If 64 is added in a number then number becomes `116%` of itself. Find the number.

Options

A. `415`
B. `400`
C. `416`
D. `113`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We need to find a number (let's call it K) such that when we add 64 to it, the result is 116% of the original number K.

### Step 2: Set Up the Equation
From the problem statement, we can set up the equation:
\[ K + 64 = 116\% \text{ of } K \]
This can be rewritten as:
\[ K + 64 = \frac{116}{100} \times K \]

### Step 3: Simplify the Equation
We can express 116% as a decimal:
\[ 116\% = 1.16 \]
Thus, the equation becomes:
\[ K + 64 = 1.16K \]

### Step 4: Rearrange the Equation
Now, we will rearrange the equation to isolate K:
\[ K + 64 = 1.16K \]
Subtract K from both sides:
\[ 64 = 1.16K - K \]
This simplifies to:
\[ 64 = 0.16K \]

### Step 5: Solve for K
To find K, we divide both sides by 0.16:
\[ K = \frac{64}{0.16} \]

### Step 6: Calculate K
Now, we can perform the division:
\[ K = \frac{64}{0.16} = 64 \div 0.16 \]
To make it easier, we can multiply the numerator and denominator by 100:
\[ K = \frac{6400}{16} \]
Now, performing the division:
\[ K = 400 \]

### Final Answer
The number K is **400**.

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