A student scored `70%,80%,50% and 48%` in four papers. It was decided to give double weight age to the 1st and the 3rd paper and half to the 2nd and 4th paper. Find the changed average marks.

Answer

To find the changed average marks of the student after applying the specified weightages to the scores, we can follow these steps:

### Step 1: Identify the Scores
The scores in the four papers are:
- Paper 1 (x1) = 70%
- Paper 2 (x2) = 80%
- Paper 3 (x3) = 50%
- Paper 4 (x4) = 48%

### Step 2: Determine the Weightages
The weightages for each paper are:
- Weightage for Paper 1 (w1) = 2 (double weightage)
- Weightage for Paper 2 (w2) = 0.5 (half weightage)
- Weightage for Paper 3 (w3) = 2 (double weightage)
- Weightage for Paper 4 (w4) = 0.5 (half weightage)

### Step 3: Calculate the Weighted Scores
Now, we will calculate the weighted scores for each paper:
- Weighted score for Paper 1 = w1 * x1 = 2 * 70 = 140
- Weighted score for Paper 2 = w2 * x2 = 0.5 * 80 = 40
- Weighted score for Paper 3 = w3 * x3 = 2 * 50 = 100
- Weighted score for Paper 4 = w4 * x4 = 0.5 * 48 = 24

### Step 4: Sum of Weighted Scores
Now, we add all the weighted scores together:
Total weighted score = 140 + 40 + 100 + 24 = 304

### Step 5: Calculate Total Weightage
Next, we calculate the total weightage:
Total weightage = w1 + w2 + w3 + w4 = 2 + 0.5 + 2 + 0.5 = 5

### Step 6: Calculate the Changed Average Marks
Finally, we calculate the changed average marks using the formula:
Changed Average = Total Weighted Score / Total Weightage
Changed Average = 304 / 5 = 60.8

### Final Answer
The changed average marks of the student is **60.8%**.

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