Let's solve the problem:

Problem Breakdown:

1. Given:

   • A, B, and C together can complete the work in 10 days.
   • A alone can complete the work in 30 days.
   • B alone can complete the work in 40 days.

   We need to calculate in how many days C alone can complete the work.

2. Solution:

   • Work done by A, B, and C together in 1 day = $\frac{1}{10}$
   • Work done by A alone in 1 day = $\frac{1}{30}$
   • Work done by B alone in 1 day = $\frac{1}{40}$

   Using the formula: $\text{Work of C in 1 day} = \text{Work of (A, B, and C together)} - \text{Work of A} - \text{Work of B}$

   Substituting values: $\text{Work of C in 1 day} = \frac{1}{10} - \frac{1}{30} - \frac{1}{40}$

3. Simplify the equation: Find the Least Common Denominator (LCD) of 10, 30, and 40, which is 120: $\text{Work of C in 1 day} = \frac{12}{120} - \frac{4}{120} - \frac{3}{120}$ $\text{Work of C in 1 day} = \frac{12 - 4 - 3}{120} = \frac{5}{120} = \frac{1}{24}$

   So, C alone can complete the work in 24 days.

Final Answer:

(2) 24 days

Let me know if you would like further clarification or have additional questions!

Related Questions:

1. How do we calculate work done when more than three workers are involved?
2. What happens if the rates of work are given in fractions instead of days?
3. How would the solution change if one worker takes a break for certain days?
4. Can we solve this problem graphically? How would the results compare?
5. How can such problems be automated programmatically?

Tip: Always reduce fractions to simplify your work rate equations for clarity.