Question

Theory of sets: Steps wanted!!!!!
A village has a total population of 2500 people.Out of which 1300 people use brand A soap and 1050 people use brand B soap and 250 people use both brands.brands. Find the percentage of population who use neither of these soaps.

Answer:16% 
I need steps and how to proceed the steps????

Answer 1

Steps:

Let the % of number of people using Soap A be x
Let the % of number of people using Soap B be y
Let the % of number of people using both Soap A and B be z
Then:

2500x/100=1300
x=1300*100/2500
x=52%

2500y/100=1050
y=1050*100/2500
y=42%

2500z/100=250
z=250*100/2500
z=10%

We need to subtract the percentage of the number of people using both Soap A and B, so that we can get the real percentage of the number of people using Soap A and Soap B.

(52%+42%)-10%
94%-10%
84%            The real percentage of the number of people using Soap A and Soap B

If we subtract 84%(The real percentage of the number of people using Soap A and Soap B), then we will get the percentage of the number of people using neither of these two)

100%-84%
16%

16/100*2500
400

400 people are using neither of these two soaps.