The ratio of income of two persons is 9: 7 and the ratio of their expenditures is 4:3. if each of them manages to save 2000 per month, find their monthly income.
Answers
Given : -
The ratio of income of two persons is 9: 7 and the ratio of their expenditures is 4:3. if each of them manages to save 2000 per month, find their monthly income.
To find : -
Monthly income of the two persons
Solution : -
Let the their income be 9x and 7x
their expenditure be 4y and 3y
According to the given condition
- 9x - 4y = 2000 ----(i)
- 7x - 3y = 2000 -----(ii)
Solve this equation by elimination method
Multiply (i) by 3 and multiply (ii) by 4
now equation becomes
- 27x - 12y = 6000 ---(iii)
- 28x - 12y = 8000 ---(iv)
Subtracting both (iii) and (iv) equation
=> (28x - 12y) - (27x - 12y) = 8000 - 6000
=> 28x - 12y - 27x + 12y = 2000
=> 28x - 27x = 2000
=> x = 2000
By substitution method
Substitute the value of x in equation (ii)
=> 7x - 3y = 2000
=> 7 × 2000 - 3y = 2000
=> 14000 - 3y = 2000
=> -3y = -14000 - 2000
=> - 3y = - 12000
=> y = 12000/3 = 4000
So Monthly incomes are
9x = 9×2000 = Rs.18000
7x = 7×2000 = Rs.14000
✞ Given :-
- The ratio of incomes of two persons is 9 : 7
- The ratio of expenditures is 4 : 3
- Each of them manages to save ₹2000 per month
❦ R.T.P :-
- To find their monthly income....
❥ Solution :-
Let the income of the first person = 9x
Income of the second person = 7x
Let the expenditure of first person = 4y
Expenditure of the second person = 3y
According to Question ,
Each of them manages to save ₹2000 per month....
➪So, 9x - 4y = 2000....(1)
➪7x - 3y = 2000....(2)
➪ Multiply 3 to (1) and 4 to (2)....
we get,
➪27x - 12y = 6000
➪28x - 12y = 8000 [ here the signs change ]
- x = - 2000
➪x = 2000
Substitute x = 2000 in (1) ,
➪9 (2000) - 4y = 2000
➪18000 - 4y = 2000
➪18000 -2000 = 4y
➪16000 = 4y
➪ y = 4000
❦ x = 2000 ; y = 4000
______________________________________
➪ Income of 1 st person = 9x = ₹ 18000
➪ Income of 2 nd person = 7x = ₹ 14000