Question

THE RATIO OF ANNUAL INCOMES OF A AND B IS 4 :3 AND THEIR ANNUAL EXPENDITURE IS 3 :2 IF EACH OF THEM SAVES SHILLINGS 1000 A YEAR FIND THEIR ANNUAL INCOMES?

Answer 1

Answer:

Annual Income of A=$4x=4*1000=4000$

and

Annual Income of B=$3y=3*1000=3000$

Step-by-step explanation:

Given Data:

Ratio of annual income of A and B=4:3

Ratio of expenditures of A and B=3:2

Saving of A and B=1000

Required: Annual Income of A and B=?

Solution:

If ratio of income of A and B is 4:3

then let Income of A=$4x$ and Income of B=$3x$

If ratio of expenditure of A and B is 3:2

then let expenditure of A=$3x$ and expenditure of B=$2x$

Therefore,

      $4x-3x=1000$...........$Eq(1)$

and $3x-2x=1000$..........$Eq(2)$

subtracting Eq(1) and Eq(2), we get

$4x-3y=1000\\-(3x-2y)=1000\\......................\\x-y=0$

$x=y.....Eq(3)$

putting $x=y$ in Eq(1), we get value of $x$ as

$4x-3x=1000$

$x=1000\\thus, y=1000$ because x and y are equal in Eq (3)

Now, Annual Income of A=$4x=4*1000=4000$

and Annual Income of B=$3y=3*1000=3000$