Question

A can do a certain job in 25 days which B alone can do in 20 days. A started the work and then joined by B after 10 days. In how many days was the whole work completed?

Answer 1

Hint: First of all calculate the rate of work done by both A and B per day. Then calculate the work done by A alone in 10 days. Then calculate the remaining work. Then calculate the rate of work done by A and B together in one day. Then calculate the time taken by A and B together to complete the remaining job. Then add that time to 10 days and we will get the total time for completion of the job.

Complete step by step solution:
In this question, we are given that A completes a job in 25 days and B can complete that same work in 20 days. Now, A starts to work and he works for 10 days alone and then B joins the work. Now, we need to find out how much time the work will be completed.
$ \Rightarrow $Work done by A in 1 day$ = \dfrac{1}{{25}}$
$ \Rightarrow $Work done by B in 1 day$ = \dfrac{1}{{20}}$
Now, first of all let us find the work done by A.
$ \Rightarrow $The work done by A in 10 days$ = \dfrac{1}{{25}} \times 10 = \dfrac{2}{5}$
Hence, $\dfrac{2}{5}$ part of work is done by A alone in 10 days.
Therefore, the remaining work is given by
$ \Rightarrow $Remaining work$ = 1 - \dfrac{2}{5}$
$
   = \dfrac{{5 - 2}}{5} \\
   = \dfrac{3}{5} \\
 $
So, this remaining work will be done by both A and B. Therefore, the work done by A and B in one day is
$ \Rightarrow $Work done by A and B in one day$ = \dfrac{1}{{25}} + \dfrac{1}{{20}}$
$
   = \dfrac{{4 + 5}}{{100}} \\
   = \dfrac{9}{{100}} \\
 $
Now,
$
  1day = \dfrac{9}{{100}}work \\
  ?days = \dfrac{3}{5}work \\
 $
Therefore,
$ \Rightarrow $Time taken by A and B to complete $\dfrac{3}{5}$ part of job$ = \dfrac{3}{5} \div \dfrac{9}{{100}}$
$
   = \dfrac{3}{5} \times \dfrac{{100}}{9} \\
   = \dfrac{{20}}{3} \\
 $
Therefore,
$ \Rightarrow $Total time taken by A and B to complete the job$ = 10 + \dfrac{{20}}{3}$
$
   = \dfrac{{30 + 20}}{3} \\
   = \dfrac{{50}}{3}days \\
$

Note:
Here the days obtained are in improper fraction form. When the denominator of a fraction is smaller than the numerator than the fraction is said to be an improper fraction. We need to convert this into a mixed number. Therefore,
$ \Rightarrow \dfrac{{50}}{3} = 16\dfrac{2}{3}$
Hence, the job will be completed in $16\dfrac{2}{3}$ days.