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 solve this problem step-by-step to find the number of copies sold on the first day of the book launch.

Step 1: Find the total number of copies sold in the first 7 days.
The average number of copies sold per day during the initial 7 days is 60.
Total copies sold in 7 days (Days 1 to 7):

$\text{Total (1 to 7)}=7\times 60=420$

Step 2: Find the total number of copies sold in the first 8 days and the number of copies sold on the 8th day.
The average number of copies sold per day during the initial 8 days is 63.
Total copies sold in 8 days (Days 1 to 8):

$\text{Total (1 to 8)}=8\times 63=504$

Number of copies sold on the 8th day (Day 8):

$\text{Day 8 sales}=\text{Total (1 to 8)}-\text{Total (1 to 7)}$

$\text{Day 8 sales}=504-420=84$

Step 3: Find the number of copies sold on the 9th day.
On the 9th day, she sells 11 copies less than on the 8th day.
Number of copies sold on the 9th day (Day 9):

$\text{Day 9 sales}=84-11=73$

Step 4: Find the total sales from the 2nd day to the 9th day.
The period from the 2nd day to the 9th day spans 8 days (Days 2, 3, 4, 5, 6, 7, 8, 9).
The average number of copies sold per day from the 2nd day to the 9th day is 66.
Total copies sold from Day 2 to Day 9:

$\text{Total (2 to 9)}=8\times 66=528$

Step 5: Calculate the number of copies sold on the 1st day.
Notice that the total sales from Day 1 to Day 9 can be represented in two ways:
1) Day 1 sales + Total sales from Day 2 to Day 9
2) Total sales from Day 1 to Day 8 + Day 9 sales

Equating the two expressions:

$\text{Day 1 sales}+\text{Total (2 to 9)}=\text{Total (1 to 8)}+\text{Day 9 sales}$

$\text{Day 1 sales}+528=504+73$

$\text{Day 1 sales}+528=577$

$\text{Day 1 sales}=577-528=49$

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