In a survey it was found that the ratio of the people who liked modern song and folk song is 8:9 out of them 50 people liked both song 40 like folk song only and it is like none of the song then find the number of people who participated in the survey
Answers
Step-by-step explanation:
In a survey of a group of people, it was found that 70% of the people like folk songs, 60% like modern songs. 4000 people liked both of them and 10% liked none of them. How many of the people were surveyed? Please solve it using set formulas.
As written, the answer to this question is all of them were surveyed. ;-)
However, I think you mean how many people are in the group that was surveyed.
Given a world divided only into those who do/don’t like folk/modern music: you have four possibilities: A: Like Folk, Dislike Modern, B: Like Folk, Like Modern, C: Dislike Folk, Like Modern, and D: Dislike Folk, Dislike Modern.
Since these four possibilities are all there are, they have to sum to 100%.
Thus, 100% = % Like Folk, Dislike Modern + % Like Folk, Like Modern + % Dislike Folk, Like Modern + % Dislike Folk, Dislike Modern
Your problem statement tells us 10% like neither (group D). It further tells us that 70% like Folk and 60% like Modern.
10% + 70% + 60% > 100% (= 140%).
Therefore, because we can’t have more than 100%, we know that the difference between 140% and 100% must be accounted for by the fact that 40% like both Modern and Folk. So, 30% must only like Folk and and 20% must only like Modern.
So, going back to our original equation, we get
100% = 30% + 40% + 20% + 10%.
If the 4,000 people that like both are 40% of the group, you simply divide 4,000 by .4 to discover the whole group consists of 10,000
10,000 = 3,000 + 4,000 + 2,000 + 1,000.
Solution:-
n(F)=70%,n(M)=60%and n(F intersection M)=4000,n(FUM)'=10%
We have,n(U)=100%
Now,
n(AUB)=n(U)-n(AUB)'
n(FUM)=100%-10%=90%
Again,(FUM)=70/100*x+60/100*x-4000
90/100*x=7x/10+6x/10–4000
9x/10+4000=7x/10+6x/10
9x+40000/10=15x/10
90x+400000=150x
90x-150x=-400000
-60x=-400000
X=400000/60
Let N = number of people surveyed.
Let F = those who like folk songs.
Let M = those who like modern songs.
Let f = those among F who also like modern songs.
Let m = those among M who also like folk songs.
f+m = 4,000.
(0.7)*N+(0.6)*N+(0.1)*N = (1.4)*N.
F+M+(0.1)*N = N.
F+M = (0.9)*N
F+M+f+m+(0.1)*N = (1.4)*N.
(0.9)*N+4,000+(0.1)*N = (1.4)*N.
4,000 = (1.4–0.9–0.1)*N.
N = 4,000/(0.4) = 10,000.
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