Question

The monthly income of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in ratio 5 : 7. If each saves ₹ 15,000 per month, find their monthly incomes.

Answer 1

Let the income of Aryan and Babban be 3x and 4x respectively.

And let their expenditure be 5y and 7y respectively.

Since each saves ₹ 15,000, we get

Aryan’s income: 3x – 5y = 15000   ...(1) 

Babban's income: 4x – 7y = 15000   ...(2)

To solve the system of equations,

We can use the elimination method.

Multiply equation (1) by 4 and equation (2) by 3:

4(3x – 5y) = 4(15000)

⇒ 12x – 20y = 60000   ...(3)

3(4x – 7y) = 3(15000)

⇒ 12x – 21y = 45000   ...(4)

Subtract equation (4) from equation (3):

(12x – 20y) – (12x – 21y) = 60000 – 45000

12x – 20y – 12x + 21y = 15000

y = 15000

Now, substitute the value of y into equation (1):

3x – 5(15000) = 15000

3x – 75000 = 15000

3x = 15000 + 75000

3x = 90000

x = `90000/3`

x = 30000

Now that we have the value of x, we can find the monthly incomes:

Aryan’s monthly income = 3x

= 3(30000)

= 90000

Babban’s monthly income = 4x

= 4(30000)

= 120000