Question

In a survey of some farmers of a community, 70% of them are found cultivating rice, 60% cultivating wheat, 20% are not cultivating both the crops, and 450 farmers are found cultivating both the crops. (i) Draw a Venn-diagram to illustrate the above information. (ii) Find the total number of farmers participated in the survey. (iii) Find the number of farmers who are cultivating rice only.​

Answer 1

Answer + Step-by-step explanation:

let R be the set of farmers cultivating rice.

let W be the set of farmers cultivating wheat.

let n be the total number of farmers.

i) Check the attachment.

ii) Card R∪W = Card R + Card W - Card R∩W

Note : Card R denotes the number of farmers cultivating rice.

`CardR\cup W=n-(20)/(100) n = (80)/(100) n`

`CardR=(70)/(100) n`

`CardW=(60)/(100)n`

`CardR \cap W=450`

Card R∪W = Card R + Card W - Card R∩W

`\Longleftrightarrow (80)/(100) n=(70)/(100) n + (60)/(100) n-450`

`\Longleftrightarrow (50)/(100) n=450`

`\Longleftrightarrow n= 2 * 450 = 900`

iiI) the number of farmers who are cultivating rice only :

`900* (70)/(100) -450=180`