If `x%` of 25 is equal to `y%` of 15 and `y%` of 15 is equal to `25%` of 20, then find the value of x.

Answer

To solve the problem, we will break it down into steps.

### Step 1: Set up the equations based on the given information.

We know:
1. \( x\% \) of 25 is equal to \( y\% \) of 15.
2. \( y\% \) of 15 is equal to \( 25\% \) of 20.

We can express these statements mathematically.

From the first statement:
\[ \frac{x}{100} \times 25 = \frac{y}{100} \times 15 \]

From the second statement:
\[ \frac{y}{100} \times 15 = \frac{25}{100} \times 20 \]

### Step 2: Simplify the second equation to find \( y \).

Starting with the second equation:
\[ \frac{y}{100} \times 15 = \frac{25}{100} \times 20 \]

Calculating \( \frac{25}{100} \times 20 \):
\[ \frac{25 \times 20}{100} = \frac{500}{100} = 5 \]

Now we have:
\[ \frac{y}{100} \times 15 = 5 \]

To isolate \( y \), multiply both sides by 100:
\[ y \times 15 = 500 \]

Now divide by 15:
\[ y = \frac{500}{15} = \frac{100}{3} \approx 33.33 \]

### Step 3: Substitute \( y \) back into the first equation to find \( x \).

Now we substitute \( y \) into the first equation:
\[ \frac{x}{100} \times 25 = \frac{y}{100} \times 15 \]

Substituting \( y = \frac{100}{3} \):
\[ \frac{x}{100} \times 25 = \frac{\frac{100}{3}}{100} \times 15 \]

This simplifies to:
\[ \frac{x}{100} \times 25 = \frac{100 \times 15}{3 \times 100} \]

The \( 100 \) cancels out:
\[ \frac{x}{100} \times 25 = \frac{15}{3} = 5 \]

### Step 4: Solve for \( x \).

Now, we have:
\[ \frac{x}{100} \times 25 = 5 \]

Multiply both sides by 100:
\[ x \times 25 = 500 \]

Now divide by 25:
\[ x = \frac{500}{25} = 20 \]

### Final Answer:
The value of \( x \) is \( 20 \).

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