The income of A and B are in the ratio of 3 : 2 and their expenditure in the ratio of 5 : 3. If each saves Rs. 2500, then the expenditure of B is:

Question

Accepted Answer

To solve the problem, we need to determine the expenditure of B given the conditions about the income and expenditure ratios and the savings of A and B.

1. **Understanding the Ratios:**
   - The income ratio of A to B is 3:2. Let's assume the income of A is 3x and the income of B is 2x.
   - The expenditure ratio of A to B is 5:3. Let's assume the expenditure of A is 5y and the expenditure of B is 3y.

2. **Savings Information:**
   - Both A and B save Rs. 2500. This means:
     - Savings of A = Income of A - Expenditure of A = 3x - 5y = 2500
     - Savings of B = Income of B - Expenditure of B = 2x - 3y = 2500

3. **Setting Up Equations:**
   - From the savings information, we have two equations:
     1. $3x - 5y = 2500$
     2. $2x - 3y = 2500$

4. **Solving the Equations:**
   - Multiply the first equation by 2 and the second equation by 3 to eliminate x:
     - $6x - 10y = 5000$
     - $6x - 9y = 7500$

- Subtract the second equation from the first:
     - $(6x - 10y) - (6x - 9y) = 5000 - 7500$
     - $-y = -2500$
     - $y = 2500$

5. **Finding the Expenditure of B:**
   - Since $y = 2500$, the expenditure of B, which is $3y$, is:
     - $3 \times 2500 = 7500$

Therefore, the expenditure of B is Rs. 7500, which corresponds to Option 2.

**Explanation for Other Options:**
- **Option 1 (Rs. 8000):** This option is incorrect because, based on the calculations, the expenditure of B is determined to be Rs. 7500, not Rs. 8000.
- **Option 3 (Rs. 8500):** This option is incorrect because the calculated expenditure of B is Rs. 7500, which does not match Rs. 8500.
- **Option 4 (Rs. 7000):** This option is incorrect because the expenditure of B, as calculated, is Rs. 7500, not Rs. 7000.

Thus, the correct answer is Option 2, Rs. 7500, as supported by the logical and mathematical reasoning provided.