# 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

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.

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