Question

In a village of $120$ families, $93$ families use firewood for cooking, $63$ families use kerosene, $45$ families use cooking gas, $45$ families use firewood and kerosene, $24$ families use kerosene and cooking gas, $27$ families use cooking gas and firewood. Find how many use firewood, kerosene and cooking gas.

• A. $10$
• B. $15$
• C. $20$
• D. $25$

Answer 1

The correct option is B $15$

Lets suppose families using firewood will be 'A', families using kerosene will

be 'B', families using cooking gas will be 'C'

From the above data we know that,

$n\left(A\right)=93$

$n\left(B\right)=63$

$n\left(C\right)=45$

$n(A\cap B)=45$

$n(B\cap C)=24$

$n(A\cap C)=27$

$n(A\cup B)=45$

$n(A\cup B\cup C)=120$. (total number of peoples)

we know the formulae,

$n(A\cup B\cup C)=n\left(A\right)+n\left(B\right)+n\left(C\right)-n(A\cap B)-n(B\cap C)-n(A\cap c)+n(A\cup B\cup c)$

put the value from above data,

$120=93+63+45-45-24-27+n(A\cup B\cup C)$

$120=105+n(A\cup B\cup C)$

so, $n(A\cup B\cup C)=15$

number of person use firewood, kerosene and cooking gas $=15$

correct option will be. 'B'