Question

2. out of group of 200 students , 100 students know English, 80 students know
kannada, 70 students know Hindi. If 40 students know all the three languages, find the number of students who know exactly two languages​

Answer 1

Answer:

English - 100

Kannada - 80

Hindi- 70

total - 100+80+70 = 250

students who don't know all language= 250-40= 210

total students 200 so students who know exactly two languages are 210-200 = 10

: • Answer is 10.

Answer 2

There are 70 students who know exactly two languages.

We can use the principle of inclusion-exclusion to find the number of students who know exactly two languages. Let's start by adding up the number of students who know each language:

Number of students who know English = 100

Number of students who know Kannada = 80

Number of students who know Hindi = 70

Now, we need to subtract the number of students who know two languages. However, we need to be careful not to count the students who know all three languages twice. We can use the formula:

number of students who know exactly two languages = (number of students who know English and Kannada) + (number of students who know English and Hindi) + (number of students who know Kannada and Hindi) - 2*(number of students who know all three languages).Let's plug in the values we have:

number of students who know exactly two languages = (unknown) + (unknown) + (unknown) - 2*(40) We still need to find the number of students who know each pair of languages. We can do this by subtracting the number of students who know all three languages from the number of students who know each language pair. For example:

Number of students who know English and Kannada = (unknown) - 40

Number of students who know English and Hindi = (unknown) - 40

Number of students who know Kannada and Hindi = (unknown) - 40

Now we can substitute these values into the formula:

number of students who know exactly two languages = [(unknown) - 40] + [(unknown) - 40] + [(unknown) - 40] - 2*(40)

Simplifying: number of students who know exactly two languages = (unknown) - 80. We also know that the total number of students is 200:

total number of students = 100 + 80 + 70 - 40 + (unknown) - 80

Simplifying:

200 = 130 + (unknown)

So, the number of students who know exactly two languages is:

number of students who know exactly two languages = 200 - 130

number of students who know exactly two languages = 70

Therefore, there are 70 students who know exactly two languages.

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