In an examination a student requires 40% of the total marks to pass if rupa gets 185 marks and fails by 15 marks, Find the total marks.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
Rupa needs 40% of the total marks to pass the examination. She scored 185 marks but failed by 15 marks. This means if she had scored 15 more marks, she would have passed.

### Step 2: Calculate the Marks Required to Pass
To find out how many marks Rupa needed to pass, we add the marks she scored (185) to the marks she needed to pass (15):
\[ \text{Marks required to pass} = 185 + 15 = 200 \text{ marks} \]

### Step 3: Set Up the Equation for Total Marks
We know that 40% of the total marks is equal to the marks required to pass (200 marks). Let the total marks be represented as \( T \). Therefore, we can write the equation:
\[ 0.40 \times T = 200 \]

### Step 4: Solve for Total Marks
To find \( T \), we can rearrange the equation:
\[ T = \frac{200}{0.40} \]

### Step 5: Calculate \( T \)
Now, we can calculate \( T \):
\[ T = \frac{200}{0.40} = 200 \div 0.40 \]
To simplify \( 200 \div 0.40 \), we can multiply both the numerator and the denominator by 100 to eliminate the decimal:
\[ T = \frac{200 \times 100}{0.40 \times 100} = \frac{20000}{40} \]
Now, divide:
\[ T = 500 \]

### Conclusion
Thus, the total marks for the examination is:
\[ \text{Total Marks} = 500 \]

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