Question : A alone can do a work in 11 days. B alone can do the same work in 22 days. C alone can do the same work in 33 days. They work in the following manner:
Day 1: A and B work.
Day 2: B and C work.
Day 3: C and A work.
Day 4: A and B work. And so on.
In how many days will the work be completed?
Option 1: 9 days
Option 2: 12 days
Option 3: 3 days
Option 4: 6 days
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Correct Answer: 9 days
Solution :
Given: A alone can do a work in 11 days.
Total work = Efficiency × Time
Let the total work be $x$.
A alone can do a work in 11 days.
A does work in 1 day = $\frac{x}{11}$
B alone can do the same work in 22 days.
B does work in 1 day = $\frac{x}{22}$
C alone can do the same work in 33 days.
C does work in 1 day = $\frac{x}{33}$
The work completed on the first day,
⇒ A and B together = $\frac{x}{11}+\frac{x}{22}=\frac{3x}{22}$
The work was completed on the second day,
⇒ B and C together = $\frac{x}{22}+\frac{x}{33}=\frac{5x}{66}$
The work completed on the third day,
⇒ C and A together = $\frac{x}{33}+\frac{x}{11}=\frac{4x}{33}$
The total work completed in 3 days = $\frac{3x}{22}+ \frac{5x}{66}+ \frac{4x}{33}=\frac{9x+5x+8x}{66}= \frac{22x}{66}$
The total work be completed in 3 days,
$\frac{22x}{66}=3$ days
⇒ $x=\frac{66\times3}{22}=9$ days
Hence, the correct answer is 9 days.
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