Targeting an overall 50%: A student scores 30% of 180 in Paper 1. What percent of 150 must he score in Paper 2 to achieve at least 50% overall?

Introduction / Context:
The student needs a target overall percentage across two papers with different maxima. Compute the required total marks, subtract Paper 1 marks, and then express the remainder as a percentage of Paper 2’s maximum.

Given Data / Assumptions:

• Paper 1 max = 180; scored = 30% of 180.
• Paper 2 max = 150; required overall ≥ 50% across both papers.
• No negative marks or scaling adjustments.

Concept / Approach:
Total maximum = 180 + 150 = 330. Target marks = 0.50 * 330 = 165. Paper 1 marks = 0.30 * 180 = 54. Needed in Paper 2 = 165 − 54. Convert this to a percentage of 150.

Step-by-Step Solution:
Paper 1 = 0.30 * 180 = 54Target overall = 0.50 * 330 = 165Required in Paper 2 = 165 − 54 = 111% on Paper 2 = 111 / 150 * 100 = 74%

Verification / Alternative check:
Total achieved with 74% on Paper 2: 54 + 0.74*150 = 54 + 111 = 165, exactly 50% overall.

Why Other Options Are Wrong:
76%, 70%, 80%, 72% overshoot or undershoot the exact requirement for reaching 50% overall.

Common Pitfalls:
Taking 50% of each paper separately; the correct approach uses the combined maximum and total marks needed.

Final Answer:
74%