The charges per hour of internet surfing is increased by 25% then find the percentage decrease in the time period of surfing of a user (a net savy) who can afford only a 10% increase in expenditure :

Options

A. 22%
B. 12%
C. 15%
D. 9.09%

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Define the original expenditure
Let the original charges per hour be \( C \) and the original time period of surfing be \( T \). Therefore, the original expenditure \( E \) can be expressed as:
\[ E = C \times T \]

**Hint:** The expenditure is calculated by multiplying the charge per hour by the time spent.

### Step 2: Calculate the new expenditure after a 10% increase
Given that the user can afford only a 10% increase in expenditure, the new expenditure \( E' \) is:
\[ E' = E + 0.1E = 1.1E \]

**Hint:** To find the new expenditure after a percentage increase, multiply the original expenditure by \( (1 + \text{percentage increase}) \).

### Step 3: Calculate the new charges after a 25% increase
The charges per hour increase by 25%. Therefore, the new charges per hour \( C' \) can be calculated as:
\[ C' = C + 0.25C = 1.25C \]

**Hint:** A percentage increase can be calculated by multiplying the original amount by \( (1 + \text{percentage increase}) \).

### Step 4: Set up the equation for the new time period
Since the new expenditure must equal the new charges multiplied by the new time period \( T' \), we have:
\[ E' = C' \times T' \]
Substituting the values of \( E' \) and \( C' \):
\[ 1.1E = 1.25C \times T' \]

### Step 5: Substitute the original expenditure into the equation
We know that \( E = C \times T \), so we can substitute \( E \) into the equation:
\[ 1.1(C \times T) = 1.25C \times T' \]

### Step 6: Simplify the equation
Dividing both sides by \( C \) (assuming \( C \neq 0 \)):
\[ 1.1T = 1.25T' \]

### Step 7: Solve for the new time period \( T' \)
Rearranging gives:
\[ T' = \frac{1.1T}{1.25} \]
To simplify:
\[ T' = \frac{1.1}{1.25}T = \frac{11}{12.5}T = \frac{11 \times 8}{100}T = \frac{88}{100}T = 0.88T \]

### Step 8: Calculate the decrease in time period
The decrease in time period is:
\[ \text{Decrease} = T - T' = T - 0.88T = 0.12T \]

### Step 9: Calculate the percentage decrease
The percentage decrease can be calculated as:
\[ \text{Percentage Decrease} = \left( \frac{\text{Decrease}}{T} \right) \times 100 = \left( \frac{0.12T}{T} \right) \times 100 = 12\% \]

### Final Answer
The percentage decrease in the time period of surfing is **12%**.

---