Question

Coffee costing Rs. $250$ per kg was mixed with chicory costing Rs. $75$ per kg in the ratio $5:2$ for a certain blend. If the mixture was sold at Rs. $230$ per kg, find the gain or loss percent.

Answer 1

Hint: First, we will define what is a cost price and selling price then we will take $5$ kg and $2$ kg of the coffee and the chicory respectively. Then we will combine it and find its cost price for the cost price of $7$ kg and then ultimately for $1$ kg and we will check that the selling price is bigger or the cost price and apply the formula for gain or loss percent whatever required.

Complete step by step answer:
First let’s see what is Cost Price and what is Selling Price, The amount paid to purchase an article or the price at which an article is made is known as its cost price. Cost Price is normally written as C.P. . The amount for which the product is sold is called Selling Price. It is usually denoted as SP.
Now, one makes a Profit, if the selling price (S.P.) of an article is greater than the cost price (C.P.). The difference between the selling price and cost price is called profit. Thus, if S.P. > C.P., then
$\begin{align}
  & \text{Profit}=S.P.-C.P. \\
 & \text{Profit }\!\!\%\!\!\text{ }=\left( \dfrac{\text{Profit}}{C.P.} \right)\times 100=\left( \dfrac{S.P.-C.P.}{C.P.} \right)\times 100 \\
\end{align}$
Similarly, a person is said to have loss, if the selling price (S.P.) of an article is less than the cost price (C.P). The difference between the cost price (C.P.) and the selling price (S.P.) is called loss.
Thus, if S.P. < C.P., then:
$\begin{align}
  & \text{Loss}=C.P.-S.P. \\
 & \text{Loss }\!\!\%\!\!\text{ }=\left( \dfrac{\text{Loss}}{C.P.} \right)\times 100=\left( \dfrac{C.P.-S.P.}{C.P.} \right)\times 100 \\
\end{align}$

Now, it is given that the cost price of the coffee is Rs. $250$ per kg and that of chicory is Rs. $75$ per kg.
Now it is given that the ratio of coffee and chicory in the bland is: $5:2$ , therefore we will take $5$ kg of the first variety that is coffee and we will take $2$ kg of the second variety that is chicory. Therefore, the total weight will be $\left( 5+2 \right)=7$ kg
Now, the total cost price of $7$ kg of the mixture = $\left( 5\times 250 \right)+\left( 2\times 75 \right)=\left( 1250+150 \right)=1400$ Rs.
Now that we have found out the cost price of $7$ kg of the mixture,
Now we will find the cost price of $1$ kg of the mixture $\dfrac{1400}{7}=200$ Rs.
It is also given that the selling price of the mixture is Rs. $230$ per kg .
As we see that $S.P.>C.P.$ , therefore it will be a profit and we will apply the formula for profit that is : $\text{Gain}=\text{S}\text{.P}\text{.}-\text{C}\text{.P}\text{.}=230-200=30$
Now, the gain percentage will be $\text{Gain }\!\!\%\!\!\text{ }=\dfrac{\text{Gain}}{C.P.}\times 100=\dfrac{30}{200}\times 100=15\%$ .
Therefore, the $\text{Gain }\!\!\%\!\!\text{ }=15\%$.

Note:
  Student might make the mistake at the end by not putting the percent sign at the end to show the gain or loss percent. Note that when the profit is $m\%$ and loss is $n\%$ then the net \% profit or loss will be: $\dfrac{\left( m-n-mn \right)}{100}$ . Also if a product is sold at $m\%$ and then again sold at $n\%$ profit then the actual cost price will be : $CP=\left[ \dfrac{100\times 100\times P}{\left( 100+m \right)\left( 100+n \right)} \right]$ and in case of loss: $CP=\left[ \dfrac{100\times 100\times P}{\left( 100-m \right)\left( 100-n \right)} \right]$.