Question

The monthly income of A and B are in the ratio 3:4 and their monthly expenditure are in the ratio 5:7. If each saves rupees 5,000 month. Find the monthly income each.​

Answer 1

Answer:

income of A = 30,000

income of B = 40,000

Step-by-step explanation:

Given :

monthly income ratio of A and B = 3 : 4

monthly expenditure ratio of A and B = 5 : 7

savings = 5,000

To find :

monthly income of A and B

solu :

let the income of A be 3x

let the income of B be 4x

let the expenditure of A be 5y

let the expenditure Of B be 7y

$income - expenditure = savings$

therefore ;

3x - 5y = 5000 .............equn 1

4x - 7y = 5000...............equn 2

equn 1 * 4 implies , 12x - 20y = 20,000

equn 2* 3 implies , 12x - 21 y = 15 ,000

on soving the equations ;

we get , y = 5,000 and x = 10,000

income of A = 3x

= 3 ( 10000)

= 30,000

income of B = 4x

= 4 ( 10000)

= 40,000

Answer 2

Required answer:

income of A = 30,000

income of B = 40,000

Given:

monthly income of A and B = 3:4

their monthly expenditures = 5:7

each saves per rupees = ₹5,000

To find:

The monthly income of each.

Solution:

Let income of A = 3x

Let income of B = 4x

3x - 5y = 5,000 .........(1)

4x - 7y = 5,000 .........(2)

We should solve this problem by multiplying coefficient of x in first equation to equation (2) and coefficient of x in second to equation (1).

By multiplying we get

12x - 20y = 20,000 ........(3)

12x - 21y = 15,000 ........(4)

We should subtract equation (3) and (4).

By subtracting we get

1y = 5,000 ( because -20y -(-21y) = -20y+21y = 1y )

Therefore y = ₹5,000

Now, substituting y value in equation (1) to get x value.

Therefore,

3x - 5(5,000) = 5,000

3x - 25,000 = 5,000

3x = 5,000 + 25,000

3x = 30,000

x = 30,000/3

x = 10,000

Now, substituting x value in monthly income ratio to find monthly income of each.

Therefore,

3x = 3(10,000) = 30,000

Then,

income of A = 30,000

Then,

4x = 4(10,000) = 40,000

So,

the income of B = 40,000.

Therefore the income of A = 30,000 and income of B = 40,000.