Question

Albert buys \[4\] horses and \[9\] cows for Rs. \[13400\]. If he sells the horses at \[10\% \] profit and the cows at \[20\% \] profit, then he earns a total profit of Rs. \[1880\]. Find the cost of a horse.

Answer 1

Hint: At first, we will assume the cost of each horse and each cow. Then using the given condition, we will prepare two equations. By solving these two equations we can find the cost of each horse and each cow.

Complete step-by-step answer:
It is given the cost of \[4\] horses and \[9\] cows for Rs. \[13400\].
Again, he sells the horses at \[10\% \] profit and the cows at \[20\% \] profit, then he earns a total profit of Rs. \[1880\].
Let us take the cost of a horse as Rs. \[x\] and the cost of a cow is Rs. \[y\].
So, the cost of \[4\] horses is Rs. \[4x\] and the cost of 9 cows is Rs. \[9y\].
According to the problem, we have
\[4x + 9y = 13400\]… (1)
Since, the profit for each horse is \[10\% \].
Using the percentage formula we have \[10\% = \dfrac{{10}}{{100}}\], the profit of each horse is found by multiplying the term with x,
So, the profit of each horse is \[\dfrac{{10x}}{{100}}\].
Therefore, the profit of 4 horses is \[\dfrac{{4x}}{{10}}\].
Since, the profit for each cow is \[20\% \].
Using the percentage formula we have \[20\% = \dfrac{{20}}{{100}}\], the profit of each cow is found by multiplying the term with y,
So, the profit of each cow is \[\dfrac{{20y}}{{100}}\].
Similarly, the profit of 9 cows is \[\dfrac{{18y}}{{10}}\].
According to the problem, as he earns a total profit of Rs. \[1880\] we get,
\[\dfrac{{4x}}{{10}} + \dfrac{{18y}}{{10}} = 1880\]
Multiplying the above equation by 10 on both sides we get,
\[4x + 18y = 18800\]…. (2)
Let us subtract equation (1) from (2) we get,
\[4x + 18y - 4x - 9y = 18800 - 13400\]
By simplifying the above equation we get,
\[9y = 5400\]
So, \[y = 600\]
Therefore, the cost of each cow is Rs. \[600\].
Let us substitute the value of \[y = 600\] in (1) to find x we get,
\[4x + 9(600) = 13400\]
Let us solve the above equation to find x we get,
\[x = \dfrac{{13400 - (9 \times 600)}}{4}\]
So, \[x = 2000\]
Hence, the cost of a horse is Rs.\[2000\]

Note: Here we have two variables\[x,y\]. So, we also need two equations also. Otherwise we cannot find the solution. If the number of equations equals the number of variables we can find value for each variable else it cannot be done.