Question : Ruchi, Khushi, and Teju can do a piece of work in 30, 40, and 60 days respectively. In how many days can Ruchi do the work, if she is assisted by both Khushi and Teju on every third day?
Option 1: $\frac{550}{12}$
Option 2: $\frac{85}{4}$
Option 3: $\frac{71}{2}$
Option 4: $\frac{360}{17}$
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Correct Answer: $\frac{85}{4}$
Solution :
Let the total work be 120 units.
As LCM of 30, 40 and 60 is 120 units.
The efficiency of Ruchi, Khushi and Teju = 4, 3, 2
In 3 days, the total work complete = 4 + 4 + 9 = 17 units of work
In 21 days, the total work completed = 17 × 7 = 119 units of work
The remaining 1 unit will be completed by Ruchi in $\frac{1}{4}$ days.
$\therefore$ The total time = 21 + $\frac{1}{4}$ = $\frac{85}{4}$ days
Hence, the correct answer is $\frac{85}{4}$.
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