A is twice as efficient as B. In the same time, C does one-third as much work as A and B together. If C alone can do the work in 24 days, in how many days can A, B and C together do the same work?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6 days
Write every efficiency in terms of B's, then use C's 24 days to fix the actual one-day work of each person.
Let B do \(b\) of the work per day; then A does \(2b\)
C does \(\displaystyle \frac{1}{3}(2b+b)=b\) per day
\(\displaystyle b=\frac{1}{24}\); A does \(\frac{1}{12}\) per day
Together \(\displaystyle =\frac{1}{12}+\frac{1}{24}+\frac{1}{24}=\frac{2+1+1}{24}=\frac{1}{6}\) per day
Time \(=6\) days