CAT 2025Slot 2QAQuestion & Solution
Question
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
Solution
1. Concept Used
- Topic: Averages — Sum = Average × Number of Terms
- Formula: $$\text{Sum} = \text{Average} \times n$$
2. Calculation
Let the copies sold on days 1 through 9 be $$d_1, d_2, \dots, d_9$$.
Step 1: Find the total for the first 7 and first 8 days.
$$d_1 + d_2 + \cdots + d_7 = 7 \times 60 = 420$$
$$d_1 + d_2 + \cdots + d_8 = 8 \times 63 = 504$$
Step 2: Find copies sold on Day 8.
Subtracting the two equations:
$$d_8 = 504 - 420 = 84$$
Step 3: Find copies sold on Day 9.
She sells 11 copies less than Day 8:
$$d_9 = 84 - 11 = 73$$
Step 4: Use the average from Day 2 to Day 9.
$$d_2 + d_3 + \cdots + d_9 = 8 \times 66 = 528$$
Step 5: Express the Day 2 to Day 9 sum in terms of known quantities.
$$d_2 + d_3 + \cdots + d_9 = (d_1 + d_2 + \cdots + d_8) - d_1 + d_9$$
$$= 504 - d_1 + 73 = 577 - d_1$$
Step 6: Solve for $$d_1$$.
$$577 - d_1 = 528$$
$$d_1 = 577 - 528 = 49$$
3. Solution
Answer = 49 ✅
The number of copies sold on the first day of the book launch is 49.