Question

There are 76 persons. 53 can read hindu,46 can read times,39 can read deccan and 15 can read all. If 22 can read hindu and deccan and 23 can read deccan and times then

what is the number of persons who read only times and hindu ?

Answer 1

let { here u denotes union/or and "and denotes intersection "

Total person :n(H u T u D) = 76
no of people read Hindi -n(H) = 53
no of people read times n(T) = 46
no of people read Deccan n(D) = 39
no of people read Hindi and times n (H and T) = ? ( say x)
no of people read times and Deccan n (T and D) = 23
no of people read Deccan and Hindi n (D and H) = 22
no of people read Hindi Deccan and times n (H and T and D) = 15

Now
We have

n(H u T u D)=n(H)+n(T)+n(D)-n(H and T)-n(T and D)-n(D and H)+n( H and T and D)

so now just plug in the values
we get

76=53+46+39-x-23-22+15
solving that equation we get
x = 32 .
so no. of people who read Hindu and times are 32 .

Answer 2

32 people read hindu and times only