Find out the balance if beer bottles divided between seven friends?

Question

A box contains beer bottles if divided between 4 friends 4 bottles are balance and if divided between 5 friends 3 bottles are balance what will be the balance if divided between 7 friends (the box contains minimum no of bottles.)

Answer 1

Let’s say total number of beer bottles in box are x. then we can say

x = 4m + 4, where m is integer greater than or equal to 0.
x = 5n + 3, where n is integer greater than or equal to 0.

From above two eequations
4m+4 = 5n + 3 = x
=> 5n – 4m = 1, where m and n are integers greater or equal to 0.
For bottles to be minimum, lets assume m and n are 0
thus from above equation 0 = 1, which is not true, so they cant be both 0 at same time.

If you observe neither of them can be zero at a time, so Now lets take next case where m and n are 1.
5m -4n = 1
5 – 4 = 1
1 = 1, which is true
thus total number of bottles are 5+3 or 4 + 4, i.e. 8
and if divided between 7 friends, 1 bottle will be extra.