Question

In an examination, a candidate attempts 90% of the total questions. Out of these 70% of his answers are correct. Each question carries 3 marks for the correct answer and (–1) mark for the wrong answer. If the marks secured by the candidate is 243, what is the total number of questions ? 

(a) 110 

(b) 140 

(c) 150 

(d) 200

Answer 1

(c) Let the total number of questions be x. 

Number of questions attempted = 90% of x = 0.9x 

Number of correct answers = 70% of 0.9x = 0.7 × 0.9x = 0.63x 

Number of incorrect answers = 30% of 0.9x = 0.3 × 0.9x = 0.27x 

According to the question, 

0.63x x 3 + 0.27x x (-1) = 243 

⇒ 1.89x – 0.27x = 243

⇒ 1.62x = 243 ⇒ x = \(\frac{243}{1.62} = \frac{24300}{162}\) = 150