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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 4 · Set 1 · Q27
The monthly incomes of two persons are in the ratio 9: 7 and their monthly expenditures are in the ratio 4: 3. If each saved ₹ 5,000, express the…
The monthly incomes of two persons are in the ratio $\displaystyle 9$ : $\displaystyle 7$ and their monthly expenditures are in the ratio $\displaystyle 4$ : 3. If each saved ₹ $\displaystyle 5,000$, express the given situation algebraically as a system of linear equations in two variables. Hence, find their respective monthly incomes.
Marking-scheme solution
Let us assume that income of two persons be ₹ \(\displaystyle 9 x\) and ₹ \(\displaystyle 7 x\) and their expenitures be ₹ \(\displaystyle 4 y\) and ₹ \(\displaystyle 3 y\)
ATQ
\[9 x-4 y=5000
\]
and \(\displaystyle 7 x-3 y=5000\)
Solving the two equations, we get \(\displaystyle x=5000\)
∴ Monthly incomes of two persons are ₹ $\displaystyle 45000$ and ₹ $\displaystyle 35000$ respectively.
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