Ratio and Proportion

Concept:Use given ratios to express incomes and expenditures, then solve using savings equations.Explanation:Let incomes of A and B be $3x$ and $2x$ respectively.Let expenditures of A and B be $5y$ and $3y$ respectively.Each saves ₹1500, so:For A: $3x - 5y = 1500$ ...(1)For B: $2x - 3y = 1500$ ...(2)Multiply (1) by 3: $9x - 15y = 4500$Multiply (2) by 5: $10x - 15y = 7500$Subtract: $(10x - 15y) - (9x - 15y) = 7500 - 4500$This gives $x = 3000$.Substitute $x = 3000$ into (2):$2(3000) - 3y = 1500$$6000 - 3y = 1500$$3y = 4500$$y = 1500$B's income = $2x = 2 \times 3000 = 6000$.Answer:₹6000