Question

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

Answer 1

Let the income of “A” be “x” and the income of “B” be “y”.

By the given first condition

x : y = 3 : 4

4x = 3y ...(Product of the extreme is equal to the product of the means)

4x – 3y = 0 → (1)

Expenditure of A = x – 5000

Expenditure of B = y – 5000

By the given second condition

x – 5000 : y – 5000 = 5 : 7

7(x – 5000) = 5(y – 5000)

7x – 35000 = 5y – 25000

7x – 5y = –25000 + 35000

7x – 5y = 10000 → (2)

(1) × 5 ⇒ 20x – 15y = 0 → (3)

(2) × 3 ⇒ 21x – 15y = 30000 → (4)

(3) – (4) ⇒ x + 0 = 30000

x = 30000

Substitute the value of x in (1)

4(30000) – 3y = 0

120000 = 3y

y = `120000/3` = 40000

∴ Monthly income of A is Rs 30,000

Monthly income of B is Rs 40,000