Question

A and B together can dig a pond in 20 days. They worked together for 8 days and then B leaves the work. How long will A take to finish the work if A alone can dig the pond in 30 days?

Answer 1

Hint: In the given question, we have been given the speed of working of a given number of entities. Then it has been given that some entities worked for a few days and then left. We have to calculate the amount of time taken by the given entity to complete the work. We are going to solve it by taking the work to be a quantity, then applying the given information for the given number of days and simplifying the values.

Complete step by step solution:
Let the work be a quantity being represented by \[x\].
It has been given that A takes a total of \[30\] days, so A’s one day work is \[\dfrac{x}{{30}}\].
Then, together they can do the work in \[20\] days, so one day’s work is \[\dfrac{x}{{20}}\].
Hence, B’s one day work is \[\dfrac{x}{{20}} - \dfrac{x}{{30}} = \dfrac{x}{{60}}\].
So, for \[8\] days, the total amount of work done is,
\[\dfrac{x}{{20}} \times 8 = \dfrac{{2x}}{5}\]
Hence, amount of work left,
\[x - \dfrac{{2x}}{5} = \dfrac{{3x}}{5}\]
Now, in one day, A does \[\dfrac{x}{{30}}\] work, so, number of days for the remaining work is,
\[\dfrac{{\dfrac{{3{x}}}{5}}}{{\dfrac{{{x}}}{{30}}}} = \dfrac{{3 \times 30}}{5} = 18\]
Hence, \[18\] days are taken by A to complete the work.

Note: In this question, we were given the speed of working of a given number of entities. Also, we were given that some entities worked for a few days and then left. We had to calculate the amount of time taken by the given entity to complete the work when its speed of working alone was given. We solved it by taking the work as a quantity and then applying the given information for the given number of days and solving. So, we must know the procedure and formula for calculating the answer to such types of questions.