Joint Family and Newspapers

There is a joint family. The family members bring many newspapers. Each person reads 5 newspapers and each newspaper is read by 21 people. The number of newspapers they bring is 15.

Can you find the number of people in the joint family?


Hint 1

There are three known data and one unknown datum. Find a relation.


Hint 2

The unknown datum is a function of the three given data. Use (person, newspaper) combination to find the relation.


Answer

Number of people in the joint family = 63.


Solution

The problem mentions four data among which three is known and one is unknown and the problem asks us to find the unknown quantity.

Let the number of people in the family = p
Let the number of newspapers = n
Let the number of newspapers read by each person = q
Let the number of people who read a newspaper = m

Now we have the four data:
-> Three known data – n, q and m
-> One unknown datum – p

Let us try to find a relation among the four data, so that we can find the unknown datum using the three known data.

Consider the statements:
Each person in the family reads q newspapers.
There are p people in the family.
So, the total (person, newspaper) combination in the family = q x p   (1)

Consider the statements:
Each newspaper is read by m people.
There are n newspapers.
So, the total (newspaper, person) combination in the family = m x n   (2)

Number of (person, newspaper) combinations = Number of (newspaper, person) combinations.
From (1) and (2), we have



As we have to find the unknown quantity p, the above equation can be rewritten as




In the problem given, m = 21, n = 15 and q = 5.
Applying the values of m, n and q in the derived formula for p, we get




Hence, the number of people in the joint family = 63.

NOTE: Remember the relation between the four data:
Number of people in the family x Number of newspapers read by each person = Number of people who read a newspaper x Number of newspapers.