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The incomes of A and B are in the ratio ...

The incomes 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

A

Rs.8000

B

Rs.7500

C

Rs.8500

D

Rs.7000

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The correct Answer is:
To solve the problem step by step, we will follow the given ratios and the information about savings. ### Step-by-Step Solution: 1. **Define Variables for Incomes:** - Let the income of A be \(3X\) and the income of B be \(2X\) (since their incomes are in the ratio of 3:2). 2. **Define Variables for Expenditures:** - Let the expenditure of A be \(5Y\) and the expenditure of B be \(3Y\) (since their expenditures are in the ratio of 5:3). 3. **Set Up Savings Equations:** - According to the problem, both A and B save Rs. 2500. - For A: \[ \text{Income of A} - \text{Expenditure of A} = \text{Savings of A} \] \[ 3X - 5Y = 2500 \quad \text{(Equation 1)} \] - For B: \[ \text{Income of B} - \text{Expenditure of B} = \text{Savings of B} \] \[ 2X - 3Y = 2500 \quad \text{(Equation 2)} \] 4. **Eliminate Variables:** - To eliminate \(X\), we can multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of \(X\) the same: \[ 2(3X - 5Y) = 2(2500) \implies 6X - 10Y = 5000 \quad \text{(Equation 3)} \] \[ 3(2X - 3Y) = 3(2500) \implies 6X - 9Y = 7500 \quad \text{(Equation 4)} \] 5. **Subtract Equations:** - Now, subtract Equation 4 from Equation 3: \[ (6X - 10Y) - (6X - 9Y) = 5000 - 7500 \] \[ -10Y + 9Y = -2500 \] \[ -Y = -2500 \implies Y = 2500 \] 6. **Find Expenditure of B:** - Now that we have \(Y\), we can find the expenditure of B: \[ \text{Expenditure of B} = 3Y = 3 \times 2500 = 7500 \] ### Final Answer: The expenditure of B is Rs. 7500. ---
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