1. **Problem statement:** A student answered 120 True/False questions. Each correct answer gives 1 mark, each wrong answer deducts 1/4 mark. The student scored 90 marks. If all guessed answers were wrong, find how many questions he knew. 2. **Define variables:** Let $k$ = number of questions he knew, $g$ = number of questions guessed. 3. **Given:** Total questions answered: $$k + g = 120$$ 4. Since all guessed answers were wrong, each guessed question deducts $\frac{1}{4}$ mark. 5. The total score is marks from known questions (all correct) minus penalty from guessed questions: $$\text{Score} = k \times 1 - g \times \frac{1}{4} = 90$$ 6. From step 3, express $g$ as: $$g = 120 - k$$ 7. Substitute $g$ into score equation: $$k - \frac{1}{4}(120 - k) = 90$$ 8. Simplify: $$k - 30 + \frac{k}{4} = 90$$ 9. Combine like terms: $$k + \frac{k}{4} = 90 + 30$$ $$\frac{4k}{4} + \frac{k}{4} = 120$$ $$\frac{5k}{4} = 120$$ 10. Solve for $k$: $$k = \frac{120 \times 4}{5} = 96$$ **Answer:** The student knew 96 questions.