# In a survey of n students of a collage, it was found that 52% liked watching movies, 45% liked watching Web series and 65% liked watching TV Serials. Also, 22% liked watching movies and web series both, 25% liked watching web series and TV serials both and 30% liked watching movies and TV serials both. 10% liked watching all the three and 8% liked watching none of these. If the total number of students who liked watching only one of the three given programs is 190. Then, what is the value of n?

1. 550
2. 400
3. 500
4. 600
5. 800

Option 3 : 500

## Detailed Solution

Given:

Total number of students = n

The number of students who liked watching movies = 52%

The number of students who liked watching web series = 45%

The number of students who liked watching TV Serials = 65%

The number of students who liked watching movies and web series both = 22%

The number of students who liked watching web series and TV serials both = 25%

The number of students who liked watching movies and TV serials both = 30%

The number of students who liked watching all the three programs= 10%

The number of students who liked watching none of these programs = 8%

Concept:

Venn Diagram

Calculation: The number of students who liked watching only Movies and Web Series both = (22 – 10) % = 12%

The number of students who liked watching only Movies and TV Serials both = (30 – 10) % = 20%

The number of students who liked watching only Web Series and TV Serials both = (25 – 10) % = 15%

The number of students who liked watching only movies = (52 – 30 – 12) % = 10%

The number of students who liked watching only web Series = (45 – 22 – 15) % = 8%

The number of students who liked watching only TV Serials = (65 – 30 – 15) % = 20%

∴ The total number of students who liked watching only one of the three given programs = (10 + 8 + 20) %

⇒ 38%

Given, 38% = 190

⇒ 1% = 5

⇒ 100% = 500

∴ n = 500

The value of n is 500.
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