Question : A and B are equally efficient and each could individually complete a piece of work in 30 days if none took any holiday. A and B started working together on this piece of work, but A took a day off after every four days of work, while B took a day off after every five days of work. If the duo had started work on 01 August 2022, on which date was the work completed?
Option 1: 19 August 2022
Option 2: 17 August 2022
Option 3: 16 August 2022
Option 4: 18 August 2022
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Correct Answer: 18 August 2022
Solution : Time taken by A and B individually to do the work = 30 days Let total work = 30 units Since A and B have equal efficiency, Work done by A in a day = work done by B in a day = 1 In 18 days A takes 3 leaves and B takes 3 leaves. $\therefore$ Work done in 18 days = work done by A in 15 days + work done by B in 15 days = 15 + 15 = 30 units $\therefore$ On the 18th day, the date will be 18 August 2022. Hence, the correct answer is 18 August 2022.
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Question : Ravi can do a piece of work in 40 days and Sudha can do the same piece of work in 60 days. If they work on alternative days, starting with Sudha on the first day, then in how many days will the work be completed?
Option 1: 40
Option 2: 60
Option 3: 48
Option 4: 45
Question : A and B together can do a piece of work in 36 days and B and C together can do it in 24 days. A and C together can do it in 18 days. The three working together can finish the work in:
Option 1: 8 days
Option 2: 16 days
Option 3: 30 days
Option 4: 32 days
Question : A and B together can complete a piece of work in 12 days. They worked together for 5 days and then A alone finished the rest of the work in 14 days. A single person can complete the work in:
Option 1: 24 days
Option 2: 22 days
Option 3: 20 days
Option 4: 18 days
Question : A can do a piece of work in 6 days, working 8 hours a day, while B can do the same work in 4 days, working 10 hours a day. If the work has to be completed in 5 days, how many hours do they need to work together in a day?
Option 1: $4$
Option 2: $5\frac{4}{11}$
Option 3: $6\frac{4}{11}$
Option 4: $4\frac{4}{11}$
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
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