Question
A survey shows that $$61\% ,\,46\% $$ and $$29\%$$ of the people watched "3 idiots", "Rajneeti" and "Avatar" respectively. $$25\%$$ people watched exactly two of the three movies and $$3\%$$ watched none. What percentage of people watched all the three movies ?
A.
$$39\%$$
B.
$$11\%$$
C.
$$14\%$$
D.
$$7\%$$
Answer :
$$7\%$$
Solution :
The given condition is as follows-
$$\eqalign{ & {\text{We know that}} \cr & \left\{ {\left( {a + d + e + g} \right) + \left( {b + d + f + g} \right) + \left( {c + e + f + g} \right)} \right\} - \left( {d + e + f} \right) - 2g = a + b + c + d + e + f + g \cr & {\text{or, }}61x + 46x + 29x - 25x - 2g = 97x \cr & {\text{or, }}2g = 14x \cr & {\text{or, }}g = 7 \cr} $$
The given condition is as follows-
$$\eqalign{ & {\text{We know that}} \cr & \left\{ {\left( {a + d + e + g} \right) + \left( {b + d + f + g} \right) + \left( {c + e + f + g} \right)} \right\} - \left( {d + e + f} \right) - 2g = a + b + c + d + e + f + g \cr & {\text{or, }}61x + 46x + 29x - 25x - 2g = 97x \cr & {\text{or, }}2g = 14x \cr & {\text{or, }}g = 7 \cr} $$