Question

A survey of a village showed that 1 / 10 of the total population speak neither hindi nor english. 1 / 5 of them cannot speak english and 3 / 7 of them cannot speak hindi. what percentages of people know only one language?

Answer 1

Solution :-

1/10th of the total population does not speak English or Hindi 

Let us assume that 1/10th of the total population be Set A

1/5th of them cannot speak English

3/7 of them cannot speak Hindi

Out of the total, 1/5th people who cannot speak English, some of them are in Set A.

Therefore, remaining are = 1/5 - 1/10 

= 1/10

Remaining 1/10 people only speak Hindi.

Similarly, out of 3/7 people who cannot speak Hindi, some of them are in Set A.

Therefore, remaining are = 3/7 - 1/10

Taking L.C.M. of the denominator and then solving it.

⇒ = (30 - 7)/70

= 23/70

Remaining 23/70 people only speak English.

So, the people who speak only one language = 1/10 + 23/70

= (7 + 23)/70

= 30/70

Percentage of the 30/70 people = 30*100/70

= 42.857 %

Answer.