Question

The monthly incomes of A and B and in the ration of 5:4 and their monthly expenditures are in the
Ration of 7:5. If each saves Rs 3000 per month, find the monthly income of each.​

Answer 1

Let the incomes of A and B be 5M and 4M & monthly expenditures be 7N and 5N.

Both A and B saves Rs. 3000 per month.

We have to find the monthly income of A and B.

Income of A - Monthly expenditure of A = Saving per month

$\implies\:5M\:-\:7N\:=\:3000$ ____ (eq 1)

Similarly,

Income of B - Monthly expenditure of B = Saving per month

$\implies\:4M\:-\:5N\:=\:3000$ _____ (eq 2)

Multiply (eq 1) with 4 and (eq 2) with 5

$\Rightarrow\:5M\:-\:7N\:=\:3000\:\:(\times\:4)$

$\Rightarrow\:20M\:-\:28N\:=\:12000$ _____ (eq3)

$\Rightarrow\:4M\:-\:5N\:=\:3000\:\:(\times\:5)$

$\Rightarrow\:20M\:-\:25N\:=\:15000$ _____ (eq 4)

Subtract (eq 3) from (eq 4)

→ 20M - 25N - (20M - 28N) = 15000 - 12000

→ 20M - 25N - 20M + 35N = 3000

→ 3N = 3000

→ N = 1000

Put value of N in (eq 1)

→ 4M - 5(1000) = 3000

→ 4M - 5000 = 3000

→ 4M = 8000

→ M = 2000

So,

Monthly income of A = 5M

→ 5(2000)

→ 10000

Monthly income of B = 4M

→ 4(2000)

→ 8000

Expenditure income of A = 7N

→ 7(1000)

→ 7000

Expenditure income of B = 5N

→ 5(1000)

→ 5000