Question : Raju, Shobh, and Mohan can do a work in 15 days, 20 days and 25 days respectively. In how many days, will the work be finished, if they do it on alternate days, starting from Raju?
Option 1: $15 \frac{9}{10}$ days
Option 2: $18 \frac{7}{10}$ days
Option 3: $21 \frac{7}{10}$ days
Option 4: $18 \frac{9}{10}$ days
Correct Answer: $18 \frac{9}{10}$ days
Solution :
Time taken by Raju to do the work = 15 days
Time taken by Shobh to do the work = 20 days
Time taken by Mohan to do the work = 25 days
Work done by Raju in a day = $\frac{1}{15}$ days
Work done by Shobh in a day = $\frac{1}{20}$ days
Work done by Mohan in a day = $\frac{1}{25}$ days
Work done by Raju, Shobh and Mohan in 3 days if they work alternatively
= ($\frac{1}{15}+\frac{1}{20}+\frac{1}{25}$) = $\frac{47}{300}$ days
Work done by Raju, Shobh and Mohan in 18 days if they work alternatively
= $\frac{47}{300}\times 6$ = $\frac{282}{300}$
Work left = $1-\frac{282}{300}$ = $\frac{18}{300}$
Time taken by Raju to complete the remaining work = $\frac{\frac{18}{300}}{\frac{1}{15}}$ = $\frac{9}{10}$
So, the total time taken $= 18+\frac{9}{10}=18\frac{9}{10}$ days
Hence, the correct answer is $18\frac{9}{10}$ days.
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