If 28 is added in a number then result increased by `116(2)/(3)%` of itself. Find the number (a) 28 (b) 24 (c) 38 (d) 42

Options

A. `28`
B. `24`
C. `38`
D. `42`

Answer

To solve the problem step by step, we will define the unknown number as \( x \) and follow the information given in the question.

### Step 1: Understand the Problem
We need to find a number \( x \) such that when we add 28 to it, the result is increased by \( 116\frac{2}{3}\% \) of itself.

### Step 2: Convert Percentage to Fraction
The percentage \( 116\frac{2}{3}\% \) can be converted to a fraction:
\[ 116\frac{2}{3}\% = \frac{116 \times 3 + 2}{3 \times 100} = \frac{350}{300} = \frac{7}{6} \]

### Step 3: Set Up the Equation
According to the problem, when we add 28 to \( x \), the result is equal to \( x \) plus \( \frac{7}{6} \) of \( x \):
\[ x + 28 = x + \frac{7}{6}x \]

### Step 4: Simplify the Equation
Combine the terms on the right side:
\[ x + 28 = x + \frac{7}{6}x = \frac{6}{6}x + \frac{7}{6}x = \frac{13}{6}x \]

### Step 5: Isolate \( x \)
Now, we can isolate \( x \) by subtracting \( x \) from both sides:
\[ 28 = \frac{13}{6}x - x \]
\[ 28 = \frac{13}{6}x - \frac{6}{6}x \]
\[ 28 = \frac{7}{6}x \]

### Step 6: Solve for \( x \)
To solve for \( x \), multiply both sides by \( \frac{6}{7} \):
\[ x = 28 \times \frac{6}{7} \]
\[ x = 24 \]

### Final Answer
The number is \( 24 \).