The ratio of the incomes of A and B is 3:4. The ratio of their expenditure is 7:10. If A and B save ₹2,500 and ₹3,000, respectively, then what is the ratio of the income of B to the combined expenditure of A and B?

Let the incomes of A and B be 3x and 4x, respectively.
We know that Expenditure=Income−Savings:

Expenditure of A = 3x−2500

Expenditure of B = 4x−3000

The ratio of their expenditures is given as 7:10:

4x−3000
3x−2500
​
=
10
7
​

Cross-multiply to solve for x:

10(3x−2500)=7(4x−3000)
30x−25000=28x−21000
30x−28x=25000−21000
2x=4000⟹x=2000
Now, calculate the absolute values required:

Income of B = 4x=4×2000=8000

Expenditure of A = 3(2000)−2500=6000−2500=3500

Expenditure of B = 4(2000)−3000=8000−3000=5000

Combined expenditure of A and B = 3500+5000=8500

We need to find the ratio of the income of B to the combined expenditure of A and B:

Ratio=
8500
8000
​
=
85
80
​
=
17
16
​
=16:17