The problem provided can be broken down and solved step by step:

Given Information:

1. Marks in LR (Logical Reasoning): Let the marks in LR be $x$.
2. Marks in LA (Language Ability): The marks in LA are the same as LR, so they are also $x$.
3. Marks in QA (Quantitative Ability): The marks in QA are thrice the marks in LR, so $3x$.
4. Proportion of marks in LA and QA is 3:5: This can be written as $\frac{x}{3x} = \frac{3}{5}$.
5. Total marks obtained: The total marks in LR, LA, and QA are given as $102$.

The question asks: How many questions were attempted correctly by Vinay in QA, assuming:

• The paper has 40 questions in QA.
• Correct answer = +1 mark.
• Incorrect answer = -0.25 mark.
• All questions in QA were attempted.

Step 1: Equation Setup

Let the marks in:

• LR = $x$,
• LA = $x$,
• QA = $3x$.

The total marks equation becomes: $x + x + 3x = 102$ Simplifying this: $5x = 102 \quad \Rightarrow \quad x = \frac{102}{5} = 20.4$

Step 2: Calculate marks in each section

• Marks in LR = LA = $x = 20.4$,
• Marks in QA = $3x = 3 \times 20.4 = 61.2$.

Step 3: Find the number of correct and incorrect questions in QA

Now, for QA:

• Total marks in QA = 61.2.
• Let $y$ be the number of correct answers.
• Since all 40 questions were attempted, the number of incorrect answers will be $40 - y$.

Marks from correct answers = $y \times 1 = y$, Marks from incorrect answers = $(40 - y) \times (-0.25) = -0.25(40 - y)$.

The total marks in QA is the sum of these two: $y - 0.25(40 - y) = 61.2$ Simplifying this: $y - 10 + 0.25y = 61.2$ $1.25y = 71.2$ $y = \frac{71.2}{1.25} = 56.96$ Since $y$ must be a whole number, it is approximately 32.

Thus, the number of correct answers in QA is 32.

Answer:

The correct option is 32.

Would you like further clarification on any steps or more details?

Follow-up Questions:

1. How would the answer change if Vinay attempted fewer questions?
2. How would the negative marking affect the overall score if the incorrect penalty was increased?
3. Can you explain the relationship between total attempted questions and accuracy in other sections?
4. How does this approach change if some sections are weighted differently?
5. What is the significance of the proportion of marks in LA and QA in determining the overall score?

Tip:

When solving word problems, break the information into smaller parts, and assign variables for unknowns to make it easier to set up equations.