Question

A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how many days can the two of them complete the work together?
a) 20 days
b) 25 days
c) 30 days
d) 35 days

Answer 1

Hint: Find the work done by A in 10 days. Find the days taken by B to complete the pending work. Thus find the total work done by A and B on the work day. From that find days taken by A and B to finish work.

Complete step-by-step answer:
It is said that A can do a piece of work in 80 days.
So the work done by A in one day\[=\dfrac{1}{80}\].
It is said that B alone can do the remaining piece of work in 42 days.
Now it is said that A works on it for 10 days\[=\dfrac{1}{80}\times 10=\dfrac{1}{8}\].
Thus A completes \[\dfrac{1}{8}\]of the work. The remaining work can be said as \[1-\dfrac{1}{8}=\dfrac{7}{8}\].
So, \[\dfrac{7}{8}\]of the work is completed by B in 42 days.
\[\therefore \]The whole work completed by B\[=\dfrac{42}{\dfrac{7}{8}}=\dfrac{42\times 8}{7}=48\]days.
Thus the whole work completed by B takes 48 days.
\[\therefore \]So, the work done by B in one day\[=\dfrac{1}{48}\].
Now let us find the work done by both A and B in one day.
(A + B)’s work for 1 day\[=\dfrac{1}{80}+\dfrac{1}{48}\].
Let us simplify the above expression,
\[\dfrac{48+80}{80\times 48}=\dfrac{128}{80\times 48}=\dfrac{1}{30}\]
Therefore (A + B)’s 1 day work\[=\dfrac{1}{30}\].
\[\therefore \]A and B can complete the whole work together in 30 days.
\[\therefore \]Option (c) is the correct answer.
Note: Remember that A only completes the work of 10 days. Remember to find the remaining work which B has to do. Skipping this step will get us the wrong answer. After finding 1 day work and (A + B), reverse it to get the work for 30 days.