Question

In a colony, 30 families read both The Hindu and Indian Express. 40 families read neither of these two news papers. If 40% of the families read The Hindu and 55% of the families read Indian Express What percentage of the total number of families read The Hindu only?​

Answer 1

Answer:

you should solve it by probably theroram in 10th syllabus

Answer 2

40.

A total of 40 families read the Hindu only.

Considering a Venn diagram, where A = families reading the Hindu and B = families reading IE.

Given,

n (A∩B) = 30

n (A) = 0.4* U

n (B) = 0.55*U

We know,

n (A∪B) = n(A) + n(B) - n(A∩B)

∴ n (A∪B) = 0.4*U + 0.55*U - 30

we know, U = n (A∪B) + families that read neither

∴ U = n (A∪B) + 40

∴ n (A∪B) = 0.4*(n (A∪B) + 40) + 0.55*(n (A∪B) + 40) - 30

∴ n (A∪B) = 0.95*n(A∪B) + 0.95*40 - 30

∴ 0.05 × n (A∪B) = 38 - 30

∴ n (A∪B) = 160.

∴ U = 200 families.

Given that 40% of U read The Hindu

∴ n(A) = 80

Now, families reading only Hindu = n(A) - n(A∩B)

∴ Families reading only Hindu = 80 - 40

∴ Families reading only Hindu = 40 Families