Question

The ratio of incomes of two persons is 9:7 and the ratio of expenditure is 4:3. If each of them saves Rs 200 per month, find their monthly incomes.

Answer 1

Hint:We will be using the concepts of ratio and proportion to solve the problem. We will be using the conditions given in the question to form an equation by using the fact that the savings is equal to expenditure subtracted from the total income. We will have two equations using the fact that they have been saving rupees 200.

Complete step-by-step answer:
Now, we have been given that the ratio of incomes is 9:7 and the ratio of expenditure is 4:3.
So, we let the incomes of the two person be,
Income of person A = 9x
Income of person B = 7x
Also, we let the expenditure of two persons be,
Expenditure of person A = 4y
Expenditure of person B = 3y
Now, we have been given that both the person saves Rs 200 per month. We know that savings is equal to total income – expenditure.
So, we have far person A,
Total income – expenditure = 200
$9x-4y=200...........\left( 1 \right)$
For person B we have,
Total income- expenditure = 200
$7x-3y=200..........\left( 2 \right)$
Now, we will solve equation (1) and (2) for the values of x and y. On equating (1) and (2) we have,
$\begin{align}
  & 9x-4=+x-3y \\
 & 2x=4y-3y \\
 & 2x=y \\
\end{align}$
Now, we will use this in (1). So, we have,
$\begin{align}
  & 9x-8x=200 \\
 & x=200 \\
 & y=2x \\
 & y=2\times 200 \\
 & =400 \\
\end{align}$
Now, we have the incomes of
$\begin{align}
  & Person\ A=9\times x=9\times 200=1800 \\
 & Person\ B=7\times x=7\times 200=1400 \\
\end{align}$

Note: To solve these types of questions it is important to convert the conditions given in the question into equations and solve these equations to get the desired answer also it is important to note that we have taken the income of two persons as 9x ,7x respectively and their expenditure as 4y and 3y respectively.