While preparing the progress reports of the students, the class t… - Vidyadip

MCQ

While preparing the progress reports of the students, the class teacher found that $70\%$ of the students passed in Hindi, $80\%$ passed in English and only $65\%$ passed in both the subjects. Find out the percentage of students who failed in both the subjects.

✓
$15\%$
B
$20\%$
C
$30\%$
D
$35\%$

✓

Answer

Correct option: A.

$15\%$

The sets $E$ and $H$ represent the students failing in the respective subjects.
$\ce{n(H ∪ E)} = 1− 0.65 = 0.35$
By set theory
$\ce{n(H ∩ E) = n(H) + n(E) − n(N ∪ E)}$
$= 0.3 + 0.2 − 0.35 = 0.15$
Hence $15\%$ of students failed in both subjects.

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