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
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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