A wizard having the powers of mystic in candations and magical medicines seeing a cock fight going on, spoke privately - Maths - Pair of Linear Equations in Two Variables

Question

A wizard having the powers of mystic in candations and magical
medicines seeing a cock fight going on, spoke privately to both the
owners of the cocks To one he said; if ur bird wins then you give
me your stake money but if you don't win i shall give you two third
of that Going to the other he promised in the same way to give
3/4th from both of them his gain could only be 12 gold coins find
the stake of money of each of the cock-owners have

Ankush Jain · Accepted Answer

Let the stake of money first owner has = x

and the stake of money second owner has = y.

Case 1: First owner wins and seconds owner loss.

Money got by wizard $= x - \frac{3}{4} y$

Given, he gain only 12 coins.

$\Rightarrow x - \frac{3}{4} y = 12 \Rightarrow 4 x - 3 y = 48 ... (1)$

Case 2 : First owner loss and second owner wins

Money got by wizard $= - \frac{2}{3} x + y$

$Again, y - \frac{2}{3} x = 12 \Rightarrow 3 y - 2 x = 36 or 6 y - 4 x = 72 ... (2)$

On adding (1) and (2), we get

$4 x - 3 y + 6 y - 4 x = 48 + 72 \Rightarrow 3 y = 120 \Rightarrow y = 40 (1) \Rightarrow 4 x - 3 (40) = 48 \Rightarrow 4 x = 48 + 120 = 168 \Rightarrow x = 42$

Hence, the first owner has 42 coins and second owner has 40 coins.