P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score?

Correct Option

Let Q's score be represented by $x$. According to the problem statement, P scored 40 marks more than Q. Therefore, P's score is $x+40$.

The problem also states that Q scored 10% less marks than P. This implies that Q's score is 90% of P's score. We can set up the equation as follows:

$$x=90\mathrm{\%}\text{ of }(x+40)$$ $$x=\frac{90}{100}(x+40)$$

To solve for $x$:

$$100x=90(x+40)$$ $$100x=90x+3600$$ $$100x-90x=3600$$ $$10x=3600$$ $$x=\frac{3600}{10}$$ $$x=360$$

Thus, Q scored 360 marks.

Incorrect Options

Options 2 (380), 3 (400), and 4 (420) are incorrect because they do not satisfy the conditions given in the problem. If any of these values were Q's score, the relationship that Q scored 10% less than P (where P scored 40 more than Q) would not hold true upon verification. For instance, if Q scored 380, P would score 420. 10% less than 420 is $420\times 0.90=378$, which is not 380. Similar discrepancies arise with 400 and 420.