Question

A farmer sold 2 bullocks for Rs.24000 each. On one bullock he gained 25% and on the other lost 20%. Find his total profit or loss percent.

Answer 1

Hint: Find the cost price for which each of the bullocks is bought. The final profit or loss can then be calculated by subtracting the cost price from the selling price of the bullocks. The profit or loss percentage is calculated by dividing total profit or loss to the total cost price multiplied by 100.

Complete step by step answer:

Let the cost price of the first bullock be $x$. The selling price of the bullock is 24000 and is sold at a profit of 25%.
Thus 24000 must be equal to the sum of $x$ and 25% of $x$.
Thus \[x + \dfrac{{25}}{{100}}x = 24000\]
The above equation can be solved for $x$.
$
  x = \dfrac{{24000}}{{1.25}} \\
   \Rightarrow x = 19200 \\
$

Similarly, let the cost price of the second bullock be $y$. The selling price of the bullock is 24000 and is sold at a loss of 20%.
Thus 24000 must be equal to the difference of $y$ and 20% of $y$.
Thus \[y - \dfrac{{20}}{{100}}y = 24000\]
The above equation can be solved for $y$.
$
  y = \dfrac{{24000}}{{0.8}} \\
   \Rightarrow y = 30,000 \\
$
The total cost price of the two bullocks will be $x + y$
Substituting 19200 for $x$ and 30000 for $y$, we get the total cost price as
49200.
The total selling price of the two bullocks will be twice of 24000, that is 48000.
The difference between the total selling price and the total cost price is \[48000 - 49200\] is \[ - 1200\].
Since the difference is negative and thus represents a total loss of 1200.
The percent of loss will be given as total loss divided by the total cost price multiplied by 100.
${\text{loss% = }}\dfrac{{{\text{loss}}}}{{{\text{C}}{\text{.P}}}} \times 100$
The loss percent is therefore
$
  1200/49200*100 \\
  \dfrac{{1200}}{{49200}} \times 100 = 2.43\% \\
$
Thus, the farmer had a loss of 2.43% on selling both at the bullocks at 24,000.

Note: Whenever the selling price is more than the cost price, there is a profit and if the selling price is less than the cost price of any articles, then there is a loss. Loss or profit percent are calculated by dividing the loss or profit by cost price and then multiplying it by 100.