 Ram scored 20% more than Rakesh and Rakesh scored 25% less than Ritesh in an exam having
 200 as maximum marks. If Ritesh’s marks is 16 more than Ram’s marks. What is the percentage
 marks obtained by Rakesh.?

Let the marks of Ram, Rakesh, and Ritesh be denoted by \( R_{\text{ram}} \), \( R_{\text{rakesh}} \), and \( R_{\text{ritesh}} \) respectively.

### Step 1: Express Ram's marks in terms of Rakesh's marks.
We know that Ram scored 20% more than Rakesh:
\[
R_{\text{ram}} = R_{\text{rakesh}} + 0.20 \times R_{\text{rakesh}} = 1.2 \times R_{\text{rakesh}}
\]

### Step 2: Express Rakesh's marks in terms of Ritesh's marks.
We are told that Rakesh scored 25% less than Ritesh:
\[
R_{\text{rakesh}} = R_{\text{ritesh}} - 0.25 \times R_{\text{ritesh}} = 0.75 \times R_{\text{ritesh}}
\]

### Step 3: Relating Ritesh's and Ram's marks.
It is given that Ritesh’s marks are 16 more than Ram’s marks:
\[
R_{\text{ritesh}} = R_{\text{ram}} + 16
\]

### Step 4: Substituting values.
Now, substitute \( R_{\text{ram}} = 1.2 \times R_{\text{rakesh}} \) and \( R_{\text{rakesh}} = 0.75 \times R_{\text{ritesh}} \) into the equation for Ritesh's marks:
\[
R_{\text{ritesh}} = 1.2 \times R_{\text{rakesh}} + 16
\]
Substitute \( R_{\text{rakesh}} = 0.75 \times R_{\text{ritesh}} \):
\[
R_{\text{ritesh}} = 1.2 \times (0.75 \times R_{\text{ritesh}}) + 16
\]
Simplifying:
\[
R_{\text{ritesh}} = 0.9 \times R_{\text{ritesh}} + 16
\]
Now subtract \( 0.9 \times R_{\text{ritesh}} \) from both sides:
\[
R_{\text{ritesh}} - 0.9 \times R_{\text{ritesh}} = 16
\]
\[
0.1 \times R_{\text{ritesh}} = 16
\]
\[
R_{\text{ritesh}} = \frac{16}{0.1} = 160
\]

### Step 5: Finding Rakesh's marks.
Now that we know \( R_{\text{ritesh}} = 160 \), we can find Rakesh's marks:
\[
R_{\text{rakesh}} = 0.75 \times 160 = 120
\]

### Step 6: Calculating percentage marks obtained by Rakesh.
The maximum marks are 200, so Rakesh's percentage marks are:
\[
\text{Percentage} = \frac{120}{200} \times 100 = 60\%
\]

Thus, Rakesh obtained **60%** marks.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. If Ram scored 20% less than Ritesh, how would the marks change?
2. What is the percentage difference between Ram's and Rakesh's marks?
3. If Ritesh had scored 10 marks more, how would Rakesh's percentage change?
4. How would the solution change if the total marks were 250 instead of 200?
5. Can you derive the marks of Ram and Rakesh if they both scored 10% more than Ritesh?

**Tip:** When dealing with percentage problems, converting all relationships into equations makes the solution more straightforward.

Ram scored 20% more than Rakesh and Rakesh scored 25% less than Ritesh in an exam having 200 as maximum marks. If Ritesh’s marks is 16 more than Ram’s marks, what is the percentage marks obtained by Rakesh?

Find out how to calculate the percentage marks obtained by Rakesh based on the given conditions: Ram scored 20% more than Rakesh, and Rakesh scored 25% less than Ritesh. Ritesh's marks are 16 more than Ram's, and the maximum marks are 200. Detailed step-by-step solution provided.

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