Scoring System Analysis

We need to determine the difference in incorrect answers between Candidate A and Candidate B, given they scored equally.

• Marks awarded: +4 for correct, -1 for incorrect.
• Candidate A: Attempted 18 questions.
• Candidate B: Attempted 13 questions.

Setting Up Equations

Let $C_A$ and $I_A$ be the number of correct and incorrect answers for Candidate A, respectively.

Let $C_B$ and $I_B$ be the number of correct and incorrect answers for Candidate B, respectively.

From the number of questions attempted:

• Equation 1: $C_A + I_A = 18 \implies C_A = 18 - I_A$
• Equation 2: $C_B + I_B = 13 \implies C_B = 13 - I_B$

From the equal marks scored:

Marks for A = Marks for B

$ 4 \times C_A - 1 \times I_A = 4 \times C_B - 1 \times I_B $

Calculating Incorrect Answers Difference

Substitute the expressions for $C_A$ and $C_B$ from the attempt equations into the marks equation:

$ 4(18 - I_A) - I_A = 4(13 - I_B) - I_B $

Simplify the equation:

$ 72 - 4I_A - I_A = 52 - 4I_B - I_B $

$ 72 - 5I_A = 52 - 5I_B $

Rearrange the terms to find the difference $I_A - I_B$:

$ 72 - 52 = 5I_A - 5I_B $

$ 20 = 5(I_A - I_B) $

$ I_A - I_B = \frac{20}{5} $

$ I_A - I_B = 4 $

Therefore, Candidate A has 4 more incorrect answers compared to Candidate B.