Question

In a school all the students have to learn drawing or painting. If 36% of the students learn drawing and painting and 40% of those who learn drawing do not learn painting, then what % of the students learn painting?

• A. 40%
• B. 60%
• C. 76%
• D. 80%

Answer 1

The correct option is C

76%

If we assume the total number of students = 100

As the students need to learn draing or painting, n(D U P) = 100.

$n(D\cap P)$ = 36.

Let n(D) = x

Then the number of students who do not paint represents the set of students who only draw,i.e. D - P

n(D - P) = 0.4x.

Thus,$0.4x+36=x\Rightarrow x=60$

$n(D\cup P)=n\left(D\right)+n\left(P\right)-n(D\cap P)$

100 = 60 + n(P) - 36

n(P) = 100 - 24

n(P) = 76%

Alternate: $n\left(P\right)=n(D\cap P)+n(P-D)$

n(P) = 36 + (100 - 60)

= 36 + 40

= 76%