Question

The monthly incomes of two persons are in the ratio 9 : 7 and their expenses are in the ratio of 4 : 3. If each of them saves $200 per month, find their monthly incomes?

Answer 1

Solution:

 

Suppose monthly incomes of two persons be 9x and 7x and their expensive be 4y and 3y respectively.

 

From the question:

9x - 4y = 200 - Eq.I

7x - 3y = 200 - Eq.II

 

Multiplying Eq.I by 3 and Eq.II by 4, we have:

27x - 12y = 600 - Eq.III

28x - 12y = 800 - Eq.IV

 

Subtracting Eq. III from Eq. IV:

(28x - 12y) - (27x - 12y) = 800 - 600

⇒ x = 200

 

Substitute x = 200 in Eq. I:

9(200) - 4y = 200

⇒ - 4y = 200 - 1800 = - 1600

⇒ 4y = 1600

⇒ y = 1600 / 4 = 400

 

So, the monthly incomes of two persons are:

9x = 9 (200) = 1800 and

7x = 7 (200) = 1400

 

i.e. the monthly incomes of two persons are $1,800 and $1,400.

The monthly incomes of two persons are $1,800 and $1,400.