Average, Mixture and Alligation Question 1 - CAT 2025
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 the second day to the ninth day becomes 66. The number of copies sold on the first day of the book launch is:
Step-by-Step Explanation
Let the number of copies sold on days 1 through 9 be represented by d₁, d₂, …, d₉.
- Find the sales on Day 8 (d₈):
Total sales for the first 7 days = 7 × 60 = 420 copies.
Total sales for the first 8 days = 8 × 63 = 504 copies.
d₈ = 504 − 420 = 84 copies
- Find the sales on Day 9 (d₉):
On the ninth day, she sells 11 copies less than the eighth day:
d₉ = 84 − 11 = 73 copies
- Find the sales on Day 1 (d₁):
The total sales from Day 1 to Day 9 can be written as:
Total (1 to 9) = Total (1 to 8) + d₉ = 504 + 73 = 577 copies
We are given that the average sales from the second day to the ninth day (8 days total) is 66:
Total (2 to 9) = 8 × 66 = 528 copies
Since Total (1 to 9) − Total (2 to 9) = d₁, we get:
d₁ = 577 − 528 = 49 copies
The number of copies sold on the first day was 49.
Correct Answer: 49
💡 FundaMakers Tip:
Think of consecutive averages as a sliding window. When the window shifts from Days 1–8 to Days 2–9, Day 1 drops out and Day 9 enters. You don't need to track the middle days at all. Finding the absolute sums of the two boundary states lets you isolate the missing day immediately through subtraction.