MAT Exam 2021 Paper

Concept:Compare the time taken by both teams using the common scheduled time.Explanation:Team A had $10\%$ fewer questions than Team B.So, questions for Team A are:$$300 \times \frac{90}{100} = 270$$Let Team A answer $x$ questions per hour.Then Team B answers $x + 7$ questions per hour.Time taken by Team A:$$\frac{270}{x} \text{ hours}$$Time taken by Team B:$$\frac{300}{x + 7} \text{ hours}$$Team A finished 3 hours before schedule.Team B finished 6 hours before schedule.Therefore:$$\frac{270}{x} + 3 = \frac{300}{x + 7} + 6$$Simplify:$$\frac{270}{x} = \frac{300}{x + 7} + 3$$Multiply throughout by $x(x + 7)$:$$270(x + 7) = 300x + 3x(x + 7)$$$$270x + 1890 = 300x + 3x^2 + 21x$$$$3x^2 + 51x - 1890 = 0$$Divide by 3:$$x^2 + 17x - 630 = 0$$Factorize:$$(x - 18)(x + 35) = 0$$So, $x = 18$ or $x = -35$.Rate cannot be negative, so $x = 18$.Answer:Team A answered 18 questions per hour.