A student needs 40% to pass. She scores 178 marks and fails by 22 marks. What are the maximum marks?
500. Pass marks = 178 + 22 = 200, and 200 is 40% of the maximum, so maximum = 200 / 0.40 = 500.
Explain it simply
"Fails by 22 marks" means she was 22 marks short of the pass line. So the pass line is her score plus 22. Once you know what number 40% stands for, finding 100% is just scaling up: if 40 parts are 200 marks, one part is 5 marks and 100 parts are 500.
Example
Question: Pass mark is 40%. A student scores 178 and fails by 22. Find the maximum marks.
- Pass marks = 178 + 22 = 200.
- 40% of maximum = 200.
- Maximum = 200 x 100 / 40 = 500.
A two-student version is common: A gets 30% and fails by 25 marks, B gets 45% and gets 50 marks more than the pass mark. The gap 45% - 30% = 15% equals 25 + 50 = 75 marks, so maximum = 75 / 0.15 = 500, and pass mark = 0.30 x 500 + 25 = 175.
console.log((178 + 22) / 0.4); // Output: 500
console.log((75 * 100) / 15); // Output: 500What to say in the interview
"The pass mark is the score plus the shortfall, 200. That is 40 percent of the total, so the total is 200 divided by 0.4, which is 500."
Common mistakes
- Subtracting the 22 instead of adding it.
- In the two-student version, forgetting that one student is below and the other above the pass mark, so the marks add.