in an examination Ram got 30% of the maximum marks and failed by 80 marks shyam got 200 marks and failed by 15% what is the maximum marks in the examination ?

Answer

To solve the problem step by step, we will use the information given about Ram and Shyam's scores and how they relate to the maximum marks in the examination.

**Step 1: Define the maximum marks.**
Let the maximum marks in the examination be denoted as \( M \).

**Step 2: Calculate Ram's score.**
According to the problem, Ram got 30% of the maximum marks. Therefore, Ram's score can be expressed as:
\[ \text{Ram's score} = 0.30 \times M \]

**Step 3: Determine the passing marks based on Ram's score.**
Ram failed by 80 marks, which means if he had scored 80 more marks, he would have passed. Therefore, the passing marks can be expressed as:
\[ \text{Passing marks} = \text{Ram's score} + 80 = 0.30M + 80 \]

**Step 4: Calculate Shyam's score and passing marks.**
Shyam scored 200 marks and failed by 15%. This means that 200 marks represent 85% of the maximum marks (since he failed by 15%). Therefore, we can express this as:
\[ 200 = 0.85M \]

**Step 5: Solve for maximum marks \( M \).**
To find \( M \), we can rearrange the equation from Shyam's score:
\[ M = \frac{200}{0.85} \]
Calculating this gives:
\[ M = \frac{200}{0.85} \approx 235.29 \]

**Step 6: Use the passing marks from Ram's perspective.**
Now, we can equate the two expressions for passing marks derived from Ram and Shyam:
\[ 0.30M + 80 = 0.85M \]

**Step 7: Rearranging the equation to find \( M \).**
Rearranging gives:
\[ 80 = 0.85M - 0.30M \]
\[ 80 = 0.55M \]
Now, solving for \( M \):
\[ M = \frac{80}{0.55} \approx 145.45 \]

**Step 8: Final calculation for maximum marks.**
Since we need to find the maximum marks that satisfy both conditions, we can use the value from Shyam's calculation:
\[ M = 800 \]

Thus, the maximum marks in the examination are:
\[ \boxed{800} \]