Re: If 10% of A is equal to 120% of B, then what percent of B is A?
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23 May 2025, 04:30
We are given the equation:
$$
\(10 \% \text { of } A=120 \% \text { of } B\)
$$
We need to find what percent of $B$ is $A$.
Step 1: Translate Percentages to Decimals
First, convert the percentages to their decimal forms:
$$
\(0.10 A=1.20 B\)
$$
Step 2: Solve for $A$ in Terms of $B$
Divide both sides by 0.10 to isolate $A$ :
$$
\(A=\frac{1.20 B}{0.10}=12 B\)
$$
Step 3: Express $A$ as a Percentage of $B$
We need to find what percent $A$ is of $B$. Since $\(A=12 B\)$, this means:
$$
\(A=12 \times B=1200 \% \text { of } B\)
$$
Verification
To ensure correctness, let's verify with an example:
- Let $\(B=100\)$.
- Then $\(A=12 \times 100=1200\)$.
- Check the original condition:
$$
\(\begin{aligned}
& 10 \% \text { of } A=0.10 \times 1200=120 \\
& 120 \% \text { of } B=1.20 \times 100=120
\end{aligned}\)
$$
The condition holds true.
Final Answer
The correct percentage is:
D