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

Hint: To solve this question, we will first find the total number of Sundays and other days in the given month, then we’ll find the total number of visitors on Sunday and on other days. After this we can add both these numbers to get the total number of visitors in a month. And then to find the average visitors per day, we will divide the total number of visitors with the number of days that is \[30\].

Complete step-by-step answer:
In a month starting with Sunday and having 30 days, the total number of days will be \[(7 \times 4) + 2\].
Here, there will be \[4\] complete weeks and two extra days. Out of the two days, one day will be Sunday as the month is starting with Sunday, so at the end of fourth week of the month, it will be Saturday, this means that the next two days will be Sunday and Monday.
Now we have the exact number of Sundays and other days, that is \[5\] Sundays and \[25\] other days.
Now, using this we can find the total number of visitors on Sunday and on other days.
As the average visitors on Sunday are \[510\], then the total number of visitors in \[5\] will be \[5 \times 510 = 2550\]. Thus the total number of visitors only on Sunday in a month will be \[2550\].
Now the average visitors on any other day is \[240\], so the total number of visitors on \[25\] other days except Sunday will be \[25 \times 240 = 6000\]. So the total number of visitors on any other day except Sunday in one month will be \[6000\].
Now we will add both the number of visitors to get the total number of visitors in this month.
The total number of visitors in this month will be \[2550 + 6000 = 8550\] visitors.
Now, we can easily find the average visitors per day in this month by dividing the total visitors in the month by the total number of days in this month.
Thus, the average number of visitors per day is \[\dfrac{{8550}}{{30}} = 285\] visitors per day.
Hence, option (A) is the correct option.

Note: The average value of visitors per day is closer to \[240\] than \[510\] because the number of other days except Sundays are more than Sundays themselves. Here, we can appreciate how average changes as per the data considered, as the number of visitors on Sundays are almost double than the average visitors per day in the whole month.