Question : S alone can do a piece of work in 14 days. T alone can do the same work in 21 days. U alone can do the same work in 28 days. Working together, in how many days will they complete the work?
Option 1: $\frac{84}{13}$ days
Option 2: $\frac{77}{13}$ days
Option 3: $\frac{71}{13}$ days
Option 4: $\frac{87}{13}$ days
Correct Answer: $\frac{84}{13}$ days
Solution :
One day's work of S = $\frac{1}{14}$
One day's work of T = $\frac{1}{21}$
One day's work of U = $\frac{1}{28}$
One day's work of S + T + U = $\frac{1}{14}+\frac{1}{21}+\frac{1}{28}$
= $\frac{6+4+3}{84}$
= $\frac{13}{84}$
So, the work will be completed in $(1÷\frac{13}{84})=\frac{84}{13}$ days.
Hence, the correct answer is $\frac{84}{13}$ days.
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