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?

Correct Option (B)

Let 'x' represent the marks scored by A.

• According to the problem statement, A scored 20 marks more than B. Therefore, B's score can be expressed as (x - 20).
• It is also given that B scored 5% less marks than A. This implies that the difference in marks between A and B is 5% of A's score.
• Mathematically, this can be written as: x - (x - 20) = 5% of x.
• Simplifying the equation: 20 = (5/100) * x.
• To find x (A's score): x = (20 * 100) / 5 = 400.
• To determine B's score, substitute the value of x into B's score expression: B = x - 20 = 400 - 20 = 380.

Incorrect Options:

The derived correct score for B is 380, which satisfies both conditions: A scores 20 more than B (A=400, B=380) and B scores 5% less than A (20 is 5% of 400). The other options do not concurrently satisfy these conditions.

• If B's score were 360 (Option 1), then A's score would be 360 + 20 = 380. The 20-mark difference would be (20/380) * 100 ≈ 5.26% of A's score, which is not 5%.
• If B's score were 400 (Option 3), then A's score would be 400 + 20 = 420. The 20-mark difference would be (20/420) * 100 ≈ 4.76% of A's score, which is not 5%.
• If B's score were 420 (Option 4), then A's score would be 420 + 20 = 440. The 20-mark difference would be (20/440) * 100 ≈ 4.54% of A's score, which is not 5%.