A number is increased by `15%` and then decreased by `25%` and the number becomes `22` less than the original number. The original number is .

Options

A. a) `160`
B. b) `120`
C. c) `140`
D. d) `180`

Answer

To solve the problem step by step, we need to find the original number based on the conditions given.

### Step 1: Define the Original Number
Let the original number be \( x \).

### Step 2: Calculate the Increased Number
When the number is increased by 15%, the new value becomes:
\[ x + 0.15x = 1.15x \]

### Step 3: Calculate the Decreased Number
Next, this increased number is decreased by 25%. The new value after the decrease is:
\[ 1.15x - 0.25(1.15x) = 1.15x \times (1 - 0.25) = 1.15x \times 0.75 = 0.8625x \]

### Step 4: Set Up the Equation
According to the problem, this decreased number is 22 less than the original number. Therefore, we can set up the equation:
\[ 0.8625x = x - 22 \]

### Step 5: Solve the Equation
Now, we will solve for \( x \):
\[ 0.8625x + 22 = x \]
\[ 22 = x - 0.8625x \]
\[ 22 = 0.1375x \]
\[ x = \frac{22}{0.1375} \]
\[ x = 160 \]

### Conclusion
The original number is \( 160 \).

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