Question

A company produces on an average $4000$ items per month for the first $3$ months. How many items must it produce on an average per month over the next $9$ months to average $4375$ items per month over the whole year?

• A. $4500$
• B. $4600$
• C. $4680$
• D. $4710$

Answer 1

The correct option is A $4500$

Given that first $3$ months average is $4000$

Therefore, $4000=\frac{\text{sum of the three months items}}{3}$

$⟹\text{sum of the three months items}=12000$ ------(1)

Given that whole year average is $4375$

Therefore, $4375=\frac{\text{sum of the 12 months items}}{12}$

$⟹\text{sum of the 12 months items}=52500$

$⟹\text{sum of the 3 months items + sum of the next 9 months items}=52500$

$⟹12000+\text{sum of the next 9 months items}=52500$ (from (1))

$⟹\text{sum of the next 9 months items}=40500$

Therefore, average for next 9 months is $\frac{\text{sum of the next 9 months items}}{9}$

$=\frac{40500}{9}=4500$

The company must produce on an average $4500$ items per month over the next nine months.