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: We will be using the concept of the word problem to make equations from the given condition, then we will be using the concept of the system of linear equations in the true variable to solve the equation further and simplify the answer.

Complete step-by-step solution -
Now, we let the money first cock owner have = x.
The money the second cock owner has = y.
Now, we have been given that if cock owner win the wizard then the owner will give him money equal to his stake, otherwise the wizard will give money to ${{\dfrac{2}{3}}^{rd}}$of the owner’s stake and for other the wizard will give ${{\dfrac{3}{4}}^{th}}$of the owner stake.
Now, we first suppose the first cock owner win, so the equation is,
$x-\dfrac{3}{4}y=12...........\left( 1 \right)$
Now, if second cock owner win, so the equation is,
$y-\dfrac{2}{3}x=12.........\left( 2 \right)$
Now, we have to solve (1) and (2). So, we substitute the value of x from (1) in (2).
$\begin{align}
  & y-\dfrac{2}{3}\left( \dfrac{3}{4}y+12 \right)=12 \\
 & y-\dfrac{1}{2}y-8=12 \\
 & \dfrac{y}{2}=20 \\
 & y=40 \\
\end{align}$
Now, we substitute y = 40 in (1). So, we have,
$\begin{align}
  & x=12+\dfrac{3}{4}\left( 40 \right) \\
 & =12+30 \\
 & x=42 \\
\end{align}$
The stake of money of each of the cock – owners is 42, 40 respectively.

Note: To solve these types of questions it is important to note that the money wizard will have 12 coins in both cases if the first or second cock owner wins. Therefore, we have formed two equations and solved them for the answer.