Question

The monthly incomes of A and B are in the ratio 5 : 4 and their monthly expenditures are in the ratio 7 : 5. If each saves ₹9,000 per month, find the monthly income of each.

Answer 1

Let the monthly income of A and B are ₹x and ₹y respectively.
Then as per the question
$$\begin{gathered} \frac{x}{y}=\frac{5}{4} \\ \Rightarrow y=\frac{4x}{5}.....\left(i\right) \end{gathered}$$
Since each save ₹9,000, so
Expenditure of A = ​₹$\left(x-9000\right)$
Expenditure of B = ​₹$\left(y-9000\right)$
The ratio of expenditures of A and B are in the ratio 7 : 5.
$$\begin{gathered} \therefore \frac{x-9000}{y-9000}=\frac{7}{5} \\ \Rightarrow 7y-63000=5x-45000 \\ \Rightarrow 7y-5x=18000.....\left(ii\right) \end{gathered}$$
From (i), substitute $y=\frac{4x}{5}$ in (ii) to get
$$\begin{gathered} 7\times \frac{4x}{5}-5x=18000 \\ \Rightarrow 28x-25x=90000 \\ \Rightarrow 3x=90000 \\ \Rightarrow x=30000 \end{gathered}$$
Now, putting x = 30000, we get
$y=\frac{4\times 30000}{5}=4\times 6000=24000$
Hence, the monthly incomes of A and B are ​₹30,000 and ​₹24,000.