`x%` of y is 10.y% of 120 is 48. What is x?

Answer

To solve the problem step by step, we start with the two statements given in the question.

### Step 1: Set up the equations
From the first statement, "x% of y is 10", we can express this mathematically as:
\[ \frac{x}{100} \times y = 10 \]

From the second statement, "y% of 120 is 48", we can express this as:
\[ \frac{y}{100} \times 120 = 48 \]

### Step 2: Simplify the second equation
We can simplify the second equation:
\[ \frac{y \times 120}{100} = 48 \]
Multiplying both sides by 100 gives:
\[ y \times 120 = 4800 \]
Now, divide both sides by 120:
\[ y = \frac{4800}{120} \]
Calculating this gives:
\[ y = 40 \]

### Step 3: Substitute y into the first equation
Now that we have found \(y = 40\), we substitute this value back into the first equation:
\[ \frac{x}{100} \times 40 = 10 \]

### Step 4: Solve for x
To isolate \(x\), we can multiply both sides by 100:
\[ 40x = 1000 \]
Now, divide both sides by 40:
\[ x = \frac{1000}{40} \]
Calculating this gives:
\[ x = 25 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{25} \]

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