Question

From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read

i) at least one of the newspaper
ii) neither Marathi nor English newspaper
iii) only one of the newspaper

Answer 1

Hint: Use a Venn diagram to solve the question. Depict the total literate individuals as the universal set. Let the individuals who read Marathi be one subset of the universal set and the individuals who read English be another subset of the universal set.

Complete step-by-step answer:

According to the question, it is given that

The number of total literate individuals = 2000.

70% of the total population read Marathi newspaper,

No. of Marathi newspaper reader = \[2000\times \dfrac{70}{100}=1400\]

50% of the total population read English newspaper,

No. of English newspaper reader = \[2000\times \dfrac{50}{100}=1000\]

No. of literates who read both English newspaper reader = \[2000\times \dfrac{32.5}{100}=650\]

Representing these all figures using a Venn diagram, we have

The commonly shared region will have 650 individuals who read Marathi as well as English newspapers.

i.)The number of individuals who read at least one newpaper=750+650+350=1750

ii.)The Number of individuals who read neither Marathi nor English newspaper = 2000-1750 = 250.

iii.)The number of individuals who read one newspaper=750+350=1100.


Note: In this type of question, first find the number of individuals using the percentage as per the information provided in the question. Then, represent these numbers of individuals using the venn diagram.