The monthly incomes of A and B are in the ratio of 5 : 4 and their monthly expenditures are in the ratio of 7 : 5. If each saves Rs. 3000 per month, find the monthly income of each.
Given ratio of incomes = 5:4
And the ratio of their expenditures = 7:5
Saving of each person = Rs. 3000
Let incomes of two persons = 5x and 4x
And their expenditures = 7y and 5y
According to the question,
5x – 7y = 3000 …(i)
4x – 5y = 3000 …(ii)
On multiplying Eq. (i) by 4 and Eq. (ii) by 5 to make the coefficients of x equal, we get
20x – 28y = 12000 …(iii)
20x – 25y = 15000 …(iv)
On subtracting Eq. (iii) from (iv), we get
20x – 25y – 20x + 28y = 15000 – 12000
⇒ 3y = 3000
⇒ y = 1000
On putting the y = 1000 in Eq. (i), we get
5x – 7y = 3000
⇒ 5x – 7(1000) = 3000
⇒ 5x = 10000
⇒ x = 2000
Thus, monthly income of both the persons are 5(2000) and 4(2000), i.e. Rs. 10000 and Rs. 8000
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