Question

A man bought two goats for Rs. 3000. He sold one at loss of 25% and the other at profit of 50%. If each goat was sold for the same price, the cost price of the goat which was sold at a loss was:
(a) Rs. 1648
(b) Rs. 1256
(c) Rs. 2000
(d) Rs. 2048

Answer 1

Hint:Here, we are given total cost price of two goats i.e. Rs. 3000 along with that, he made loss by selling 1 goat and made profit by selling another goat at the same selling price. So, we need to make equation on both loss and profit percentage by using the formula
$SP=\dfrac{\left( 100-loss\% \right)}{100}\times CP$ and $SP=\dfrac{\left( 100+profit\% \right)}{100}\times CP$

Complete step-by-step answer:
We have a total cost price of Rs. 3000. Let us assume the cost price of goat 1 as ${{x}_{1}}$ and cost price of goat 2 as ${{x}_{2}}$ . So, we can say that
${{x}_{1}}+{{x}_{2}}=3000$ …………………………(i)
Now, it is said that the selling price of both goats are the same. So, $S{{P}_{1}}=S{{P}_{2}}$ where $S{{P}_{1}}$ and $S{{P}_{2}}$ are selling price of goat 1 and 2 respectively.
Using the formula for selling price, we will make an equation for both goats.
$S{{P}_{1}}$ at loss of 25% will be $S{{P}_{1}}=\dfrac{\left( 100-loss\% \right)}{100}\times CP$
$S{{P}_{1}}=\dfrac{\left( 100-25 \right)}{100}\times {{x}_{1}}$ Where CP $={{x}_{1}}$ , $Loss\% = 25$
On solving, we get
$S{{P}_{1}}=\dfrac{\left( 75 \right)}{100}\times {{x}_{1}}$
$S{{P}_{1}}=0.75{{x}_{1}}=\dfrac{3}{4}{{x}_{1}}$ ……………………………(ii)
Similarly,
$S{{P}_{2}}$ at profit of 50% will be $S{{P}_{2}}=\dfrac{\left( 100+profit\% \right)}{100}\times CP$
$S{{P}_{2}}=\dfrac{\left( 100+50 \right)}{100}\times {{x}_{2}}$ Where CP $={{x}_{2}}$ , $profit\% =50$
$S{{P}_{2}}=\dfrac{\left( 150 \right)}{100}\times {{x}_{2}}$
$S{{P}_{2}}=1.5{{x}_{2}}=\dfrac{3}{2}{{x}_{2}}$ ……………………………..(iii)
Now given that the selling price is the same. Therefore, comparing equation (ii) and (iii) we get
$\Rightarrow \dfrac{3}{4}{{x}_{1}}=\dfrac{3}{2}{{x}_{2}}$
On equating, we get
$\Rightarrow {{x}_{1}}=2{{x}_{2}}$ …………………………(iv)
Thus, we get the CP of goat 1 is twice the CP of goat 2.
Now doing substitution of equation (iv) in equation (i), we get
$2{{x}_{2}}+{{x}_{2}}=3000$
$3{{x}_{2}}=3000$
${{x}_{2}}=1000$
Putting the above value in equation (iv) to get the value of ${{x}_{1}}$ .
${{x}_{1}}=2\times 1000$
${{x}_{1}}=2000$
Thus, we are asked to find the cost price of goat 1 which is ${{x}_{1}}$ and is equal to Rs. 2000.
Hence, option (c) is correct.

Note: Students should know the formula of profit and loss percentage and be careful while doing calculations. There are also chances of making mistakes by taking 25% as profit and 50% as loss. Also, the formula to find profit is equal to selling price minus cost price i.e $SP-CP$ and to find loss, the formula is cost price minus selling price i.e $CP-SP$..