Question

A can do a piece of work in 20 days and B in 15 days. They worked together on it for 6 days and then, A left. In how many days will B finish the remaining work?
A.\[2\dfrac{5}{2}\]
B.\[3\dfrac{7}{3}\]
C.\[2\dfrac{6}{5}\]
D.\[4\dfrac{1}{2}\]

Answer 1

Hint: First find A and B’s together in the number of days they complete the work. Then find the remaining work. Then find the work done by B after A.

Complete step-by-step answer:
A can do a piece of work \[=\,20\] days
B can do a piece of work \[=\,15\] days
L.C.M. of their work \[=\,60\]
Let the\[\,60\]is the total work which A and B have to do.
So, A do the work in a day \[=\,\dfrac{60}{20}\,=\,3\]
And B do the work in a day \[=\,\dfrac{60}{15}\,=\,4\]
When A and B work together they do the work in a day \[=\,4+3\,=7\]
A left the work after days, so after days work finished \[=7\times 6\,=\,42\]
Remaining work \[\begin{align}
  & =\,60-42 \\
 & =\,18 \\
\end{align}\]
So B will complete remaining work in \[=\,\dfrac{18}{4}\]
On dividing \[4\] days and \[12\] hours.
\[4\dfrac{1}{2}\]

Note: In this type of questions firstly go through the concepts as there are many concepts like work together, work alone. Sometimes there are three elements there to work together and two left in the idle of the work. So understand the concept of work together and work alone. Always find the total word done first then find the work fraction of each. By doing this, the question became easy and understandable. So always find total work done then work done by each and together and put the value in formula. This will help you a lot.