The ratio of the incomes of A and B is 5: 7 and the ratio of their expenditures is 3: 4. If A and B save ₹5,000 and ₹9,000, respectively, then what is the difference (in ₹) between the income of A and two times the savings of B?

Let the income of A and B be 5x and 7x respectively.
Let their expenditures be 3y and 4y respectively.

We know that: Income−Savings=Expenditure
For A:

5x−5000=3y⟹y=
3
5x−5000
​

For B:

7x−9000=4y
Substitute the value of y into B's equation:

7x−9000=4(
3
5x−5000
​
)
3(7x−9000)=4(5x−5000)
21x−27000=20x−20000
21x−20x=27000−20000
x=7000
Now, find the income of A:

Income of A=5x=5×7000=₹35,000
Savings of B = ₹9,000
Two times the savings of B =2×9000=₹18,000

The required difference is:

Difference=35000−18000=₹17,000