The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is

The correct answer is 49.

Let's break down the information given in the problem step-by-step.

First, we are told that the average number of copies sold per day for the initial 7 days is 60. We can find the total number of copies sold in these 7 days by multiplying the average by the number of days:

$\text{Total copies for first 7 days}=60\times 7=420$

Next, the average for the initial 8 days is given as 63. The total copies sold in these 8 days is:

$\text{Total copies for first 8 days}=63\times 8=504$

By subtracting the total copies sold in the first 7 days from the total copies sold in the first 8 days, we can determine the exact number of copies sold on the 8th day:

$\text{Copies sold on the 8th day}=504-420=84$

We are given that on the 9th day, the shopkeeper sells 11 copies less than she did on the 8th day. So, the number of copies sold on the 9th day is:

$\text{Copies sold on the 9th day}=84-11=73$

Now, let's find the total number of copies sold from the 1st day through the 9th day. This is the sum of the total copies for the first 8 days and the copies sold on the 9th day:

$\text{Total copies for 9 days}=504+73=577$

The problem states that the average number of copies sold per day from the 2nd day to the 9th day is 66. Because this period covers exactly 8 days (days 2, 3, 4, 5, 6, 7, 8, and 9), the total number of copies sold from the 2nd day to the 9th day is:

$\text{Total copies from 2nd to 9th day}=66\times 8=528$

Finally, to find the number of copies sold on the 1st day, we subtract the total copies sold from the 2nd day to the 9th day from the overall total copies sold across all 9 days:

$\text{Copies sold on the 1st day}=\text{Total copies for 9 days}-\text{Total copies from 2nd to 9th day}$

$\text{Copies sold on the 1st day}=577-528=49$

Therefore, the number of copies sold on the first day of the book launch is 49.