Question

The monthly pocket money of Ravi and Sanjeev are in the ratio $5:7$. Their expenditures are in the ratio $3:5$. If each saves ₹$80$ every month, find their monthly pocket money.

Answer 1

Hint: Firstly , we will suppose monthly pocket money and expenditure and then we will convert the given ratio in the equation. Further by using elimination method, we will calculate the value of $x\,\,and\,\,y$. And then we will find their monthly pocket money.


Complete step by step solution:
Let the monthly pocket money of Ravi be equal to $5x$ and Sanjeev by $7x$.
Let the expenditure of Ravi be $3y$ and Sanjeev be $5y$.
According to given information in the question each of them saves ₹$80$
Ravi, $5x - 3y = 80$ ……(i)
Sanjeev $7x - 5y = 80$ ……(ii)
Now, we will use elimination method, to calculate the value of $x\,\,and\,\,y$
We will multiply equation (i) by $(5)$ and equation (ii) by $3,$ we have
$
  \underline
  25x - 15y = 400 \\
  21x - 15y = 240 \\
    \\
  4x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 160 \\
 $
$x = \dfrac{{160}}{4}$
$x = 40$
Then, we will substitute the value of $x = 40$ in equation (i), we will get
$
  5x - 3y = 80 \\
  5(40) - 3y = 80 \\
 $
$
  200 - 3y = 80 \\
   - 3y = 80 - 200 \\
 $
$ - 3y = - 120$
$
  3y = 120 \\
  y = \dfrac{{120}}{3} \\
 $
$y = 40$
Therefore $x = 40,\,\,y = 40$
We will find their monthly pocket money
So,
The monthly pocket money of Ravi $ = 5x$
The monthly pocket money of Ravi$ = 5 \times 40$
The monthly pocket money of Ravi $ = 200$
The monthly pocket money of Sanjeev $ = 7x$
The monthly pocket money of Sanjeev $ = 7 \times 40$
The monthly pocket money of Sanjeev $ = 280$
Hence, their monthly pocket money be $200\,\,and\,\,280$


Note: Students must know that expenditures is the amount which is spent from the salary whereas savings that amount which will be accumulated and will add up to the total amount at the end.