Question

The annual income of A and B are in the ratio3:4 and their annual expenditure is at the ratio 5:7 .If each save Rs5000,find the annual income of A and B

Answer 1

let income 3x , 4x
expenditure 5y , 7y
ATQ
3x-5y = 4x-7y = 5000
3x-4x = -7y+5y
x= 2y
put x = 2y in any one above Equation
3(2y) -5y = 5000
y = 5000
x = 10000
income of A = 3x = 30000
income of B = 4x = 40000

Answer 2

Given that annual income of A and B is in the ratio 3:4

So, Let A's annual income be 3x and B's be 4x

Also the annual expenditure of A and B will be 5y and 7y respectively


We know that,

Money saved= Annual income - Annual expenditure

ATQ,
Money saved by A--
⇒ 5000= 3x - 5y ..... (1)

And, Money saved by B--
⇒ 5000 = 4x - 7y ....... (2) 

To solve eq (1) and (2), first multiply eq(1) by 4 and eq(2) by 3, we get:

12x - 20y = 20000..... (3)
12x - 21y= 15000...... (4)

Now subtract eq (3) from (4), we get:
⇒ -y = -5000
⇒y= 5000

Put y = 5000 in eq (2) we get:
5000 = 4x - 35000
4x = 40,000
x= 10,000

Therefore, A's income= Rs. 30,000
B's income= 40,000