For the past $m$ days, the average daily production at a company was $100$ units per day.

If today’s production of $180$ units changes the average to $110$ units per day, What is the value of $m$?

1. $18$
2. $10$
3. $7$
4. $5$

Given that, for the past $m$ days, the average daily production at a company was $100$ units per day.

• $1\;\text{day} \longrightarrow 100\;\text{units}$
• ${\color{Blue}{m\;\text{days} \longrightarrow 100m\;\text{units}}}$

If today’s production of $180$ units changes the average to $110$ units per day.

Now, $\dfrac{\underbrace{100m}_{{\color{Red}{m \;\text{days production}}}} + \underbrace{180}_{{\color{purple}{\text{Today’s production}}}}}{m+1} = 110$

$\Rightarrow 100m + 180 = 110m + 110$

$\Rightarrow 10m = 70$

$\Rightarrow {\color{Blue}{\boxed{m = 7}}}$

Correct Answer $:\text{C}$

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