A number decreased by `27(1)/(2)%` gives 87. The number is

Options

A. 58
B. 110
C. 120
D. 135

Answer

To solve the problem step by step, let's denote the unknown number as \( x \).

### Step 1: Understand the Problem
The problem states that a number decreased by \( 27\frac{1}{2}\% \) gives 87. We need to find the value of \( x \).

### Step 2: Convert the Percentage
First, convert \( 27\frac{1}{2}\% \) into an improper fraction:
\[ 27\frac{1}{2} = 27 + \frac{1}{2} = \frac{54}{2} + \frac{1}{2} = \frac{55}{2} \]
So, \( 27\frac{1}{2}\% = \frac{55}{2}\% \).

### Step 3: Express the Decrease in Terms of \( x \)
The decrease in \( x \) can be expressed as:
\[ \text{Decrease} = \frac{55}{2} \% \text{ of } x = \frac{55}{2} \times \frac{x}{100} = \frac{55x}{200} \]

### Step 4: Set Up the Equation
According to the problem, when we decrease \( x \) by this amount, we get 87:
\[ x - \frac{55x}{200} = 87 \]

### Step 5: Simplify the Equation
To simplify the left side, we need a common denominator:
\[ x - \frac{55x}{200} = \frac{200x}{200} - \frac{55x}{200} = \frac{145x}{200} \]
Thus, we have:
\[ \frac{145x}{200} = 87 \]

### Step 6: Solve for \( x \)
To isolate \( x \), multiply both sides by 200:
\[ 145x = 87 \times 200 \]
Calculating the right side:
\[ 145x = 17400 \]
Now, divide both sides by 145:
\[ x = \frac{17400}{145} \]

### Step 7: Calculate \( x \)
Now, perform the division:
\[ x = 120 \]

### Conclusion
The number is \( 120 \).