Question

For the past n days, the average (arithmetic mean) daily production at a company was $50$ units. If today's production of 90 units raises the average to $55$ units per day, what is the value of $n$?

• A. $30$
• B. $18$
• C. $10$
• D. $9$
• E. $7$

Answer 1

Answer: (E)

$7$

Given that the average for $n$ days is $50$ units.

Therefore, $50=\frac{\text{sum of n days production}}{n}$

$⟹\text{sum of n days production}=50n$ -------(1)

Given that today's production of $90$ units raises the average to $55$ units.

Therefore, $55=\frac{\text{sum of n days production}+90}{n+1}$

$⟹\text{sum of n days production}+90=55n+55$ -------(2)

substituting (2) in (1) we get

$50n+90=55n+55$

$⟹55n-50n=90-55$

$⟹5n=35$

$⟹n=7$