GATE Mechanical 2022 Set 2 | GA | Question: 7

Question

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 $m$?

• A. $18$
• B. $10$
• C. $7$
• D. $5$

Answer 1

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 $:\text{C}$

Comments

Alternate approach:

this image has four parts:

1. daily production of $m$ days.
2. avg of daily production of $m$ days $= 100$ unit per day, achieved using adjusting daily production of $m$ days, making each day's production $100$ units.
3. today's production is added in the adjusted daily production of $m$ days (each of the $m$ bars $= 100$ unit)
4. excess amount above $100$ unit from the today's production (180 - 100 = 80 unit) is divided among $m+1$ days to achieve avg. production of $m+1$ days $= 110$ unit so each day now holds 110 unit.

$80$ unit will be divided b/w each of $m+1$ days and each day has increased $= 110 - 100 = 10$ unit. so,

 

 $\dfrac{80}{m+1} = 10$

$80 = 10(m+1)$

$80 = 10m+10$

$80 - 10 = 10m$

$70 = 10m$

$\boxed{7 = m}$

Reference: https://youtube.com/playlist?list=PLC36xJgs4dxE43Au1FGRQvwHTr7NbgDCS&feature=shared

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@Lakshman Bhaiya sir Use the color which is easily visible to us. 

Thanks