This question can be solved using the
weighted averages approach as well.
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Weighted averages - Approach 1We are given the total production cost - 300
Price per roll = 300/n, where n is the number of rolls
If all the rolls were sold at a price greater than 50% of the average roll price - then the total selling price will be 450
How 450 ? - The average price of each roll is 300/n, and the total cost price is (300/n)n = 300
So, if the selling price of the roll is 50% greater than the price of roll - (1.5)(300/n)n = 450
If all the rolls were sold at a price greater than 20% less than of the average roll price - then the total selling price will be 360
(How did we come to the 20% value - Question says that the price on day 2 is 20% less than that of day 1... Let's say total production cost is x, then total selling price on Day 1 is 1.5x, so day 2 will be (0.8)1.5x = 1.2x i.e. 20% greater than the total production cost)
If all rolls sold at 1.2 times the price If all rolls sold at 1.5 times the price
360 450
1 4
The actual total selling price should be closer to the day 2, as its weightage is more. The difference, 90 is split in 5 parts, and since its closer to 450, the actual cost is 1 part less than 450 i.e. 450-18 = 432.
432-300=132
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Weighted averages - Approach 2We can also figure out the weighted averages based on change in percentage on each day, and the fraction of rolls sold on each day will be the weights.
Day 1 Day 2
20% 50%
1 4
So the average percent increase is 44%.
44% of 300 is 132.