Question : Raju, Sunil and Vishal can separately finish a work in 20, 30 and 40 days, respectively. In how many days Raju can finish the work, if he is assisted by Sunil and Vishal on alternate days, starting with Sunil?
Option 1: $12 \frac{3}{5}$
Option 2: $12 \frac{1}{20}$
Option 3: $11 \frac{1}{20}$
Option 4: $11 \frac{3}{5}$
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Correct Answer: $12 \frac{3}{5}$
Solution :
Time taken by Raju to complete the work = 20 days
⇒ Part of work done by Raju in a day = $\frac{1}{20}$
Time taken by Sunil to complete the work = 30 days
⇒ Part of work done by Sunil in a day = $\frac{1}{30}$
Time taken by Sunil to complete the work = 40 days
⇒ Part of work done by Sunil in a day = $\frac{1}{40}$
Work done by Raju and Sunil on the first day = $\frac{1}{20}$ + $\frac{1}{30}$ = $\frac{5}{60}$
Work done by Raju and Vishal in the second day = $\frac{1}{20}$ + $\frac{1}{40}$ = $\frac{6}{80}$ = $\frac{3}{40}$
Work done in first 2 days = $\frac{5}{60}$ + $\frac{3}{40}$ = $\frac{10+9}{120}$ = $\frac{19}{120}$
Work done in first (2×6) i.e.12 days = $\frac{19×6}{120}$ = $\frac{114}{120}$
Work left = $1-\frac{114}{120}$ = $\frac{6}{120}$
Work done by Raju and Sunil on 13th day = $\frac{\frac{6}{120}}{\frac{5}{60}}$ = $\frac{3}{5}$
Total time taken = $12 + \frac{3}{5}$ = $12\frac{3}{5}$ days
Hence, the correct answer is 12 $\frac{3}{5}$.
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