In an examination, 25% of students failed in Mathematics, 20% failed in Economics, and 5% failed in both. What percentage passed in both subjects?

Introduction / Context: Passing in both subjects is the complement of failing in at least one. Use inclusion–exclusion to find the percentage failing in at least one subject, then subtract from 100%.

Given Data / Assumptions:

• % fail Mathematics = 25.
• % fail Economics = 20.
• % fail both = 5.

Concept / Approach: % failing at least one = 25 + 20 − 5 = 40%. Therefore, % passing both = 100% − 40% = 60%.

Step-by-Step Solution:

Verification / Alternative check: A Venn diagram confirms the arithmetic: the intersection is not double-counted.

Why Other Options Are Wrong: 45% and 39% mis-handle inclusion–exclusion; 62% is a rounding/guess.

Common Pitfalls: Adding the single-subject failure rates without subtracting the overlap.

Final Answer: 60%