A is 50% as efficient as B. In the same time, C does half as much work as A and B together. If C alone can do the work in 20 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) → \(6\frac{2}{3}\) days
Write every efficiency in terms of B's, then use C's 20 days to fix the actual one-day work of each person.
Let B do \(b\) of the work per day; then A does \(\frac{1}{2}b\)
C does \(\displaystyle \frac{1}{2}\left(\frac{1}{2}b+b\right)=\frac{3}{4}b\) per day
\(\displaystyle \frac{3}{4}b=\frac{1}{20}\), so \(\displaystyle b=\frac{1}{15}\); A does \(\frac{1}{30}\) per day
Together \(\displaystyle =\frac{1}{30}+\frac{1}{15}+\frac{1}{20}=\frac{2+4+3}{60}=\frac{3}{20}\) per day
Time \(\displaystyle =\frac{20}{3}=6\frac{2}{3}\) days