Answer

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**Hint:**In the problem we can clearly notice that the time given is in hours and the target time is in minutes, so first of all we need to convert the given hours into minutes. We know that for every hour there is $60$ minutes i.e. $1$hour $=60$ minutes. From this relation we will convert the given hours into the minutes. Now they have mentioned that Reenu types $540$ words during half an hour. From this statement we will calculate how many words she can type in one minute/unit time by dividing the words typed in half an hour with the minutes in a half an hour. From this value we can calculate how many words she can type in $8$ minutes by multiplying the words she can type in one minute with $8$.

**Complete step by step answer:**

Given that, Reenu types $540$ words during half an hour.

We know that $1\text{ hour}=60\text{ minutes}$.

From this we can calculate how many minutes for half an hour by multiplying the above equation with $\dfrac{1}{2}$ on both sides.

$\begin{align}

& \Rightarrow \dfrac{1}{2}\times 1\text{ hour}=\dfrac{1}{2}\times 60\text{ minutes} \\

& \Rightarrow \dfrac{1}{2}\text{hour}=30\text{ minutes} \\

\end{align}$

So, we have $30$ minutes for half an hour. Now the words typed by Reenu in one minute can be calculated by dividing the words typed in half an hour with the minutes in half an hour. Mathematically

Words typed by Reenu in one minute $=\dfrac{540}{30}=18\text{ wpm}$

Now the words typed by Reenu in $8$ minutes is given by

$\begin{align}

& {{W}_{8}}=18\text{ wpm}\times 8\text{ m} \\

& \Rightarrow {{W}_{8}}=144 \\

\end{align}$

**$\therefore $ Reenu can type $144$ words in $8$ minutes.**

**Note:**We can find the words typed by Reenu for any given time period by using the value of Words typed per Minute (wpm). The value of wpm is equal to the words typed in Minute. IF you want to calculate the words typed in two minutes, then ${{W}_{2}}=18\times 2=36\text{ words}$. Again, if you want to calculate the words typed by Reenu in $3$ minutes, then ${{W}_{3}}=18\times 3=54\text{ words}$ likewise we can calculate words typed for any interval of time.

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