The problem provided is as follows:

A company divided a bonus among its employees A, B, and C in the ratio 2:3:7. C's bonus was X% more than the combined bonus of A and B. We are asked to find the value of X.

Step-by-step solution:

1. Let the total amount of the bonus be $k$. The bonuses for A, B, and C are given in the ratio of 2:3:7. So, let:

   • A's bonus = $2k$
   • B's bonus = $3k$
   • C's bonus = $7k$

2. The combined bonus of A and B is: $2k + 3k = 5k$

3. C's bonus is given as X% more than the combined bonus of A and B. This can be expressed as: $7k = 5k + \frac{X}{100} \times 5k$

4. Simplify the equation: $7k = 5k \left(1 + \frac{X}{100}\right)$ Divide both sides by $5k$: $\frac{7}{5} = 1 + \frac{X}{100}$

5. Solve for X: $\frac{7}{5} - 1 = \frac{X}{100}$ $\frac{2}{5} = \frac{X}{100}$ Multiply both sides by 100: $X = \frac{2}{5} \times 100 = 40$

So, X = 40.

Would you like further clarification or details on any part of the solution?

Here are 5 related questions for further practice:

1. If the total bonus is $10,000, how much does each employee receive?
2. What would happen if the ratio of the bonuses was 3:5:8 instead of 2:3:7?
3. How would the result change if C's bonus was X% less than the combined bonuses of A and B?
4. If the total bonus distribution changes such that the combined bonus of A and B is twice that of C, what would be the new ratio?
5. Can you express the combined bonuses of A and B as a percentage of the total bonus?

Tip: When solving percentage problems, breaking the relationship into algebraic equations often simplifies the process and makes the solution more apparent.