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(B) Let the monthly incomes of $A$ and $B$ be $8x$ and $5x$ respectively.Let the monthly expenditures of $A$ and $B$ be $5y$ and $3y$ respectively.We

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$42$

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(B) Let the monthly incomes of $A$ and $B$ be $8x$ and $5x$ respectively.Let the monthly expenditures of $A$ and $B$ be $5y$ and $3y$ respectively.We know that $	ext{Income} - 	ext{Expenditure} = 	ext{Savings}$.For $A$: $8x - 5y = 12,000$  --- (Equation $1$)For $B$: $5x - 3y = 10,000$  --- (Equation $2$)To solve for $x$,multiply Equation $1$ by $3$ and Equation $2$ by $5$:$24x - 15y = 36,000$  --- (Equation $3$)$25x - 15y = 50,000$  --- (Equation $4$)Subtract Equation $3$ from Equation $4$:$(25x - 24x) - (15y - 15y) = 50,000 - 36,000$$x = 14,000$Monthly income of $A = 8x = 8 	imes 14,000 = 1,12,000$.Monthly income of $B = 5x = 5 	imes 14,000 = 70,000$.Difference in monthly incomes $= 1,12,000 - 70,000 = 42,000$.

$A$ and $B$ have their monthly incomes in the ratio $8: 5,$ while their monthly expenditures are in the ratio $5: 3.$ If they save ₹ $12,000$ and ₹ $10,000$ monthly respectively,then the difference in their monthly incomes is (in ₹): (in $,000$)

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