Pranita got 30 marks more in Math than what she got in Science. Her Math marks are `60%` of the sum of her Math and Science marks. What are her Science marks ?

Options

A. `90`
B. `150`
C. `120`
D. `60`

Answer

To solve the problem, let's define the variables and set up the equations based on the information given.

1. **Define Variables**:
- Let the Science marks be \( S \).
- Then, the Math marks will be \( S + 30 \) (since Pranita got 30 marks more in Math than in Science).

2. **Set Up the Equation**:
- According to the problem, her Math marks are 60% of the sum of her Math and Science marks.
- The sum of her Math and Science marks can be expressed as:
\[ \text{Sum} = S + (S + 30) = 2S + 30 \]
- Therefore, we can express the relationship as:
\[ S + 30 = 0.6 \times (2S + 30) \]

3. **Solve the Equation**:
- Expanding the right side:
\[ S + 30 = 1.2S + 18 \]
- Rearranging the equation to isolate \( S \):
\[ S + 30 - 18 = 1.2S \]
\[ 12 = 1.2S - S \]
\[ 12 = 0.2S \]
- Now, divide both sides by 0.2:
\[ S = \frac{12}{0.2} = 60 \]

4. **Conclusion**:
- Therefore, Pranita's Science marks are \( S = 60 \).

### Summary of Steps:
1. Define the variables for Science and Math marks.
2. Set up the equation based on the relationship given in the problem.
3. Solve the equation to find the value of Science marks.