Question : Rohan and Mohit, together, can build a wall in 8 days. Mohit and Vikas can build the same wall in 10 days and Vikas and Rohan can Build the same wall in 12 days. In how many days can all three complete the same wall while working together?
Option 1: $\frac{240}{37}$
Option 2: $\frac{120}{37}$
Option 3: $\frac{150}{37}$
Option 4: $\frac{180}{37}$
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Correct Answer: $\frac{240}{37}$
Solution :
Word done by Rohan and Mohit in one day = $\frac{1}{8}$ ---------------------(1)
Work done by Mohit and Vikas in one day = $\frac{1}{10}$ ----------------------(2)
Work done by Vikas and Rohan in one day = $\frac{1}{12}$ ---------------------(3)
Adding (1), (2), and (3), we get
2(Work done by Rohan, Mohit and Vikas in one day) = $\frac{1}{8}+\frac{1}{10}+\frac{1}{12}$
⇒ Work done by Rohan, Mohit and Vikas in one day = $\frac{37}{120}\times \frac{1}{2}$ = $\frac{37}{240}$
$\therefore$ Together they will complete the wall in $\frac{240}{37}$ days.
Hence, the correct answer is $\frac{240}{37}$.
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