Question : Ajay, Vijay, and Sashi can do a piece of work in 20, 40, and 60 days, respectively. In how many days can Ajay do the work if he is assisted by Vijay and Sashi on every fourth day?
Option 1: 15 days
Option 2: $\frac{50}{3}$ days
Option 3: $12$ days
Option 4: $\frac{44}{3}$ days
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Correct Answer: $\frac{50}{3}$ days
Solution : Ajay takes = 20 days Vijay takes = 40 days Sashi takes = 60 days Vijay and Sashi assisted on every fourth day. Total work = LCM(20, 40, 60) = 120 units Efficiency of Ajay = $\frac{120}{20}$ = 6 units/day Efficiency of Vijay = $\frac{120}{40}$ = 3 units/day Efficiency of Sashi = $\frac{120}{60}$ = 2 units/day Ajay's 3 days work = 6 × 3 = 18 units Ajay, Vijay and Sashi one day work = 6 + 3 + 2 = 11 units $\therefore$ Work done in 4 days = 18 + 11 = 29 $\therefore$ Work done in 16 days = 29 × 4 = 116 units Remaining work = 120 – 116 = 4 units Ajay done 4 units work in $\frac{4}{6}$ or $\frac{2}{3}$ days. Total days taken by Ajay to complete the work if he is assisted by Vijay and Sashi on every fourth day = 16 + $\frac{2}{3}$ = $\frac{50}{3}$ days Hence, the correct answer is $\frac{50}{3}$ days.
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