Question

In a factory 70% of the workers like oranges and 64% likes apples. If x% like both oranges and apples, then the possible values of x are

• A. $x\ge 34$
• B. $x\le 64$
• C. $34\le x\le 64$
• D. $x\ge 44$

Answer 1

The correct option is C

$34\le x\le 64$

Given data:

Percentage of workers like oranges = 70%

Percentage of workers like apples = 64%

Percentage of workers like both oranges and apples = x%

Fo find the possible values of x, We need to find the minimum and maximum value of x.

For minimum value of the intersection (x).

If all the workers like either oranges or apples

Then,

n(A∪B) = n(A) + n(B)- n(A∩B)

100 = 70 +64 - n(A∩B) [$\because$ Since the number of wokers is given in percenatge, the total percentage of workers is 100%]

n(A∩B) = 34%

$\Rightarrow$ The minimum value value of intesection(x) is 34%.

$\Rightarrow x\ge 34$

For maximum value of intersection(x)

Maximum possible common area of intersection for Oranges and apples is, area of apples which is 64% of workers.

The maximum value of Intersection(x) 64%.

$\Rightarrow x\le 64$

$\Rightarrow xliesin34\le x\le 64$