Question

A wizard having powers of mystic incantations 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

Hint: In this particular question use the concept that assume any different variables be the stack money of two cock-owners, then try to make the linear equations according to the given information in the question (for example: The gain of the wizard = first cock owner give his stack money to the wizard - ${\left( {\dfrac{3}{4}} \right)^{th}}$ stack money of the second cock owner given to the second cock owner) and solve them using any method so use these concepts to reach the solution of the question.

Complete step by step answer:
Let us assume that the first cock owner has x amount of stack money.
And the second cock owner has y amount of stack money.
Now the wizard said to one that 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.
So, case – 1: If first cock owner wins
So according to wizard,
The gain of the wizard = first cock owner give his stack money to wizard - ${\left( {\dfrac{3}{4}} \right)^{th}}$stack money of second cock owner give to second cock owner.
Now according to the question the total gain of the wizard is 12 gold coins.
So, $12 = x - \dfrac{3}{4}y$
$ \Rightarrow 12 = \dfrac{{4x - 3y}}{4}$
$ \Rightarrow 4x - 3y = 48$.................... (1)
Case – 2: If second cock owner wins
So according to wizard,
The gain of the wizard = second cock owner give his stack money to wizard - ${\left( {\dfrac{2}{3}} \right)^{th}}$stack money of first cock owner give to first cock owner.
Now according to the question the total gain of the wizard is 12 gold coins.
So, $12 = y - \dfrac{2}{3}x$
$ \Rightarrow 12 = \dfrac{{3y - 2x}}{3}$
$ \Rightarrow 3y - 2x = 36$.................... (2)
Now from equation (1) we have,
$ \Rightarrow x = \dfrac{{48 + 3y}}{4}$............. (3)
Now substitute this value in equation (2) we have,
$ \Rightarrow 3y - 2\left( {\dfrac{{48 + 3y}}{4}} \right) = 36$
$ \Rightarrow 3y - \left( {\dfrac{{48 + 3y}}{2}} \right) = 36$
$ \Rightarrow 6y - 48 - 3y = 72$
$ \Rightarrow 3y = 72 + 48 = 120$
$ \Rightarrow y = \dfrac{{120}}{3} = 40$ Gold coins.
Now substitute this value in equation (3) we have,
$ \Rightarrow x = \dfrac{{48 + 3\left( {40} \right)}}{4} = 12 + 30 = 42$ Gold coins.
So the first cock owner has 42 gold coins and the second cock owner has 40 gold coins.

Note: Whenever we face such types of questions in which linear equations are involved, so there are lots of methods to solve these linear equations such as elimination, substitution, cross multiplication, graphical method etc. here we use substitution method to solve in which from any one of the equation calculate the value of any variable in terms of other variable and substitute into other linear equation and solve them we will get the required answer.