Directions:In the following questions are to be based on the details g...
We represent the whole scenario as a Venn diagram.
Now according to the question, we need to find g:
Total population = a + b + c + d + e + f + g = 300.
People who speak French = a + b + d + e = 180.
People who only speak Italian = c = 20.
People who don’t know Italian = 190. Hence people who know Italian = b + c + e + f = 300 - 190 = 110.
People who speak exactly two languages = b + d + f = 110.
People who know both French and English = d + e = 60.
People who know only French and Italian = b = 30.
Since b + c + e + f = 110 and c = 20, then b + e + f = 90.
Now, b + e + f = 90 and b + d + f = 110. Subtracting, we get d - e = 20. Also, d + e = 60. Solving, we get d = 40 and e = 20.
Now, b = 30, d = 40, e = 20 and a + b + d + e = 180. Solving, we get a = 90.
Now b + d + f = 110, b = 30 and d = 40, hence f = 40.
Finally, g = 300 – (a + b + c + d + e + f) = 60.
Hence English alone is spoken by 60 people.