Question

A town has a total population of 50,000. Out of it 28,000 read the newspaper X and 23,000 read Y while 4000 read both the papers. The number of persons not reading X and Y both is:

a)2,000
b)3,000
c)2,500
d)None of these

Answer 1

Using the principle of Inclusion-Exclusion, the number of people not reading either newspaper X or Y is calculated to be 3,000, which is option (b).

Step-by-step explanation:

The student's question is about finding the number of people who do not read either of the two newspapers, X and Y, out of a total town population of 50,000 people. Given that 28,000 read newspaper X, 23,000 read newspaper Y, and 4,000 read both newspapers, we can use the principle of Inclusion-Exclusion to solve this problem.

To calculate the number of people who read at least one of the newspapers, we sum the readers of newspapers X and Y and then subtract the number of people who read both, to avoid double-counting:

Number of people reading at least one paper = (Readers of X) + (Readers of Y) - (Readers of both X and Y)

= 28,000 + 23,000 - 4,000

= 47,000.

Since the total population is 50,000, by subtracting the readers of at least one paper from the total population, we get the number of people not reading either newspaper:

Number of people not reading either paper = Total population - Number of people reading at least one paper

= 50,000 - 47,000

= 3,000.

Therefore, the number of persons not reading either X or Y is 3,000, which corresponds to option (b).