The ratio of the incomes of A and B is 5:7 and their savings are ₹5,000 and ₹9,000, respectively. If the ratio of their expenditures is 3:4, then what is the sum of the incomes (in ₹) of A and B?
- A72,000
- B84,000
- C60,000
- D96,000
Solution & Step-by-step Explanation
Let the incomes of A and B be 5x and 7x, respectively.
We know that:
Expenditure=Income−Savings
Expenditure of A = 5x−5000
Expenditure of B = 7x−9000
The ratio of their expenditures is 3:4:
7x−9000
5x−5000
=
4
3
Cross-multiply to find x:
4(5x−5000)=3(7x−9000)
20x−20000=21x−27000
21x−20x=27000−20000⟹x=7000
The sum of their incomes is:
Sum=5x+7x=12x=12×7000=₹84,000
We know that:
Expenditure=Income−Savings
Expenditure of A = 5x−5000
Expenditure of B = 7x−9000
The ratio of their expenditures is 3:4:
7x−9000
5x−5000
=
4
3
Cross-multiply to find x:
4(5x−5000)=3(7x−9000)
20x−20000=21x−27000
21x−20x=27000−20000⟹x=7000
The sum of their incomes is:
Sum=5x+7x=12x=12×7000=₹84,000