Question

The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves rupees 200, find the income of each.

Answer 1

Let the incomes of the two persons be x and y.
$$\begin{gathered} \frac{x}{y}=\frac{9}{7} \\ \Rightarrow 7x=9y \\ \Rightarrow 7x-9y=0.....\left(\mathrm{I}\right) \end{gathered}$$
Savings of the two persons = Rs 200
Expenses = Income $-$ Savings
$$\begin{gathered} \frac{x-200}{y-200}=\frac{4}{3} \\ \Rightarrow 3x-600=4y-800 \\ \Rightarrow 3x-4y=-200.....\left(\mathrm{II}\right) \end{gathered}$$
Multiply (I) with 3 and (II) with 7.
$$\begin{gathered} 21x-27y=0.....\left(\mathrm{III}\right) \\ 21x-28y=-1400.....\left(\mathrm{IV}\right) \\ \left(\mathrm{IV}\right)-\left(\mathrm{III}\right) \\ -y=-1400 \\ \Rightarrow y=1400 \end{gathered}$$
Putting the value y in (I) we get
x = 1800
Thus, the income of the two persons is Rs 1800 and Rs 1400.