Question

There was a father who had five sons. He sent his all five sons to sell lemons. The first son has 20 lemons, second son has 40 lemons , third son has 60 lemons, fourth son has 80 lemons and the fifth son has 100 lemons. They all have to sell the lemons at the same price and in the end they should have the same amount in their hand but they can't share money to each other. What is the price of lemon?

Answer 1

If the price of lemon should be the same during all sale and can't be changed, then we have the next equation:

20x = 40x = 60x = 80x = 100x, where x is the price of lemon.

In this case the only solution is: x = 0.

If it is possible for all brothers to change the price at least once to the same level, then let the first price is $1 per bundle of 5 lemons (or $0.2 per lemon) and $1 per lemon for the remaining.

First son: $1*0 bundles + $1*20 lemons = $20,

Second son: $1*5 bundles + $1*15 lemons = $20,

Third son: $1*10 + $1*10 = $20,

Fourth son: $1*15 + $1*5 = $20,

Fifth son: $1*20 + $1*0 = $20.