Last year in CAT, each section of the question paper had different weightage. The weightage of QA, DI and VA/RC sections were 8,9 and 10 respectively . The maximum marks in all the three sections together was 810. Wrong answer did not carry negative marks as a penalty. If Padma had gotten `20%`more marks in QA and `8%` more marks in DI and `7.14...%` more marks in VA/RC, then she must had gotten `100%` marks in all the three sections. The total marks that Padma had scored:

Options

A. 718.98
B. 700
C. 750
D. 775

Answer

To solve the problem, we need to determine the total marks Padma scored in each section based on the given weightages and the conditions provided. Let's break this down step by step.

### Step 1: Determine the weightage of each section
The weightage of the sections is given as follows:
- QA (Quantitative Ability) = 8
- DI (Data Interpretation) = 9
- VA/RC (Verbal Ability/Reading Comprehension) = 10

### Step 2: Calculate the total weightage
The total weightage of all sections combined is:
\[ \text{Total Weightage} = 8 + 9 + 10 = 27 \]

### Step 3: Calculate the maximum marks for each section
The maximum marks for all three sections together is given as 810. We can find the maximum marks for each section by using the ratio of their weightages.

- Maximum marks for QA:
\[ \text{Max Marks in QA} = \left(\frac{8}{27}\right) \times 810 = 240 \]

- Maximum marks for DI:
\[ \text{Max Marks in DI} = \left(\frac{9}{27}\right) \times 810 = 270 \]

- Maximum marks for VA/RC:
\[ \text{Max Marks in VA/RC} = \left(\frac{10}{27}\right) \times 810 = 300 \]

### Step 4: Determine the percentage of marks Padma would need to score 100%
According to the problem:
- If Padma had gotten 20% more marks in QA, she would have scored 100%.
- If Padma had gotten 8% more marks in DI, she would have scored 100%.
- If Padma had gotten 7.14% more marks in VA/RC, she would have scored 100%.

### Step 5: Calculate the actual marks Padma scored in each section
1. **QA**:
- Let \( x \) be the marks scored by Padma in QA.
- According to the condition, \( x + 0.20x = 240 \) (100% marks)
- This simplifies to \( 1.20x = 240 \)
- Therefore, \( x = \frac{240}{1.20} = 200 \)

2. **DI**:
- Let \( y \) be the marks scored by Padma in DI.
- According to the condition, \( y + 0.08y = 270 \)
- This simplifies to \( 1.08y = 270 \)
- Therefore, \( y = \frac{270}{1.08} = 250 \)

3. **VA/RC**:
- Let \( z \) be the marks scored by Padma in VA/RC.
- According to the condition, \( z + 0.0714z = 300 \)
- This simplifies to \( 1.0714z = 300 \)
- Therefore, \( z = \frac{300}{1.0714} \approx 280 \)

### Step 6: Calculate the total marks scored by Padma
Now, we add the marks from all three sections:
\[ \text{Total Marks} = x + y + z = 200 + 250 + 280 = 730 \]

### Conclusion
Padma scored a total of **730 marks**.

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