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MathematicsPercentage
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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?

A

120%

B

150%

C

180%

D

200%

Correct Answer

ЁЯУР MA тАв Math Ratio MethodMathematicsPercentage
Option B

150%

Quick Summary:

Calculate the gap (55 - 22 = 33) and find what percentage of the base (22) it is: 3322=1.5\frac{33}{22} = 1.52233тАЛ=1.5, which corresponds to 150%.

ЁЯУРMAMath SolutionRatio Method
ЁЯУЛ Given

Fiction books = 55, Non-fiction books = 22

ЁЯФв Formula Used

Percentage┬аIncrease=Target┬аValueтИТInitial┬аValueInitial┬аValue├Ч100%\text{Percentage Increase} = \frac{\text{Target Value} - \text{Initial Value}}{\text{Initial Value}} \times 100\%Percentage┬аIncrease=Initial┬аValueTarget┬аValueтИТInitial┬аValueтАЛ├Ч100%

тЪб Exam Hall Shortcut / Speed Trick

Calculate the gap (55 - 22 = 33) and find what percentage of the base (22) it is: 3322=1.5\frac{33}{22} = 1.52233тАЛ=1.5, which corresponds to 150%.

тЪая╕П Common Student Trap / Pitfall

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%.

ЁЯУК Diagram / Illustration
Percentage Increase Calculation 1 Given Data Fiction: 55 | Non-Fiction: 22 | Required Increase: 55 - 22 = 33 2 Percentage Increase Formula Percentage Increase = (Increase / Original Value) ├Ч 100% 3 Calculation Step (33 / 22) ├Ч 100% = 1.5 ├Ч 100% = 150% 4 Final Result The number of non-fiction books must increase by 150% Correct Option: B) 150%
ЁЯФв Step-by-Step Solution
1

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=3355 - 22 = 3355тИТ22=33

2

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=3322├Ч100%\text{Percentage Increase} = \frac{33}{22} \times 100\%Percentage┬аIncrease=2233тАЛ├Ч100%

3

Perform the final calculation

Simplify the fraction 3322\frac{33}{22}2233тАЛ by dividing by 11, which gives 32\frac{3}{2}23тАЛ, and then multiply by 100.

32├Ч100=1.5├Ч100=150%\frac{3}{2} \times 100 = 1.5 \times 100 = 150\%23тАЛ├Ч100=1.5├Ч100=150%

тЬЕ

B is correct because the required increase of 33 books represents a 150% growth over the initial 22 books.

Core Concepts Used
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Percentage Growth Relative Change Ratio Analysis
ЁЯТб EXAM TIP

This concept of 'percentage increase relative to base' is identical to the calculation for Profit Percentage, where the cost price is the base.

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