If `13(1)/(3)%` of a number is subtracted from itself then result becomes `7891`. Find the original number

Options

A. a) `9105`
B. b) `4105`
C. c) `4150`
D. d) `3850`

Answer

To solve the problem step by step, we will follow the instructions provided in the question.

### Step 1: Understand the Problem
We need to find a number (let's call it \( X \)) such that when \( 13 \frac{1}{3}\% \) of it is subtracted from itself, the result is \( 7891 \).

### Step 2: Convert the Percentage
First, we convert \( 13 \frac{1}{3}\% \) into a fraction:
\[ 13 \frac{1}{3}\% = \frac{40}{3}\% \]
This means:
\[ \frac{40}{3}\% = \frac{40}{3} \times \frac{1}{100} = \frac{40}{300} = \frac{2}{15} \]

### Step 3: Set Up the Equation
According to the problem, we can set up the equation as follows:
\[ X - \frac{2}{15}X = 7891 \]

### Step 4: Simplify the Equation
Now, we simplify the left side:
\[ X - \frac{2}{15}X = \frac{15X}{15} - \frac{2X}{15} = \frac{13X}{15} \]
Thus, the equation becomes:
\[ \frac{13X}{15} = 7891 \]

### Step 5: Solve for \( X \)
To isolate \( X \), we multiply both sides by \( \frac{15}{13} \):
\[ X = 7891 \times \frac{15}{13} \]

### Step 6: Calculate the Value
Now, we perform the multiplication:
\[ X = 7891 \times \frac{15}{13} = 7891 \times 1.1538461538461537 \approx 9105 \]

### Step 7: Conclusion
Thus, the original number \( X \) is:
\[ \boxed{9105} \]