In a test, Rajesh scored 112, which is 32 more than the passing marks. Sonal scored 75% of the maximum and that was 70 more than the passing marks. What is the minimum passing percentage of the test?

Introduction / Context:
Use two equations: one linking Rajesh’s score to the passing mark, and another linking Sonal’s percentage of maximum marks to the passing mark. Solve for passing marks and maximum, then compute the passing percentage.

Given Data / Assumptions:

• Rajesh score = 112 = P + 32 ⇒ P = passing marks.
• Sonal score = 75% of maximum = 0.75M, and 0.75M − P = 70.
• All marks are on the same maximum M.

Concept / Approach:
From Rajesh: P = 112 − 32 = 80. Substitute into Sonal’s equation to get M, then compute passing% = (P/M) * 100%.

Step-by-Step Solution:

Verification / Alternative check:
Sonal’s score 0.75 * 200 = 150, which is indeed 70 above the pass mark 80.

Why Other Options Are Wrong:
35%, 45%, 48% arise from arithmetic errors or using Rajesh’s score as maximum.

Common Pitfalls:
Misinterpreting phrases ”more than the passing marks” vs. ”percent of maximum.”

Final Answer:
40%