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 at least any one of the above three, then find the number of farmers who grew all the three.

• A. 70
• B. 170
• C. 200
• D. 470

Answer 1

The correct option is A 70

Each farmer grew at least one of the above three.
Let ‘a’, ‘b’ and ‘c’ be the number of farmers who grew only ‘Paddy’, ‘Ragi’ and ‘Corn’ respectively.
The number of farmers who grew all the three is x.

$a=600–(120–x+x+80–x)$
$=600–(200–x)$
$=600–200+x$
$=400+x$

$b=350–(120–x+x+100–x)$
$=350–(220–x)$
$=350–220+x$
$=130+x$

$c=280–(80–x+x+100–x)$
$=280–(180–x)$
$=280–180+x$
$=100+x$

Total farmers participated in the survey $=1000$
Therefore,
$\Rightarrow a+b+c+(120–x)+(100–x)+(80–x)+x=1000$
$\Rightarrow 400+x+130+x+100+x+120–x+100–x+80–x+x=1000$
$\Rightarrow 930+x=1000$
$\Rightarrow x=1000–930$
$\Rightarrow x=70$

Hence, 70 farmers grew all the three crops