If a number is decreased by `25%` that number becomes `96`. Find the number ?

Options

A. `122`
B. `128`
C. `126`
D. `132`

Answer

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

### Step 1: Understand the problem
We know that a number is decreased by 25% and the result is 96. We need to find the original number.

### Step 2: Define the original number
Let the original number be \( x \).

### Step 3: Express the decrease
If the number is decreased by 25%, it means we are left with 75% of the original number. We can express this mathematically as:
\[ \text{Remaining number} = x - 0.25x = 0.75x \]

### Step 4: Set up the equation
According to the problem, this remaining number equals 96:
\[ 0.75x = 96 \]

### Step 5: Solve for \( x \)
To find \( x \), we can divide both sides of the equation by 0.75:
\[ x = \frac{96}{0.75} \]

### Step 6: Calculate \( x \)
Now, we can perform the division:
\[ x = 96 \div 0.75 = 96 \times \frac{100}{75} = 96 \times \frac{4}{3} = \frac{384}{3} = 128 \]

### Conclusion
The original number is \( x = 128 \).

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