If X and Y have incomes in the ratio 5:3 and expenditures in the ratio 3:1 and each one of them saves ₹27,000, then what is the income of X?
- A₹68,500
- B₹70,000
- C₹67,500
- D₹69,500
Solution & Step-by-step Explanation
Let the incomes of X and Y be 5x and 3x respectively.
Let their expenditures be 3y and 1y respectively.
We know that:
Income−Savings=Expenditure
For X:
5x−27000=3y— (Equation 1)
For Y:
3x−27000=y— (Equation 2)
Substitute the value of y from Equation 2 into Equation 1:
5x−27000=3(3x−27000)
5x−27000=9x−81000
9x−5x=81000−27000
4x=54000
x=
4
54000
=13500
Income of X is 5x:
Income of X=5×13500=₹67,500
Let their expenditures be 3y and 1y respectively.
We know that:
Income−Savings=Expenditure
For X:
5x−27000=3y— (Equation 1)
For Y:
3x−27000=y— (Equation 2)
Substitute the value of y from Equation 2 into Equation 1:
5x−27000=3(3x−27000)
5x−27000=9x−81000
9x−5x=81000−27000
4x=54000
x=
4
54000
=13500
Income of X is 5x:
Income of X=5×13500=₹67,500