CAT 2025 Slot 2QAArithmetic • Mean, Median & ModeModerate
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
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Official Correct Answer: 49. First, the question says that the average number of copies sold per day is 60 in the initial seven days. Hmm, okay, so average is total divided by the number of days. So, if the average is 60 over seven days, that means the total copies sold in those seven days must be 60 multiplied by 7. Let me write that down:
Total copies in 7 days = 60 * 7 = 420.
Got that. So, day 1 to day 7, total is 420.
Then, it says the average number of copies sold per day in the initial eight days is 63. Wait, initial eight days? So, that's days 1 to 8. So, similar logic, average is total divided by 8. So, total copies in 8 days would be 63 * 8. Calculate that:
Total copies in 8 days = 63 * 8. Hmm, 60*8 is 480, and 3*8 is 24, so 480 +24 = 504.
So, total copies from day 1 to day 8 is 504.
Now, the question mentions that on the ninth day, she sells 11 copies less than the eighth day. Let the number of copies sold on the eighth day as something. Maybe let’s call the eighth day sales as x. So, on the ninth day, she sold x - 11 copies.
Then, it says that the average number of copies sold per day from the second day to the ninth day becomes 66. Wait, so that's days 2 to 9, which is 8 days. So, the average is 66 over 8 days. Therefore, total copies from day 2 to day 9 is 66 * 8. Compute that:
66 * 8. 60*8=480, 6*8=48, so 480+48=528.
So, total copies from day 2 to day 9 is 528.
Now, We find the number of copies sold on the first day. Let day 1 sales as y.
From the first part, total copies from day 1 to day 7 is 420. So, that includes day 1 to day 7. So, day 1 is y, and days 2 to 7 would be 420 - y.
Similarly, total copies from day 1 to day 8 is 504. So, that's y (day 1) + days 2 to 8. Days 2 to 8 is 504 - y.
But wait, days 2 to 8 is 7 days. So, the average from day 2 to day 8 would be (504 - y)/7. Hmm, but maybe that's not directly needed.
Wait, the total from day 2 to day 9 is 528. So, that includes day 2 to day 9. So, day 2 to day 9 is 8 days. So, day 2 to day 9 is 528.
But day 2 to day 9 can also be expressed as (total from day 1 to day 9) minus day 1. So, total from day 1 to day 9 is total from day 1 to day 8 plus day 9. Which is 504 + (x - 11). So, total from day 1 to day 9 is 504 + x -11 = 493 + x.
Therefore, total from day 2 to day 9 is (493 + x) - y = 528.
So, 493 + x - y = 528.
So, x - y = 528 - 493 = 35.
So, equation one: x - y = 35. (Equation 1)
Now, from the total of day 1 to day 8, which is 504, we have y + (days 2 to 8) = 504.
Days 2 to 8 is 7 days, and the average from day 2 to day 8 would be (504 - y)/7.
But wait, the average from day 2 to day 9 is 66, which is 8 days. So, maybe I can find another equation.
Wait, let's think differently. The total from day 2 to day 9 is 528, which includes day 2 to day 9. So, day 2 to day 9 is 528.
But day 2 to day 8 is 504 - y (since day 1 to day 8 is 504, so day 2 to day 8 is 504 - y). Then, day 9 is x - 11.
So, total from day 2 to day 9 is (504 - y) + (x - 11) = 528.
So, 504 - y + x -11 = 528.
Simplify: 493 + x - y = 528.
Which is the same as before: x - y = 35. So, same equation.
So, we need another equation to find y.
Wait, let's think about the total from day 1 to day 7, which is 420. So, day 1 is y, and days 2 to 7 is 420 - y.
Then, day 8 is x, and day 9 is x -11.
So, total from day 1 to day 9 is y + (420 - y) + x + (x -11) = 420 + 2x -11 = 409 + 2x.
But we also know that total from day 1 to day 9 is 504 + (x -11) = 504 + x -11 = 493 + x.
So, 409 + 2x = 493 + x.
Subtract x from both sides: 409 + x = 493.
Subtract 409: x = 493 - 409 = 84.
So, x is 84. So, day 8 is 84 copies.
Then, from equation 1: x - y = 35.
So, 8