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

$$x = 90\% \text{ of } (x + 40)$$x=90% of (x+40) $$x = \frac{90}{100}(x + 40)$$x=10090​(x+40)

To solve for $x$x:

$$100x = 90(x + 40)$$100x=90(x+40) $$100x = 90x + 3600$$100x=90x+3600 $$100x - 90x = 3600$$100x−90x=3600 $$10x = 3600$$10x=3600 $$x = \frac{3600}{10}$$x=103600​ $$x = 360$$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$420×0.90=378, which is not 380. Similar discrepancies arise with 400 and 420.