Based on the given options, we can calculate the value of A's capital used and select the correct answer.