A wizard having powers of mystic in candations 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.

Given:

A wizard having powers of mystic in candations 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.

To do:

We have to find the stake of money each of the cock-owners have.

Let the stake money of the first owner and the stake money of the second owner be $x$ and $y$ respectively.

According to the given question,

If the first owner wins,

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

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

$4x-3y=4(12)$   (On cross multiplication)

$4x-3y=48$....(i)

If the second owner wins,

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

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

$3y-2x=3(12)$   (On cross multiplication)

$3y-2x=36$....(ii)

Adding equations (i) and (ii), we get,

$4x-3y+3y-2x=48+36$

$2x=84$

$x=\frac{84}{2}$

$x=42$

Substituting the value of $x=42$ in (ii), we get,

$3y-2(42)=36$

$3y=36+84$

$3y=120$

$y=\frac{120}{3}$

$y=40$

Therefore, the stake of money of the first owner is 42 gold coins and the stake of money of the second owner is 40 gold coins.

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Updated on: 10-Oct-2022

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