The ratio of the incomes of A and B is 2:3 and the ratio of their expenditures is 5:7. If 7 times the income of A is equal to $6 times the expenditure of B, then what is the ratio of the savings of A and B?

Let the incomes of A and B be 2x and 3x respectively.
Let the expenditures of A and B be 5y and 7y respectively.

According to the given condition:

7×(Income of A)=6×(Expenditure of B)
7×2x=6×7y
14x=42y
y
x
​
=
14
42
​
=
1
3
​

So, let x=3 and y=1.

Now, substitute the values to find incomes and expenditures:

Income of A = 2x=2×3=6

Income of B = 3x=3×3=9

Expenditure of A = 5y=5×1=5

Expenditure of B = 7y=7×1=7

Savings are calculated as Income−Expenditure:

Savings of A = 6−5=1

Savings of B = 9−7=2

Therefore, the ratio of the savings of A and B is 1:2.