In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?

The correct option is 20%.

Let us break down the solution step-by-step using set theory and Venn diagrams.

First, let the total number of students who appeared in the examination be 100%.

We are given the following information:
1. Percentage of students who passed in English = 80%. This implies that the percentage of students who failed in English is:
100% - 80% = 20%
Let $E$ represent the set of students who failed in English. Thus, $P\left(E\right)=20\%$.

2. Percentage of students who passed in Hindi = 70%. This implies that the percentage of students who failed in Hindi is:
100% - 70% = 30%
Let $H$ represent the set of students who failed in Hindi. Thus, $P\left(H\right)=30\%$.

3. Percentage of students who failed in both subjects = 15%.
This represents the intersection of students who failed in English and failed in Hindi. Thus, $P(E\cap H)=15\%$.

Now, let us find the percentage of students who failed in only one subject. A student fails in only one subject if they fail in English but not Hindi, or if they fail in Hindi but not English.

The percentage of students who failed only in English is:
$P\left(\text{Failed only in English}\right)=P\left(E\right)-P(E\cap H)=20\%-15\%=5\%$

The percentage of students who failed only in Hindi is:
$P\left(\text{Failed only in Hindi}\right)=P\left(H\right)-P(E\cap H)=30\%-15\%=15\%$

Therefore, the total percentage of students who failed in only one subject is the sum of those who failed only in English and those who failed only in Hindi:
$5\%+15\%=20\%$