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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Question : A, B, and C can complete a piece of work separately in 10, 20, and 40 days, respectively. In how many days will the work be completed if A is assisted by both B and C on every third day?
Option 1: $8\frac{2}{7}$
Option 2: $9$
Option 3: $10 \frac{2}{3}$
Option 4: $6$
Question : A and B can complete a piece of work in 13 and 17 days respectively. A begins to do the work, and they work alternatively one at a time for one day each. The whole work will be completed in:
Option 1: $17 \frac{11}{17}$ days
Option 2: $17 \frac{17}{19}$ days
Option 3: $14 \frac{11}{17}$ days
Option 4: $11 \frac{11}{17}$ days
Question : A, B, and C can do a piece of work in 30, 20, and 10 days respectively. A is assisted by B on one day and by C on the next day, alternately. How long would the work take to finish?
Option 1: $9 \frac{3}{8}$ days
Option 2: $4 \frac{8}{8}$ days
Option 3: $8 \frac{4}{13}$ days
Option 4: $3 \frac{9}{13}$ days
Question : A, B, and C can do a piece of work in 20, 30, and 60 days, respectively. In how many days can A do the work if he is assisted by both B and C on every third day?
Option 1: 10
Option 2: 15
Option 3: 12
Option 4: 18
Question : A, B, and C can do a piece of work in 30 days, 40 days, and 50 days, respectively. Beginning with A, if A, B, and C do the work alternatively then in how many days will the work be finished?
Option 1: $38 \frac{1}{12}$
Option 2: $36 \frac{1}{2}$
Option 3: $36$
Option 4: $39 \frac{1}{12}$
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