If x is `90%` of y, then y is percentage of x-

Options

A. 90
B. 190
C. 101.1
D. 111.1

Answer

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

### Step 1: Understand the relationship between x and y
We know from the question that:
\[ x = 90\% \text{ of } y \]

This can be expressed mathematically as:
\[ x = \frac{90}{100} \times y \]
or
\[ x = 0.9y \]

### Step 2: Rearranging the equation to find y in terms of x
To find y in terms of x, we can rearrange the equation:
\[ y = \frac{x}{0.9} \]

### Step 3: Simplifying the expression for y
Now, we can simplify the expression:
\[ y = \frac{x}{0.9} = \frac{x \times 10}{9} = \frac{10x}{9} \]

### Step 4: Finding y as a percentage of x
Now, we need to express y as a percentage of x. The formula for percentage is:
\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\% \]
Here, y is the part and x is the whole. Thus, we have:
\[ \text{Percentage of } x = \left( \frac{y}{x} \right) \times 100\% \]

Substituting the value of y:
\[ \text{Percentage of } x = \left( \frac{\frac{10x}{9}}{x} \right) \times 100\% \]

### Step 5: Simplifying the percentage calculation
This simplifies to:
\[ \text{Percentage of } x = \left( \frac{10}{9} \right) \times 100\% \]

Calculating this gives:
\[ \text{Percentage of } x = \frac{1000}{9} \approx 111.1\% \]

### Conclusion
Thus, y is approximately \( 111.1\% \) of x.

### Final Answer
The answer is \( 111.1\% \).

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