Ratio of the income of A and B is 6 : 5 and the ratio of the savings of A and B is 3 : 1. If the expenditure of A and B is Tk. 12000 and Tk.16000 respectively, then find the difference between the income of A and B?

Question: Ratio of the income of A and B is 6 : 5 and the ratio of the savings of A and B is 3 : 1. If the expenditure of A and B is Tk. 12000 and Tk.16000 respectively, then find the difference between the income of A and B?

Solution:
Let,
Income of A = 6x and Income of B = 5x
And
Savings of A = 3y and Savings of B = y

We know,
Income = Savings + Expenditure

ATQ,
6x = 3y + 12000 ......(1) (for A)
5x = y + 16000 (for B)
⇒ y = 5x - 16000 ...... (2)

Puting this value in (1) then we get,
⇒ 6x = 3y + 12000
⇒ 6x = 3(5x - 16000) + 12000
⇒ 6x = 15x - 48000 + 12000
⇒ 6x = 15x - 36000
⇒ 15x - 6x = 36000
⇒ 9x = 36000
∴ x = 4000
(2) ⇒ y = 5x - 16000 = 20000 - 16000 = 4000

∴ Income of A = 24000
∴ Income of B = 20000

∴ Difference = 24000 - 20000 = Tk. 4000