Question

A wizard having powers of mystic incantations and magical medicines. Seeking a cock fight going on, spoke privately on 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 the money each of the cock-owners have.
(a) 27 gold coins and 30 gold coins respectively
(b) 12 gold coins and 20 gold coins respectively
(c) 33 gold coins and 30 gold coins respectively
(a) 42 gold coins and 40 gold coins respectively

Answer 1

Hint: Firstly, we will suppose the stake money for the first cock owner has been x and the stake money for the second cock owner has been y. Then, we have to consider the two conditions given in the question as first cock owner wings will get the three-fourth share and second cock owner will get the two-third of the share. Then, by using the two equations to get the value of the gold coins for first cock owner and second cock owner.

Complete step-by-step answer:
In this question, we are supposed to find the number of the gold coins both the cock owners have.
In this type of the question, we should have been having a good quality of assuming things to solve in particular conditions as given in the question.
So, let the stake money for the first cock owner be x.
Similarly, let the stake money for the second cock owner have been y.
Here, we also know that the total profit share is 12 gold coins only in both cases.
Then, from the given condition in the question as first cock owner wings will get the three-fourth share as:
$x-\dfrac{3y}{4}=12.....\left( i \right)$
Then, again using the second condition given in question which states that the second cock owner will get the two-third of the share as:
$y-\dfrac{2x}{3}=12.....\left( ii \right)$
Now, by multiplying the whole equation (i) with 4, we get
$4x-3y=48.....\left( iii \right)$
Now, by multiplying the whole equation (ii) with 3, we get
$3y-2x=36....\left( iv \right)$
Now, by using the equation (iii) and (iv), we can calculate the value of x and y.
So, by using substitution from equation (iii) and finding the value of 3y from equation (iii) as:
$3y=4x-48.....\left( v \right)$
Then, substitute the above calculated value of 3y in equation (iv), we get:
$4x-48-2x=36$
Now, solve for the value of x as:
$\begin{align}
  & 2x=84 \\
 & \Rightarrow x=42 \\
\end{align}$
Then, by substituting the value of x in equation (v) to get value of y as:
$\begin{align}
  & 3y=4\times 42-48 \\
 & \Rightarrow 3y=168-48 \\
 & \Rightarrow 3y=120 \\
 & \Rightarrow y=40 \\
\end{align}$
So, from the above calculations done the following results are deducted:
The stake money of first cock owner is 42 gold coins
The stake money of second cock owner is 40 gold coins
Hence, option (d) is correct.

Note: Here, we can also use the other methods of solving the two equations as elimination method and cross multiplication method for the equations (iii) and (iv) from the above solution. Here, elimination method is simple to use as both the equations have the term 3y with opposite sign and it easily gets cancelled as:
$\begin{align}
  & \text{ }4x-3y=48 \\
 & -2x+3y=36 \\
\end{align}$
If we add these equations variable wise we get the result as:
$\begin{align}
  & 2x=84 \\
 & \Rightarrow x=42 \\
\end{align}$
So, the above method can also be used to calculate the value of x and y.