Question

‘A’ can do a piece of work in 40 days. He worked at it for 5 days, then ‘B’ finished it in 21 days. The number of days that ‘A’ and ‘B’ take together to finish the work are:
(A). 15 days
(B). 14 days
(C). 13 days
(D). 10 days

Answer 1

Hint: Find the work done by A in 1 day. Thus get the work done by A in 5 days. Now find the remaining work B has to do in 21 days. Thus fixed the total no. of days B has to work and work done by B in one day. Now, find work done by $\left( A+B \right)$in one day. Thus get the no. of days that $\left( A+B \right)$takes to finish the work.

Complete step-by-step solution -
We have been told that A can do work in 40 days, which means that a takes 40 days to complete the work given to him.
Now let us find the work done by A in one day.
Work of A in 1 day $=\dfrac{1}{40}$ .
Now it is said that A does the work for 5 days.
$\therefore $ The work done by A in 5 days $=\dfrac{5}{40}=\dfrac{1}{8}$ .
Hence we can say that $\dfrac{1}{8}$ part of the work is done by A. We have been told that A does the work for 5 days and the left of work is done by B in 21 days. Now out of this work A finished $\dfrac{1}{8}$ of the work. Thus, let us find the work done by B.
The remaining work $=1-\dfrac{1}{8}=\dfrac{8-1}{8}=\dfrac{7}{8}$ .
Hence B has to do $\dfrac{7}{8}$ of the work in 21 days.
Hence the total work done by B $=\dfrac{\text{No}\text{. of days}}{\text{Remaining work}}$ .
$\therefore $ Total work will be done by B in \[=\dfrac{21}{{}^{7}/{}_{8}}=\dfrac{21}{7}\times 8=24\] .
$\therefore $ B will finish all the work in 24 days.
Now, let us fix the work done by B in one day.
The work done by B in one day $=\dfrac{1}{24}$ .
Let us fix the work done by A and B together in one day will be equal to, work done by A in one day and work done by B in one day. We found that work done by A in one day $=\dfrac{1}{40}$ .
Similarly work done by B in one day $=\dfrac{1}{24}$ .
$\therefore $ Work done by $\left( A+B \right)$ in one day = work done by A + work done by B
$\begin{align}
  & =\dfrac{1}{40}+\dfrac{1}{24}=\dfrac{24+40}{24\times 40} \\
 & =\dfrac{64}{960}=\dfrac{1}{15} \\
\end{align}$
Hence work done by $\left( A+B \right)$ in one day $=\dfrac{1}{15}$ .
$\therefore $A and B will take 15 days to complete the work together.
Hence we got the no. of days that A and B take together to finish the work are 15 days.
$\therefore $Option (A) is the correct answer.

Note: It is important that you find the remaining work that B has to do skipping this important step, you can’t find the working days of B or even how many work B completes in1 day. Now after finding work done by $\left( A+B \right)$ don’t forget to find the total no. of days $\left( A+B \right)$ work together.