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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


Team Careers360 13th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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