Explanation:

- Let's first understand the speed of work:

- X men can complete the work in Y days.

- Y women can complete the work in X days.

- 20 men and 16 women can complete the work in $53\frac{1}{3}$ days.

- For combined work of girls, men, and women:

- (G + 24) girls and (10 men and 14 women) can complete the work in 16 days.

- If G girls work alone, the same work takes 26 days.

- We need to find the value of G.

- By comparing the equations generated from the given data, we can determine the work rate relationships.

- The calculations reveal that G, the number of girls, would be 70.

- Therefore, the correct option is Option 3: 70.

The Correct Answer is Option:3, 70.