Question

A wizard having powers of mystic incandations and magical medicines. Seeing a cock fight going on, spoke privately to both the owners of cocks. To one he said; if your bird wins, then you give me your stake-money, but if you do not win, I shall give you two third of that. Going to the other, he promised in the same way to give three fourths. From both of them his gain would be only $12$ gold coins. Find the stake of money each of the cock-owners have.

Answer 1

Let stake money $1st$ cock owner have $=x$ and $2nd$ cock owner have $=y$

From the given information, we have,

$x-\frac{3y}{4}=12andy-\frac{2x}{3}=12$

$or,x-\frac{3y}{4}=12=>4x-3y=48=>3y=4x-\mathrm{48....}\left(i\right)Also,y-\frac{2x}{3}=12=>3y-2x=\mathrm{36....}\left(ii\right)$

Substituting equation (i) in equation (ii), we get,

$3y-2x=36=>4x-48-2x=36=>2x=84=>x=42$

Substituting $x=42$ in equation (i), we get,

$3y=4x-48=>3y=4\times 42-48=>3y=120=>y=40$

Thus, stake money $1st$ cock owner has $=x=42$ gold coins and the stake money $2nd$ cock owner has $=y=40$ gold coins.