Question

A can do a work in 8 days and B can do the same work in 16 days. If A, B and C can together do the same work in 4 days, then C can do the work in

• A. 10 days
• B. 4 days
• C. 8 days
• D. 16 days

Hint:

Use the concept of work rates and subtract known rates from the total to find unknown individual rates.

Answer 1

The Correct Option is D

Step 1: Find individual work rates
A's rate = \(\frac{1}{8}\) work/day.
B's rate = \(\frac{1}{16}\) work/day.
Step 2: Find combined rate of A, B and C
Combined rate = \(\frac{1}{4}\) work/day.
Step 3: Find C's rate
\[ \text{C's rate} = \text{combined rate} - \text{A's rate} - \text{B's rate} = \frac{1}{4} - \frac{1}{8} - \frac{1}{16}. \] Find a common denominator (16): \[ = \frac{4}{16} - \frac{2}{16} - \frac{1}{16} = \frac{4 - 2 - 1}{16} = \frac{1}{16}. \]
Step 4: Find time taken by C
Time = reciprocal of work rate = 16 days.
Step 5: Conclusion
C alone can do the work in 16 days.