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The monthly incomes of A and B are in the ratio $8 : 7$ and their expenditures are in the ratio $19 : 16$. If each saves ₹2500 per month, find the monthly income of each.
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Let the monthly incomes of A and B be $\text{Rs}8x$ and $\text{Rs}7x$ respectively and the expenditures of A and B be $\text{Rs}19y$ and $\text{Rs}16y$ respectively.
A.T.Q.
$$\begin{aligned}& 8x - 19y = 2500 \dots (1) \\ & 7x - 16y = 2500 \dots (2) \\ & Solving (1)\end{aligned}$$ and $(2)$, we have $$\begin{aligned}& x = 1500 \\ & \therefore\end{aligned}$$ Monthly income of A = $8 \times 1500 = 12000\\$and monthly income of B = $$\begin{aligned}& 7 \times 1500 = 10500 \\ & \therefore\end{aligned}$$ monthly incomes of A and B are ₹12000 and ₹10500 respectively.
A.T.Q.
$$\begin{aligned}& 8x - 19y = 2500 \dots (1) \\ & 7x - 16y = 2500 \dots (2) \\ & Solving (1)\end{aligned}$$ and $(2)$, we have $$\begin{aligned}& x = 1500 \\ & \therefore\end{aligned}$$ Monthly income of A = $8 \times 1500 = 12000\\$and monthly income of B = $$\begin{aligned}& 7 \times 1500 = 10500 \\ & \therefore\end{aligned}$$ monthly incomes of A and B are ₹12000 and ₹10500 respectively.