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 at least any one of the above three, then find the number of farmers who grew all the three. ( 3 marks)
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 at least any one of the above three, then find the number of farmers who grew all the three. ( 3 marks)
Let P, R and C represent sets of farmers who grew paddy, ragi and com respectively.
So, 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” (1.5 marks)
we know that,
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
⇒1000 = 1230 – 300 + x
⇒1000 = 930 + x
⇒1000 – 930 = x
⇒ x=70
Therefore, the number of farmers who grew all the three = 70. (1.5 marks)
Let P, R and C represent sets of farmers who grew paddy, ragi and com respectively.
So, 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” (1.5 marks)
we know that,
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
⇒1000 = 1230 – 300 + x
⇒1000 = 930 + x
⇒1000 – 930 = x
⇒ x=70
Therefore, the number of farmers who grew all the three = 70. (1.5 marks)
