Question

Coffee costing Rs. 450 per kg was mixed with Chicory costing Rs. 225 per kg in the ratio $5:2$ for a certain blend. If the mixture was sold Rs. 405 per kg, find the gain or loss percent.

Answer 1

Hint:
In this we have to find the gain or loss percent when coffee is mixed with chicory in the ratio $5:2$. For this first calculate the total cost price of the mixture by taking 5 kg of the coffee mixed with the 2 kg chicory i.e. adding the price of 5 kg coffee and the price of 2 kg of chicory. After that find the selling of that total amount of mixture obtained by mixing them. i.e. price of 7 kg of mixture. Then compare cost price and selling price, we will get to know about gain or loss. Then we can calculate the loss percent.

Complete step by step solution:
We have given that coffee and chicory are mixed in the ratio $5:2$. The cost price of coffee and chicory is given us i.e.
$ \Rightarrow C.{P_1} = Rs.450$ per kg
$ \Rightarrow C.{P_2} = Rs.225$ per kg
Where $C.{P_1}$ is the cost price of coffee and $C.{P_2}$ is the cost price of chicory.
We have given the ratio in which they mixed i.e. if we take 5 kg coffee then we have to take 2 kg of chicory as they are mixed in a ratio $5:2$. So, we can calculate the cost price of 5 kg of coffee as follows:
$ \Rightarrow $cost of 5 kg coffee $ = 5 \times C.{P_1}$
$ \Rightarrow $cost of 5 kg coffee $ = 5 \times 450$
By multiplying these numbers, we get,
$ \Rightarrow $cost of 5 kg coffee $ = Rs.2250$ …………………(1)
Now, calculate the cost price of 2kg of chicory as follows
$ \Rightarrow $cost of 2 kg chicory $ = 2 \times C.{P_2}$
$ \Rightarrow $cost of 2 kg chicory $ = 2 \times 225$
By multiplying these numbers, we get,
$ \Rightarrow $cost of 2 kg chicory $ = Rs.450$ …………………(2)
Total cost price of the mixture is equal to the addition of cost price of 5kg coffee and cost price of 2kg chicory i.e.
$ \Rightarrow C.P = $cost price of 5kg coffee $ + $ cost price of 2kg of chicory
Putting the values of 1 and 2 in the above we het,
$ \Rightarrow C.P = 2250 + 450$
By adding these numbers, we get,
$ \Rightarrow C.P = Rs.2700$ ……………….(3)

Now, after adding 5kg of coffee and 2kg of chicory we have 7kg of mixture. So, selling price of 7kg mixture can be calculated by multiplying 7 and selling price of 1kg mixture i.e.
$ \Rightarrow S.P = 7 \times $selling price of 1kg mixture
Put the value of selling price of 1kg mixture we get
$ \Rightarrow S.P = 7 \times 405$
By multiplying these numbers, we get,
$ \Rightarrow S.P = Rs.2835$ ………………(4)
From 3 and 4 it is clear that S.P is more than C.P so there is some gain and can be calculated as
$ \Rightarrow G = S.P - C.P$
Where G is gain and by putting the values of 3 and 4 in this we get,
$\begin{gathered}
   \Rightarrow G = 2835 - 2700 \\
   \Rightarrow G = Rs.135 \\
\end{gathered} $ ………………(5)
Gain percent is given by:
$ \Rightarrow G\% = \dfrac{G}{{C.P}} \times 100$
By putting values of 3 and 5 in this we get,
$ \Rightarrow G\% = \dfrac{{135}}{{2700}} \times 100$
By cancelling two zeroes of 2700 with 100 and cutting 135 with 27 we get,
$ \Rightarrow G\% = 5\% $

Therefore, there is a gain of $5\% $.

Note:
Some students make mistakes in this question by adding the cost price of 1kg of coffee with 1kg of chicory to find the total cost price and then taking the selling price of one kg mixture. In this way our answer gets wrong as they are not mixed in equal ratio but in $5:2$.
 For the Selling price we have to calculate the selling of the amount of mixture obtained i.e. $5 + 2 = 7kg$.
Also, some students make mistakes in finding whether there is gain or loss. If the selling price is greater than cost price then there is gain but if cost price is greater than selling price then there is loss.