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A and B together can do a piece of work in $ 8 $ days. B alone completes that work in $ 12 $ days. B worked alone for $ 4 $ days. In how many more days after that could A alone complete it.
A. $ 15 $ days
B. $ 18 $ days
C. $ 16 $ days
D. $ 20 $ days

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Last updated date: 12th Jul 2024
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Answer
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Hint: Here we will find the work done by A individual by finding the correlation between the work done by B only and A and B. Find the total work done and accordingly find the work done by A and days to complete it.

Complete step-by-step answer:
Given that: A and B complete work $ = 8 $ days
B alone completes work $ = 12 $ days
Take the LCM (least common multiple) for the numbers $ 8 $ and $ 12 = 24 $
Now, the LCM suggests us that the total work is $ 24 $ units
So, A and B completes work in $ 8 $ days –
Therefore, work done by A and B together $ = \dfrac{{24}}{8} = 3 $ units of work per day …. (A)
Also, given that B alone completes work in $ 12 $ days and
Therefore, work done by B $ = \dfrac{{24}}{{12}} = 2 $ units of work per day …. (B)
From the equations (A) and (B)
The work done by A alone $ = 3 - 2 = 1 $ unit of work per day
Now,
B works for $ 4 $ days, therefore work done by B in $ 4 $ days $ = 4 \times 2 = 8 $ units of work
Now, total units of work is $ 24 $
So, remaining work to be done by A $ = 24 - 8 = 16 $ units of work
A performs $ 1 $ unit of work per day and therefore for $ 16 $ units of work it will take $ 16 $ days.
From the given multiple choices, the option C is the correct answer.
So, the correct answer is “Option C”.

Note: Read the question twice and follow the step by step approach. Find the correct correlation from all the known terms to get the value of unknown terms. Be good in ratio and proportion concepts to solve these types of word problems.