Question

A survey of 1000 farmers found that 600 grew paddy, 350 grew ragi, 280 grew corn, 120 grew paddy and ragi, 100 grew ragi and corn, 80 grew paddy and corn. If each farmer grew atleast anyone of the above three, then find the number of farmers who grew all the three.

Answer 1

Let P, R and C represent the set of farmers grew paddy, ragi and corn, respectively.

n(P ∪ R ∪ C) = 1000, n(P) = 600, n(R) = 350, n(C) = 280

n(P ∩ R) = 120, n(R ∩ C) = 100, n(P ∩ C) = 80

Let the number of farmers who grew all the three be “x”

n(P ∪ R ∪ C) = n(P) + n(R) + n(C) – n(P ∩ R) – n(R ∩ C) – n(P ∩ C) + n(P ∩ R ∩ C)

1000 = 600 + 350 + 280 – 120 – 100 – 80 + x

= 1230 – 300 + x

1000 = 930 + x

1000 – 930 = x

70 = x

Number of farmers who grew all the three = 70.