Question

Working together, A and B can complete a work in 10 days, B and C can complete the same work in 12 days and C and A can complete the same work in 15 days. If A, B and C work together, then how many days will be required to complete the work?

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

The Correct Option is C

Step 1: Define Variables 

Let the work done by A, B, and C in 1 day be A, B, and C respectively.

From the given conditions:

\[ A + B = \frac{1}{10}, \quad B + C = \frac{1}{12}, \quad C + A = \frac{1}{15}. \]

Step 2: Adding All the Equations

\[ (A + B) + (B + C) + (C + A) = \frac{1}{10} + \frac{1}{12} + \frac{1}{15}. \]

Rearranging:

\[ 2(A + B + C) = \frac{6}{60} + \frac{5}{60} + \frac{4}{60} = \frac{15}{60} = \frac{1}{4}. \]

Dividing by 2:

\[ A + B + C = \frac{1}{8}. \]

Step 3: Calculate the Time Required

The total time required to complete the work when all three work together is:

\[ \text{Time} = \frac{1}{A + B + C} = \frac{1}{\frac{1}{8}} = 8 \text{ days}. \]

Conclusion

The time required to complete the work is 8 days.