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Question 48

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

Correct Answer: 49

Solution

Let the copies sold on days 1 through 9 be $$d_1,\dots,d_9$$

From the averages:

$$d_1+\cdots+d_7=7\times60=420$$

$$d_1+\cdots+d_8=8\times63=504$$

So $$d_8=504-420=84$$. Then $$d_9=84-11=73$$

The sum from day 2 to day 9 is $$8\times66=528$$

$$d_2+\cdots+d_9=(d_1+\cdots+d_8)-d_1+d_9=504-d_1+73=577-d_1$$

Thus $$577-d_1=528 \Rightarrow d_1=49$$

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