Question : A alone can do a work in 14 days. B alone can do the same work in 28 days. C alone can do the same work in 56 days. They started the work together and completed the work such that B was not working in the last 2 days and A did not work in the last 3 days. In how many days (total) was the work completed?
Option 1: $\frac{82}{7}$ days
Option 2: $\frac{79}{7}$ days
Option 3: $\frac{65}{7}$ days
Option 4: $\frac{72}{7}$ days
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Correct Answer: $\frac{72}{7}$ days
Solution :
Given: A alone can do a work in 14 days. B alone can do the same work in 28 days. C alone can do the same work in 56 days.
Use the formula, Total work = efficiency × time.
| Time | Efficiency | Total work | |
| A | 14 | $\frac{56}{14}=4$ | 56 |
| B | 28 | $\frac{56}{28}=2$ | 56 |
| C | 56 | $\frac{56}{56}=1$ | 56 |
For the last 2 days, B has not worked, while A has not worked for the last 3 days.
Let the entire work be finished in $x$ days.
⇒ $4(x–3)+2(x–2)+x=56$
⇒ $4x–12+2x–4+x=56$
⇒ $7x=56+16$
⇒ $7x=72$
⇒ $x=\frac{72}{7}$ days
Hence, the correct answer is $\frac{72}{7}$ days.
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