Earnings Of People

Twenty men, women and children earn twenty coins between them. Each man earns 3 coins, each woman 1.5 coins and each child 0.5 coin.

How many men, women and children are there?

Find number of each of them here!

Number Of Earning People

What was the question? 

Let's suppose there are m men, w women and c children.

As per given data,

m + w + c = 20   ......(1)

3m + 1.5w + 0.5c = 20   .....(2)

Multiply equation (1) by 3 and then subtracting from (2), we get,

5m + 2w = 20.

For m and w to be whole numbers, m must be 2 and w must be 5 satisfying above equation.

Hence, from (1),

c = 20 - 2 - 5 = 13.

 
To conclude, there are 2 men, 5 women and 13 children.

The Tuesday Birthday Problem

I ask people at random if they have two children and also if one is a boy born on a Tuesday. After a long search I finally find someone who answers yes. What is the probability that this person has two boys? Assume an equal chance of giving birth to either sex and an equal chance to giving birth on any day.

Tip: Don't conclude too early. 

Click here to know the correct answer! 

Finding The Correct Probability

How tricky it was?

If you think that the probability is 1/2 after reading that the couple has equal chance of having child of either sex then you are in wrong direction.

Take a look at the table below.

There are 27 possible combinations when boy is born on Tuesday. Out of which there are only 13 possible combinations where either boy (first or second) is born on Tuesday. 

Hence the probability that the person having at least 1 boy off his 2 boys born on Tuesday is 13/27.