`36%` of the maximum marks is required to pass a test `A` students gets `123` marks and is declared fail by `39` marks find the maximum marks

Options

A. `450`
B. `460`
C. `470`
D. `480`

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step-by-Step Solution:

1. **Understand the Problem**:
- We know that 36% of the maximum marks is required to pass the test.
- The student scored 123 marks but failed by 39 marks.

2. **Calculate the Marks Required to Pass**:
- Since the student failed by 39 marks, we can find the marks required to pass by adding the marks the student scored to the marks by which he failed.
- Required Marks to Pass = Marks Scored + Marks Failed By
- Required Marks to Pass = 123 + 39 = 162

3. **Set Up the Equation**:
- We know that 36% of the maximum marks (let's denote maximum marks as M) is equal to the marks required to pass (which we found to be 162).
- This can be expressed mathematically as:
\[ 36\% \text{ of } M = 162 \]
- In decimal form, 36% can be written as 0.36.
- So, we can rewrite the equation as:
\[ 0.36M = 162 \]

4. **Solve for Maximum Marks (M)**:
- To find M, we can divide both sides of the equation by 0.36:
\[ M = \frac{162}{0.36} \]
- Now, performing the division:
\[ M = 450 \]

5. **Conclusion**:
- The maximum marks for the test are 450.

### Final Answer:
The maximum marks are **450**.