Work done by A in one day is half of the work done by B in one day. Work done by B is half of the work done by C in one day. If C alone can do the work in 7 days, then in how many days can A, B and C together complete the work?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4
Work rates (the part of the work done in one day) add up when people work together, and the time taken is 1 ÷ the combined rate.
C does the work in 7 days: C’s rate \(\displaystyle =\frac{1}{7}\)
B does half as much as C in a day: B’s rate \(\displaystyle =\frac{1}{14}\)
A does half as much as B in a day: A’s rate \(\displaystyle =\frac{1}{28}\)
Together: \(\displaystyle \frac{1}{28}+\frac{1}{14}+\frac{1}{7}=\frac{1+2+4}{28}=\frac{7}{28}=\frac{1}{4}\) of the work a day
Time taken together \(=\) 4 days