Question : X can do a piece of work in 14 days, Y can do the same work in 28 days and Z can do it in 42 days. In how many days can X, Y, and Z together complete the work?
Option 1: $7 \frac{9}{11}$
Option 2: $7 \frac{7}{11}$
Option 3: $7 \frac{5}{11}$
Option 4: $7 \frac{3}{11}$
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Correct Answer: $7 \frac{7}{11}$
Solution :
The time taken by X, Y, and Z to complete work alone is 14, 28 and 42 days, respectively.
So, 1 day's work of X, Y, and Z, respectively is $\frac{1}{14}, \frac{1}{28}, \frac{1}{42}$.
Their total 1 day's work
= $\frac{1}{14}+ \frac{1}{28}+ \frac{1}{42}$
= $\frac{(6+3+2)}{84}$
= $\frac{11}{84}$
So, total time is taken if X, Y, and Z working together = $\frac{84}{11}=7\frac{7}{11}$ days
Hence, the correct answer is $7\frac{7}{11}$.
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