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UPSC CDS I 2019 Math Paper

Question Numbers: 16-18

Direction: Consider the following for the next three (03) items:

In a certain town of population size 1, 00, 000 three types of newspapers (I, II and III) are available. The percentages of the people in the town who read these papers are as follows:

Newspaper	Proportion of readers
I	10%
II	30%
III	5%
Both I and II	8%
Both II and III	4%
Both I and III	2%
All the three (I, II and III)	1%

Question : 18 of 100

Marks: +1, -0

What is the number of people who do not read any of these three newspapers?

62,000
64,000
66,000
68,000

Validate

Solution:

Concept:

Use set theory and a Venn diagram to find the percentage of people who read at least one newspaper, then subtract from the total population.

Explanation:

Total population =

1,00,000

From the Venn diagram of the given data:

Percentage who read only one newspaper =

1\% + 19\% + 0\% = 20\%

Percentage who read exactly two newspapers =

7\% + 1\% + 3\% = 11\%

Percentage who read all three newspapers =

1\%

Total readers =

20\% + 11\% + 1\% = 32\%

Percentage who read none =

100\% - 32\% = 68\%

Number of non‑readers =

68\% \text{ of }

1,00,000 = 68,000

\text{D}

68,000$

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