One family of 20 members have 20 chapatis to eat, finally
- Every child gets 1/2 chapati
- Every Lady in the house gets 2 chapatis
- And every gentleman gets 3 chapatis to eat.
How many Child, Ladies and Gents are there in the family?
Answer1: Number of children = 14, Ladies= 5 and Gents = 1
Answer2: Number od children = 16, Ladies = 0 and Gents = 4.
We can form the mathematical equations and solve them, lets assume number of children = x, ladies = y and gents = z.
Then we can form these two equations
- x + y + z = 20(Total number of people in family)
- x/2 + 2y + 3z = 20 (Total number of chapati’s)
Now we can solve above two equations as below
x/2 + 2(y+z) + z = 20 x/2 + 2(20 -x) + z = 20 (replaced y+z from first equation) 40 + z -3x/2 = 20 3x/2 = 20 +z as z > 0 => 3x/2 > 20, x = 14, 16, 18...
We can see that y becomes negative for any value of x greater than or equal to 18,thus x = 14 and 16 are two possible values. we can get the corresponding values of y and z as well.
Number Puzzle #59