Question

A wizared having powers of mystic in cadations and magical medicines seeing a cock fight going on spoke privately to both the owners of cocks To one he said if you bird wins than 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

• A. 27 gold coins & 30 gold coins respectively
• B. 12 gold coins & 20 gold coins respectively
• C. 33 gold coins & 30 gold coins respectively
• D. 42 gold coins & 40 gold coins respectively

Answer 1

The correct option is D 42 gold coins & 40 gold coins respectively

Let the stake of money first owner has be x and the stake of money second owner has be y
Case 1 first owner wins and second owner loss
Money got by wizard$=x-\frac{3}{4}y$
given,he gains only 12 coins
$=x-\frac{3}{4}y=12$
$\Rightarrow 4x-3y=48$..............eq(1)
Case2 first owner looses and second owner wins
Money got by wizard$=-\frac{2}{3}x+y$
Again$y-\frac{2}{3}x=12$
$3y-2x=36$..........................................eq(2) multipied by 2
$6y-4x=72$
on adding eq 1 and 2 we get
$4x-3y=48$
$-4x+6y=72$
_____________________________
$3y=120$
y=40
putting y=40 in eq 1
$\Rightarrow 4x-3\left(40\right)=48$
$\Rightarrow 4x=48+120$
x=42
Hence the first owner has 42 coins and second owner has 40 coins.