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.

$CardR\cup W=n-\frac{20}{100} n = \frac{80}{100} n$

$CardR=\frac{70}{100} n$

$CardW=\frac{60}{100}n$

$CardR \cap W=450$

Card R∪W = Card R + Card W - Card R∩W

$\Longleftrightarrow \frac{80}{100} n=\frac{70}{100} n + \frac{60}{100} n-450$

$\Longleftrightarrow \frac{50}{100} n=450$

$\Longleftrightarrow n= 2 \times 450 = 900$

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

$900\times \frac{70}{100} -450=180$