Question

A trader bought two horses for Rs.39000. He sold one at a loss of 20% and another at a profit of 15%. If the selling price of each horse is the same, then what are their cost price respectively?

Answer 1

Hint: - Here we go through by applying the properties of profit and loss. We assume the cost price of one horse and apply the question condition on the cost price that we assume to find out its value.

Complete step-by-step answer:
Here in the question it is given that a trader bought two horses for Rs.39000.
Now let the cost price of one horse be C
And in the question it is given that the cost price of two horses is Rs.39000.
Then the cost price of another horse = 39000−C.
The selling price of a horse when he sells it at a loss of 20%.
Here it is loss % so we subtract the loss% from CP (cost price) to find out the SP (selling price)
 \[
   \Rightarrow c - 20\% ofc \\
   \Rightarrow c - \dfrac{{20}}{{100}} \times c \\
   \Rightarrow \dfrac{4}{5}c \\
 \]
Now he sales the other horse at a profit of 15%.
Here it is profit % so we add the profit% to CP (cost price) to find out the SP (selling price).
\[
   \Rightarrow (3900 - c) + 15\% of(3900 - c) \\
   \Rightarrow (3900 - c) + \dfrac{{15}}{{100}} \times (3900 - c) \\
   \Rightarrow 3900 - c + 585 - \dfrac{3}{{20}}c \\
   \Rightarrow 4485 - \dfrac{{23}}{{20}}c \\
 \]
Here in the question it is given that the selling price are same for the two horses
$
  \therefore \dfrac{4}{5}c = 4485 - \dfrac{{23}}{{20}}c \\
   \Rightarrow \dfrac{4}{5}c + \dfrac{{23}}{{20}}c = 4485 \\
   \Rightarrow \dfrac{{39}}{{20}}c = 4485 \\
   \Rightarrow c = 4485 \times \dfrac{{20}}{{39}} \\
  \therefore c = 23000 \\
 $
So, Cost price of one horse is Rs.23000 and cost price of other horse is Rs.16000

Note: - Whenever we face such a type of question the key concept for solving the question is to first assume what we have to find then apply the conditions of the question to solve further and also keep in mind the properties of percentage that we have to add in profit% and subtract in loss%.