Number Puzzle #81
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.
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Answer: There will be one extra bottle after dividing between 7 friends.
Let’s say total number of beer bottles in box are x. then we can say
x = 4*m + 4, where m is integer greater than or equal to 0.
x = 5*n + 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.