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If 20% of A is equal to 30% of B, what is the ratio A:B?
2:3
3:2
1:2
4:3
2
To find the ratio A:B when x%ofA=y%ofB, simply invert the numbers: A:B=y:x. Here, 20:30 becomes 30:20, which simplifies to 3:2.
20% of A is equal to 30% of B.
10020тАЛ├ЧA=10030тАЛ├ЧB
To find the ratio A:B when x%ofA=y%ofB, simply invert the numbers: A:B=y:x. Here, 20:30 becomes 30:20, which simplifies to 3:2.
Many students mistake the ratio to be 2:3 by directly reading the numbers in the question, forgetting that for A=B to hold, A must be larger than B because its coefficient is smaller.
Set up the equation
Translate the percentage statement into a mathematical equation.
0.20A=0.30B
Simplify the equation
Divide both sides by 10 and multiply by 100 to eliminate the decimals.
2A=3B
Find the ratio
Rearrange the terms to solve for A/B by dividing both sides by B and by 2.
BAтАЛ=23тАЛ
B is correct because the ratio A:B is calculated as 3:2.
This concept of inverse proportionality (AтЛЕx=BтЛЕyтЯ╣A:B=y:x) is fundamental in Time and Work problems where efficiency and time are inversely related.