In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored?

The correct option is 380.

Let us break down the problem step-by-step to understand why this option is correct:

Step 1: Define the variables for the marks scored.
Let $A$ represent the marks scored by A, and let $B$ represent the marks scored by B.

Step 2: Translate the given conditions into mathematical equations.
First, we are given that A scored 20 marks more than B. We can write this relation as:
$A=B+20$ (Equation 1)
Second, we are given that B scored 5% less marks than A. A score that is 5% less than A is equal to 95% of A's score:
$B=A-0.05A$
$B=0.95A$ (Equation 2)

Step 3: Solve the system of equations.
Substitute the expression for $B$ from Equation 2 into Equation 1:
$A=0.95A+20$
Subtract $0.95A$ from both sides of the equation to isolate the term with $A$:
$A-0.95A=20$
$0.05A=20$
Solve for $A$ by dividing both sides by 0.05:
$A=\frac{20}{0.05}$
$A=400$

Step 4: Find B's score.
Now that we have A's score, we can find B's score using Equation 1:
$B=A-20$
$B=400-20$
$B=380$

Thus, B scored 380 marks.