To solve the problem, we will follow these steps:
### Step 1: Understand the given data
We have four students A, B, C, and D, and we need to find the ratio of marks obtained by C and B in the written examination. The total weighted scores and marks obtained in practical exams for B and C are provided.
### Step 2: Set up the equations for B and C
1. **For Student B:**
- Total weighted score of B = 52
- Marks obtained in practical exam (B) = 55
- Weighted percentage of written exam = 60% (0.6)
- Weighted percentage of practical exam = 40% (0.4)
Using the weighted score formula:
\[
52 = (Marks \, obtained \, in \, written \, exam \, B) \times 0.6 + 55 \times 0.4
\]
2. **For Student C:**
- Total weighted score of C = 65
- Marks obtained in practical exam (C) = 50
Using the weighted score formula:
\[
65 = (Marks \, obtained \, in \, written \, exam \, C) \times 0.6 + 50 \times 0.4
\]
### Step 3: Solve for marks obtained in written exams
1. **For Student B:**
\[
52 = (Marks \, obtained \, in \, written \, exam \, B) \times 0.6 + 22
\]
\[
52 - 22 = (Marks \, obtained \, in \, written \, exam \, B) \times 0.6
\]
\[
30 = (Marks \, obtained \, in \, written \, exam \, B) \times 0.6
\]
\[
Marks \, obtained \, in \, written \, exam \, B = \frac{30}{0.6} = 50
\]
2. **For Student C:**
\[
65 = (Marks \, obtained \, in \, written \, exam \, C) \times 0.6 + 20
\]
\[
65 - 20 = (Marks \, obtained \, in \, written \, exam \, C) \times 0.6
\]
\[
45 = (Marks \, obtained \, in \, written \, exam \, C) \times 0.6
\]
\[
Marks \, obtained \, in \, written \, exam \, C = \frac{45}{0.6} = 75
\]
### Step 4: Find the ratio of marks obtained by C and B
Now we have:
- Marks obtained by B in written exam = 50
- Marks obtained by C in written exam = 75
The ratio of marks obtained by C to B is:
\[
\text{Ratio} = \frac{Marks \, obtained \, by \, C}{Marks \, obtained \, by \, B} = \frac{75}{50} = \frac{3}{2}
\]
### Final Answer
The ratio of marks obtained by C and that by B in the written examination is **3:2**.
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