Question

The cost of 3 horses and 5 cows is Rs. 20500 and the cost of 2 horses and 3 cows is Rs. 13400. Find the cost of one horse and one cow. Also, find the total cost of 5 horses and 4 cows.
(a).Cost of one horse = Rs. 5500
Cost of one cow = Rs. 800
Cost of 5 horses and 4 cows = Rs. 30700
(b).Cost of one horse = Rs. 6000
Cost of one cow = Rs. 900
Cost of 5 horses and 4 cows = Rs. 33600
(c).Cost of one horse = Rs. 4000
Cost of one cow = Rs. 500
Cost of 5 horses and 4 cows = Rs. 22000
(d).Cost of one horse = Rs. 3000
Cost of one cow = Rs. 1000
Cost of 5 horses and 4 cows = Rs. 19000

Answer 1

Hint: We can form the two equations by letting $x$ rupees as the cost of one horse and $y$ rupees as the cost of one cow and as we are given two data sets we can multiply it with the number of horse and cows given respectively and write it equal to the total price given.

Complete step-by-step answer:
Consider the first data set which says that the cost of 3 horses and 5 cows is Rs. 20500.
We will let the cost of one horse be $x$ rupees and the cost of one cow is $y$ rupees.
Now, we will form an equation by multiplying 3 horses with $x$ rupees and add it with the 5 cows which is multiplied with $y$ rupees and put it equal to the cost given that is Rs. 20500.
Thus, we get,
$3x + 5y = 20500$ ---(1)
Next, consider the second data set which says that the cost of 2 horses and 3 cows is Rs. 13400 and following the same procedure from another equation.
Thus, we get,
$2x + 3y = 13400$ ---(2)
Now, we will multiply equation (1) by 2 and multiply equation (2) by 3 and subtract the obtained equations from each other.
We get,

$$2\left( {3x + 5y} \right) = 2\left( {20500} \right) \\\ 6x + 10y = 41000 \\\$$

And

$$3\left( {2x + 3y} \right) = 3\left( {13400} \right) \\\ 6x + 9y = 40200 \\\$$

Now, we will subtract the obtained equations from each other,
Thus, we get,

$$\left( {6x + 10y} \right) - \left( {6x + 9y} \right) = \left( {41000} \right) - \left( {40200} \right) \\\ 6x + 10y - 6x - 9y = 800 \\\ y = 800 \\\$$

Thus, with this we get that the cost of one cow is Rs. 800.
Next, we will substitute the values in the equation (1) to find the cost of one horse.
Thus, we have,

$$3x + 5\left( {800} \right) = 20500 \\\ 3x + 4000 = 20500 \\\ 3x = 20500 - 4000 \\\ 3x = 16500 \\\ x = \dfrac{{16500}}{3} \\\ x = 5500 \\\$$

Thus, with this we get that the cost of one horse is Rs. 5500.
Now, as we have got the cost of one cow and one horse, we can form another equation with 5 horses and 4 cows to find the total cost.
We get,
$\Rightarrow 5x + 4y$
Now substitute the value of $x$ and $y$ to determine the total cost.
Thus, we have
$\Rightarrow 5\left( {5500} \right) + 4\left( {800} \right) = 30700$
Hence, the total cost of 5 horses and 4 cows is Rs. 30700.
Thus, we get that the cost of one horse is Rs. 5500, the cost of one cow is Rs. 800 and the total cost of 5 horses and 4 cows is Rs. 30700.
Thus, option a is correct.

Note: We can use the substitution method also to simplify the equations and get the same values of $x$ and $y$ as we have got by using elimination method. As the values of $x$ and $y$ are found we can verify it by keeping it in the equation (1) or (2) and check whether the total cost given is the same or not.