1. **State the problem:** A student scores 36% and gets 24 marks. Another student scores 43% and gets 18 marks more than the passing marks. We need to find the maximum total marks and the passing percentage. 2. **Define variables:** Let $M$ be the maximum marks. Let $P$ be the passing marks. 3. **Set up equations:** From the first student: $$0.36M = 24$$ From the second student: $$0.43M = P + 18$$ Since $P$ is passing marks. 4. **Express passing marks $P$ from the first student:** Passing marks $P$ is less than or equal to $24$ marks because the first student didn't pass (36% < 43%), but let's clarify using equation. 5. **Calculate $M$ from the first student's data:** $$M = \frac{24}{0.36} = 66.6667$$ 6. **Calculate $P$ from the second student's data:** $$0.43M = P + 18 \implies P = 0.43M - 18$$ Substitute $M=66.6667$: $$P = 0.43 \times 66.6667 - 18 = 28.6667 - 18 = 10.6667$$ 7. **Calculate passing percentage**: $$\text{Passing \%} = \frac{P}{M} \times 100 = \frac{10.6667}{66.6667} \times 100 = 16\%$$ **Final answers:** - Maximum marks $M = 66.67$ - Passing marks $P = 10.67$ - Passing percentage = $16\%$