Answer:

Total number of students who appeared in the examination = 480

Step-by-step explanation:

Let total number of students who appeared in the exam be x

Number of students who passed in Math = 80% of x

                                                                     = 0.8·x

Number of students who passed in Science = 72% of x

                                                                     = 0.72·x

Number of students who failed in both = 13% of x

                                                                 = 0.13·x

Number of students who passed in both = 312

⇒ Total students = 0.8·x + 0.72·x + (0.13·x - 312)

⇒ 0.8·x + 0.72·x + (0.13·x - 312) = x

⇒ 1.65·x - x = 312

⇒ 0.65·x = 312

⇒ x = 480

Hence, Total number of students who appeared in the examination = 480