Question

The monthly income of A and B are in ratio 7:5 and expenditures are in the ratio 3:2.If each saves repees 1500 per month,find their monthly incomes. with explaination (plz)​

Answer 1

Answer:

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Answer 2

The monthly income of A is Rs.10500 and B is Rs.15000.

Given:

The monthly income of A and B are in the ratio $7:5$. Their expenditures are in the ratio $3:2$. Each of them saves Rs.1500 per month.

To Find:

The monthly income of both A and B.

Solution:

Let $7x$ is the monthly income of A and $5x$ is the monthly income of B. Also, let their expenditures be $3y$ and $2y$.

Write two equations for the saving amount of A and B.

$7x-3y=1500\,\,\,\, ...(1)$

$5x-2y=1500\,\,\,\, ...(2)$

To solve equations (1) and (2) find the value of $x$ from the first equation.

$7x=1500+3y\\x=\frac{1500+3y}{7}$

Substitute $\frac{1500+3y}{7}$ for $x$ into the equation (2) and simplify to find $y$.

$5(\frac{1500+3y}{7}) -2y=1500\\\frac{7500+15y}{7}-2y=1500\\ 7500+15y-14y=10500\\y=3000$

Substitute 3000 for $y$ into the equation and find $x$.

$x=\frac{1500+3\cdot 3000}{7}\\=\frac{1500+9000}{7}\\ =\frac{10500}{7}\\ =1500$

Substitute 1500 for $x$ into $7x$ and find the monthly income of A.

$7(1500)=10500$

Substitute 3000 for $y$ into $5x$ and find the monthly income of B.

$5(3000)=15000$

Thus, the monthly income of A and B are Rs.10500 and Rs.15000 respectively.