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Q1718/80Q19
Q18·CSAT · Prelims 2026

Equations — Linear Simultaneous Systems

NumericalAlgebra — Linear EquationsArithmetic Problem● Easy

Question

In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?

Options

a

99

b

81

Answer
c

84

d

79

Explanation

Let c be the number of correct answers and w be the number of wrong answers attempted by the student [cite: 3809, 3810].

From the first scenario: 5 marks are added for a correct answer and 2 are subtracted for a wrong one, yielding a score of 69 [cite: 3809, 3810].

5c - 2w = 69 \quad --- (Equation 1)

From the second scenario: 4 marks are added for a correct answer and 1 is subtracted for a wrong one, yielding a score of 84 .

4c - 1w = 84 \implies w = 4c - 84 \quad --- (Equation 2)

Substitution and Solution: Substitute Equation 2 into Equation 1:

5c - 2(4c - 84) = 69 \implies 5c - 8c + 168 = 69 -3c = 69 - 168 \implies -3c = -99 \implies c = 33 correct answers

Find Wrong Answers (⟨MATH⟩w⟨/MATH⟩):

w = 4(33) - 84 = 132 - 84 = 48 wrong answers

Total Number of Questions: Since the student attempted all questions, the total size is:

Total Questions = c + w = 33 + 48 = 81 questions

System-of-equations scoring problems are easily resolved by converting the given marking scenarios into standard linear equations and isolating variables via substitution.

Answer: (b).

Question details

Year

2026

Paper

CSAT

Question

Q18

Section

Quantitative Aptitude

Sub-topic

Algebra — Linear Equations

Type

Arithmetic Problem

Difficulty

Easy

Source hint

Standard simultaneous systems — algebraic elimination framework

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