Question

Indu and Ramadhir can complete a task in $25$ days and $50$ days respectively. How long would Indu take to complete the task if Ramadhir assists her every second day?
A) $10$ days
B) $12$ days
C) $15$ days
D) $20$ days

Answer 1

Hint: We will find the speed of Indu and Ramadhir as we can say that we will find the word which can be done by Indu and Ramadhir in one day so as to find the required answer.

Complete step-by-step answer:
Given: It is given that Indu band Ramadhir can complete a task in $25$ days and $50$ days respectively.
First we will find the speed or work done in one day by Indu and Ramadhir.
Let ‘$x$ ’ be the work done by Indu in one day.
And also Indu takes $25$ days to complete the whole work.
Therefore total work $ = 25x$
Now we will find the work done by Ramadhir in one day.
Work done in one day $ = \dfrac{{{\text{total}}\,{\text{work}}}}{{{\text{total}}\,{\text{time}}\,{\text{taken}}}}$
And we found that total work $ = 25x$ and it is given that it takes $50$ days to complete the task by Ramadhir.
Therefore work done by Ramadhir in one day $ = \dfrac{{25x}}{{50}}$
$ = \dfrac{x}{2}$
And as given that Ramadhir assists Indu every second day hence he will do $\dfrac{x}{4}$ work every single day.
So work done by Indu and Ramadhir in one day if ramadhir assists her every second day $ = x + \dfrac{x}{4}$$ = \dfrac{{5x}}{4}$
Now we will apply the formula of total time taken to find the time taken to find the time taken by both to finish the work.
Total time taken $ = \dfrac{{{\text{total}}\,{\text{work}}}}{{{\text{work}}\,{\text{done}}\,{\text{in}}\,{\text{one}}\,{\text{day}}}}$
Total work$ = 25x$
Work done in one day $ = \dfrac{{5x}}{4}$
Hence, total time taken $ = \dfrac{{25x}}{{\dfrac{{5x}}{4}}}$
$ = \dfrac{{25}}{5} \times 4$
= $20$
It takes $20$ days to finish the work if Ramadhir assists Indu on every second day.
Hence, the correct option is D.

Note: Though Ramadhir assists Indu every second day, we require his work speed of one day and that is why we divide his speed by $2$ to find the work done by him in a single day.