If `60%` of `A=30%` of `B`, `B=40%` of C and `C=x%` of A, then value of x is

Options

A. `800`
B. `500`
C. `200`
D. `300`

Answer

To solve the problem step by step, let's break down the information given in the question and derive the value of \( x \).

### Step 1: Set up the equations based on the given information.
We know from the question that:
1. \( 60\% \) of \( A = 30\% \) of \( B \)
2. \( B = 40\% \) of \( C \)
3. \( C = x\% \) of \( A \)

From the first equation, we can express it as:
\[ 0.6A = 0.3B \]

### Step 2: Rearranging the first equation.
To eliminate the decimals, we can multiply both sides of the equation by \( 10 \):
\[ 6A = 3B \]
Now, dividing both sides by \( 3 \):
\[ 2A = B \quad \text{(Equation 1)} \]

### Step 3: Substitute \( B \) in the second equation.
Now, we use the second piece of information:
\[ B = 0.4C \]
Substituting \( B \) from Equation 1 into this equation:
\[ 2A = 0.4C \]

### Step 4: Rearranging to find \( C \).
To isolate \( C \), we can multiply both sides by \( 10 \) to eliminate the decimal:
\[ 20A = 4C \]
Now, dividing both sides by \( 4 \):
\[ C = 5A \quad \text{(Equation 2)} \]

### Step 5: Substitute \( C \) in the third equation.
Now we use the third piece of information:
\[ C = x\% \text{ of } A \]
This can be expressed as:
\[ C = \frac{x}{100}A \]
Now substituting \( C \) from Equation 2 into this equation:
\[ 5A = \frac{x}{100}A \]

### Step 6: Solve for \( x \).
To eliminate \( A \) from both sides (assuming \( A \neq 0 \)):
\[ 5 = \frac{x}{100} \]
Now, multiply both sides by \( 100 \):
\[ 500 = x \]

### Final Answer:
Thus, the value of \( x \) is \( 500 \).

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