Had Aarush scored 8 more marks in a Mathematics test, out of 35 marks, 7 times these marks would have been 4 less than square of his actual marks. How many marks did he get in the test ?
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
Let Aarush's actual marks = $x$
If he had scored 8 more, his marks = $(x + 8)$
According to the condition:
$$7(x + 8) = x^2 - 4$$
$$7x + 56 = x^2 - 4$$
$$x^2 - 7x - 60 = 0$$
Factorising:
$$x^2 - 12x + 5x - 60 = 0$$
$$x(x - 12) + 5(x - 12) = 0$$
$$(x + 5)(x - 12) = 0$$
So $x = -5$ or $x = 12$
Since marks cannot be negative, $x = 12$.
Aarush scored 12 marks in the test.
Source: Chapter 4, Exercise 4.2
---
Explanation
- Setting up the equation correctly is the key step (1 mark). "7 times (actual + 8) = square of actual marks − 4."
- Factorisation earns the next mark; show the middle-term split clearly.
- Rejecting the negative root with a reason (marks can't be negative) is essential for the final mark — never skip this in board exams.
- Maximum marks = 35, and 12 ≤ 35, so the answer is valid in context.