The ratio of the salaries of S to F is 2:3 and the ratio of their savings is 3:4. What is the ratio of their expenditures if their total savings are equal to the salary of S?

Let the salaries of S and F be 2x and 3x respectively.
Let the savings of S and F be 3y and 4y respectively.

According to the question, their total savings are equal to the salary of S:

Total Savings=3y+4y=7y
Salary of S=2x
So, 7y=2x⟹x=
2
7
​
y

Now, express the salaries in terms of y:

Salary of S=2x=2(
2
7
​
y)=7y
Salary of F=3x=3(
2
7
​
y)=
2
21
​
y=10.5y
Expenditure is calculated as Salary−Savings:

Expenditure of S=7y−3y=4y
Expenditure of F=10.5y−4y=6.5y
The ratio of their expenditures is:

Expenditure of F
Expenditure of S
​
=
6.5y
4y
​
=
6.5
4
​
=
13
8
​