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

+2 votes

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.)

posted Mar 23, 2014 by anonymous

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1 Answer

+1 vote

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.

answer Mar 23, 2014 by anonymous

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+1 vote

A research team went to a village somewhere between the jungles of Africa. Luckily for them, they reached on the day when quite an interesting custom was to be performed. The custom was performed once in a year as they confirmed and was performed in order to collect the taxes from every male of the region.

The taxes were to be paid in the form of grains. Everyone must pay pounds of grain equaling his respective age. Which means a 20 year old will have to pay 20 pounds of grains and a 30 years old will pay 30 pounds of grain and so on.

The chief who collects the tax have 7 weights and a large 2 pan scale to weigh. But there is another custom that the chief can weigh only with three of the seven weights.
Can you find out the weights of the seven weights? Also what is the maximum age of the man that can be weighed for the payment of taxes ?

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