GATE Electrical Engineering (EE) 2015 Shift 1 Solved Paper

The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two.
Following relations are drawn in m, p, c:
I. $\mathit{p}+\mathit{m}+\mathit{c}=27∕20$
II. $\mathit{p}+\mathit{m}+\mathit{c}=13∕20$
III. $\left(\mathit{p}\right)\times \left(\mathit{m}\right)\times \left(\mathit{c}\right)=1∕10$