Question

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is

• A. $285$
• B. $276$
• C. $280$
• D. $290$

Answer 1

The correct option is A $285$

If a month starts with Sunday, then the number of Sundays in that month is $5$

The remaining days is $30-5=25$

Given that average number of visitors on Sundays is $510$

Therefore, $510=\frac{\text{sum of the number of visitors on Sundays}}{5}$

$⟹\text{sum of the number of visitors on Sundays}=510\times 5=2550$ -----(1)

Given that average number of visitors on other days is $240$

Therefore, $240=\frac{\text{sum of the number of visitors on other days}}{25}$

$⟹\text{sum of the number of visitors on other days}=240\times 25=6000$ -----(2)

Total average is $\frac{\text{total number of visitors}}{30}=\frac{2550+6000}{30}=\frac{8550}{30}=285$

Therefore, the average number of visitors per day in a month of 30 days beginning with a Sunday is $285$