In a village 50% of the villagers produce rice, 40% of the villagers produce apples and 50% of the villagers produce vegetables, 20% of the villagers produce rice and apples both, 25% of the villagers produce apples and vegetables both, 20% of the villagers produce rice and vegetables both and 10% of the villagers produce all three. Find the percentage of villagers who do not produce anything.

In a village 50% of the villagers produce rice, 40% of the villagers produce apples and 50% of the villagers produce vegetables, 20% of the villagers produce rice and apples both, 25% of the villagers produce apples and vegetables both, 20% of the villagers produce rice and vegetables both and 10% of the villagers produce all three. Find the percentage of villagers who do not produce anything. Correct Answer 15%

n(R ∪ A ∪ V) = n(R) + n(A) + n(V) - n(R ∩ A) - n(R ∩ V) - n(A ∩ V) + n(R ∩ A ∩ V)

⇒ n(R ∪ A ∪ V) = 140% - 65% + 10%

⇒ n(R ∪ A ∪ V) = 85%