In an examination, 80% students passed in mathematics, 72% passed in Science and 13% failed in both the subjects - Maths - Sets

Question

In an examination, 80% students passed in mathematics, 72%
passed in Science and 13% failed in both the subjects If 312
students passes in both the subjects, find the total number of
students who appeared in the examination

Shridhar Kaushik · Accepted Answer

According to question,

$(\frac{80}{100} x - 312) + (312) + (\frac{72}{100} x - 312) + \frac{13}{100} x = x \Rightarrow \frac{80 x}{100} + \frac{72 x}{100} + \frac{13 x}{100} - x = 312 \Rightarrow \frac{165}{100} x - x = 312 \Rightarrow 65 x = 31200 \Rightarrow x = 480$

But this x will give the number of students failed in both subject $= \frac{13}{100} \times 480$ which is a fraction number.

So, the data given in the query is not consistent as the number of students failed can not be in fraction.

In an examination, 80% students passed in mathematics, 72% passed in Science and 13% failed in both the subjects. If 312 students passes in both the subjects, find the total number of students who appeared in the examination.