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  4. 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?

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Q. 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?

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Solution:

The given condition is as follows-
image
We know that $\{(a+d+e+g)+(b+d+f+g)+$
$(c+e+f+g)\}-(d+e+f)-2 g=a+b+c+d+e+f+g$
or $61 x+46 x+29 x-25 x-2 g=97 x$
or $2 g =14 x$ or $g =7 x$