$\frac{3}{20}$ is what percentage of $\frac{12}{25}$?

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Examoogle · Accepted Answer

The correct answer is Option A: 31.25%. Convert both fractions to have a common denominator (100). $\frac{3}{20} = \frac{15}{100}$ and $\frac{12}{25} = \frac{48}{100}$. Now calculate $\frac{15}{48} 	imes 100 = \frac{5}{16} 	imes 100 = 31.25\%$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Convert both fractions to have a common denominator (100). $\frac{3}{20} = \frac{15}{100}$ and $\frac{12}{25} = \frac{48}{100}$. Now calculate $\frac{15}{48} 	imes 100 = \frac{5}{16} 	imes 100 = 31.25\%$.

Formula Used: $$Percentage = \left( \frac{	ext{Part}}{	ext{Whole}} ight) 	imes 100$$

Given: Two fractions are given: 3/20 and 12/25. We need to find what percentage the first fraction is of the second.

Steps: Identify the Part and Whole: We need to find what percentage $\frac{3}{20}$ is of $\frac{12}{25}$.. Simplify the Division: To divide fractions, multiply by the reciprocal of the divisor: $\frac{3}{20} 	imes \frac{25}{12}$.. Reduce the Fraction: Divide numerator and denominator by 15: $\frac{75 \div 15}{240 \div 15} = \frac{5}{16}$.. Calculate Percentage: Multiply the ratio by 100 to express as a percentage: $\frac{5}{16} 	imes 100 = 31.25$.

Answer: A is correct because the ratio $\frac{3/20}{12/25}$ simplifies to $\frac{5}{16}$, which equals $31.25\%$.

Exam Tip: This concept of 'A as a percentage of B' is fundamental in profit/loss calculations where 'Profit % = (Profit/Cost Price) * 100'.

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