[m.gayatri]

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?

[PrashanthU]

The above problem can be best solved using De-Morgan's laws or using Venn diagrams
Solution:
Let Hindu be denoted by : H
Times by : T
Deccan by : D
Given,
n(H u T u D) = 76 --> Total no.of persons
n(H) = 53 --> no.of people who read Hindu
n(T) = 46 --> no.of people who read Times
n(D) = 39 --> no.of people who read Deccan
n(H and T) = ?, let it be x --> no.of people who read Hindu and Times
n(T and D) = 23 --> no.of people who read Times and Deccan
n(D and H) = 22 --> no.of people who read Deccan and Hindu
n(H and T and D) = 15 --> no.of people who read Hindu,Times and Deccan
and 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)
=>76=53+46+39-x-23-22+15
=>x=153-121
=>x=32, no.of people who read both Hindu and Times, this also includes who read all the three
Therefore,no.of people who read only Hindu and Times is : 32-15 =17