Question

Coffee costing Rs. 250 per Kg. was mixed with chicory costing Rs. 75 per Kg in the ratio of 5:2 for a certain blend. If the mixture was sold at Rs. 230 per Kg then find the gain or loss percentage.

Answer 1

Hint: We first used the method of ratio constant to find the amount of coffee and chicory were mixed. Then we find out the cost price of those two things individually and then find the total value. We also find out the selling price of the mixture. We find the profit value and percentage using formula.

Complete step by step answer:
Two types of coffee and chicory were mixed in the ratio of 5:2.
Let us take x as a ratio constant which means we have taken 5x and 2x Kg of coffee and chicory respectively.
We have been given coffee costing Rs. 250 per Kg. was mixed with chicory costing Rs. 75 per Kg.
We find out the individual cost of the two things.
So, we have 5x Kg. coffee costing Rs. 250 per Kg.
The total price will be $\left( 5x \right)\times \left( 250 \right)=1250x$ Rs.
We also have 2x Kg. chicory costing Rs. 75 per Kg.
The total price will be $\left( 2x \right)\times \left( 75 \right)=150x$ Rs.
So, the total cost price of the mixture will be the addition of the two individual prices.
The total cost price is $1250x+150x=1400x$ Rs.
Now we are selling the mixture at Rs. 230 per Kg. We need to find the total amount of mixture that was sold.
In the mixture we have taken 5x and 2x Kg of coffee and chicory respectively.
So, the total mixture is $5x+2x=7x$ Kg.
The total selling price will be $\left( 7x \right)\times \left( 230 \right)=1610x$ Rs.
We find the total amount of profit which is $1610x-1400x=210x$ Rs.
We find the percentage of profit on the cost price whose formula is $\dfrac{profit}{\cos t}\times 100$.
So, the profit percentage is $\dfrac{210}{1400}\times 100=\dfrac{210}{14}=15$.

The gain percentage is 15.

Note: We need to remember that the ratio constant always has to be a natural number. Also, if we are mentioning the word percentage then we don’t need to use the ‘%’ sign anymore. The cost price would be dependent on both the cost price of coffee and chicory as we are selling the mixture of both the items.