UPSEE Solved Model Paper 7

Given:
In a group 100 members knows Hindi, 50 knows Urdu and 25 of them Hindi and Urdu
We have to find the number of members in the group-
Let H be the set of persons who speak Hindi and U be the set of persons who speak Urdu.
∴ n 〔H) = 100, n (U) = 50 and n (H ∩ U) = 25
From addition theorem of sets, we can write
n(H ∪ U) = n(H) + n(U) - n (H ∩ U)
Using given values
⇒ (H ∪ U) = 100 + 50 - 25 = 125
Total number of members in the group = 125
Hence, option 'C' is correct