Question

In a group of $70$ people $31$ speak Hindi, $33$ speak Bengali, $32$ speak Telugu, $16$ speak both Hindi and Bengali, $14$ speak both Hindi and Telgu, $15$ speak Bengali and Telgu, $5$ person can not speak any of the three language. Find how many can speak all languages.

• A. $21$
• B. $25$
• C. $14$
• D. $51$

Answer 1

The correct option is C $14$

Total people=$70$

$5$ people can't speak any language.

$\therefore$ number of people speak=$70-5=65$

$A$=Number of people speak hindi=$31$

$B$=Number of people speak bengali=$33$

$C$=Number of people speak telugu=$32$

$A\cup B=16,A\cup C=14,B\cup C=15A\cup B\cup C=A+B+C-A\cap B+B\cap C-A\cap C+A\cap B\cap C65=31+33+32-16-14-15+A\cap B\cap CA\cap B\cap C=14$

Number of people speak all language$=14$