After three successive equal percentage rise in the salary the sum of `Rs. 100` turned into `Rs.140` and `49` paise. Find the percentage rise in the salary. (a) 10 % (b) 8 % (c) 17 % (d) 12 %

Options

A. `10%`
B. `8%`
C. `17%`
D. `12%`

Answer

To solve the problem of finding the percentage rise in salary after three successive equal percentage increases that turn Rs. 100 into Rs. 140.49, we can follow these steps:

### Step 1: Understand the Problem
We need to find the percentage increase (let's denote it as \( x \% \)) that, when applied three times successively to Rs. 100, results in Rs. 140.49.

### Step 2: Set Up the Equation
When a percentage increase of \( x \% \) is applied, the new salary after one increase can be expressed as:
\[ \text{New Salary} = \text{Old Salary} \times \left(1 + \frac{x}{100}\right) \]
After three successive increases, the equation becomes:
\[ 100 \times \left(1 + \frac{x}{100}\right)^3 = 140.49 \]

### Step 3: Simplify the Equation
Now, we can simplify the equation:
\[ \left(1 + \frac{x}{100}\right)^3 = \frac{140.49}{100} \]
This simplifies to:
\[ \left(1 + \frac{x}{100}\right)^3 = 1.4049 \]

### Step 4: Take the Cube Root
To solve for \( 1 + \frac{x}{100} \), we take the cube root of both sides:
\[ 1 + \frac{x}{100} = \sqrt[3]{1.4049} \]

### Step 5: Calculate the Cube Root
Using a calculator, we find:
\[ \sqrt[3]{1.4049} \approx 1.12 \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):
\[ \frac{x}{100} = 1.12 - 1 \]
\[ \frac{x}{100} = 0.12 \]
\[ x = 0.12 \times 100 = 12 \]

### Conclusion
The percentage rise in the salary is \( 12\% \).