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

The correct answer is 360.

Step-by-step Explanation:

Step 1: Define the variables based on the given information.
Let the marks scored by P be $P$ and the marks scored by Q be $Q$.

According to the problem statement, P scored 40 marks more than Q:

$P-Q=40$

or equivalently,

$P=Q+40$    --- (Equation 1)

Step 2: Express Q's score in terms of P's score.
We are also given that Q scored 10% less marks than P. This means Q's score is 90% of P's score:

$Q=P-0.10P=0.90P$    --- (Equation 2)

Step 3: Solve the system of equations.
Substitute the value of $Q$ from Equation 2 into Equation 1:

$P-0.90P=40$

$0.10P=40$

Solve for $P$:

$P=\frac{40}{0.10}=400$

So, P scored 400 marks.

Step 4: Calculate Q's score.
Using Equation 2:

$Q=0.90\times 400=360$

Alternatively, since $Q=P-40$:

$Q=400-40=360$

Thus, Q scored 360 marks.