If 90% of A = 30% of B and B = x% of A, then the value of x

Options

A. 800
B. 300
C. 700
D. 400

Answer

To solve the problem step by step, let's break it down clearly.

### Step 1: Set up the equation
We are given that:
\[ 90\% \text{ of } A = 30\% \text{ of } B \]

This can be expressed mathematically as:
\[ 0.9A = 0.3B \]

### Step 2: Rearrange the equation to express B in terms of A
To isolate B, we can rearrange the equation:
\[ B = \frac{0.9A}{0.3} \]

### Step 3: Simplify the expression
Now, simplify the right side:
\[ B = \frac{0.9}{0.3}A \]
\[ B = 3A \]

### Step 4: Use the second condition
We are also given that:
\[ B = x\% \text{ of } A \]
This can be expressed as:
\[ B = \frac{x}{100}A \]

### Step 5: Set the two expressions for B equal to each other
Now we can set the two expressions for B equal to each other:
\[ 3A = \frac{x}{100}A \]

### Step 6: Cancel A from both sides
Assuming A is not zero, we can divide both sides by A:
\[ 3 = \frac{x}{100} \]

### Step 7: Solve for x
To find x, multiply both sides by 100:
\[ x = 3 \times 100 \]
\[ x = 300 \]

### Final Answer
Thus, the value of x is:
\[ x = 300 \]

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