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In a library, there are 55 fiction books and 22 non-fiction books. By what percentage should the number of non-fiction books be increased so that it becomes equal to the number of fiction books?
120%
150%
180%
200%
150%
Calculate the gap (55 - 22 = 33) and find what percentage of the base (22) it is: 2233тАЛ=1.5, which corresponds to 150%.
Fiction books = 55, Non-fiction books = 22
Percentage┬аIncrease=Initial┬аValueTarget┬аValueтИТInitial┬аValueтАЛ├Ч100%
Calculate the gap (55 - 22 = 33) and find what percentage of the base (22) it is: 2233тАЛ=1.5, which corresponds to 150%.
Many students incorrectly calculate the percentage based on the final total (55) instead of the initial non-fiction count (22), leading to the wrong result of 60%.
Calculate the required increment
To make the number of non-fiction books equal to fiction books, the increase needed is the difference between the two counts.
55тИТ22=33
Set up the percentage increase formula
We need to find what percentage 33 is of the original number of non-fiction books (22).
Percentage┬аIncrease=2233тАЛ├Ч100%
Perform the final calculation
Simplify the fraction 2233тАЛ by dividing by 11, which gives 23тАЛ, and then multiply by 100.
23тАЛ├Ч100=1.5├Ч100=150%
B is correct because the required increase of 33 books represents a 150% growth over the initial 22 books.
This concept of 'percentage increase relative to base' is identical to the calculation for Profit Percentage, where the cost price is the base.