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?

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

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

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

Therefore, $240 = \frac{sum of the number of visitors on other days}{2 5}$

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

Total average is $\frac{total number of visitors}{3 0} = \frac{2 5 5 0 + 6 0 0 0}{3 0} = \frac{8 5 5 0}{3 0} = 285$

Therefore, the average number of visitors per day in a month of 30 days beginning with a Sunday is $28 5 .$

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