Question

A trader mixes three varieties of groundnut costing Rs.50, Rs.20, and Rs.30 per kg in the ratio 2:4:3 in terms of weight and sells the mixture at Rs.33 per kg. What percentage of profit does he make?
A. 8%
B. 9%
C. 10%
D. None of the above.

Answer 1

Hint: First of all, find the cost of groundnuts which the trader mixes in a given ratio i.e. 2:4:3. Consider the ratio as 2kg, 4kg and 3kg. Then, we can find the cost by multiplying the per kg cost and the ratio, i.e. for the first variety we get \[Rs.50/kg\times 2kg=Rs.100\]. Then, find the total cost of a newly made mixture of groundnut by adding the total kg \[\Rightarrow 2+4+3=9kg\] and multiplying with Rs.33. Subtract the above two prices and divide it with the initially found price to get profit. Profit percentage can be calculated by multiplying the result with 100.

Complete step by step solution:
A trader mixes groundnuts in the ratio of weight 2:4:3 i.e. the first variety of groundnut are 2kg, second variety is 4kg and third variety is 3kg.
We know the prices of the given 3 varieties are Rs.50, Rs.20 and Rs.30 per kg respectively.
Now, find the total cost of all the varieties used to make new mixtures, i.e.
\[\begin{align}
  & {{1}^{st}}\text{variety}=Rs.50/kg \\
 & \Rightarrow 2kg=50\times 2=Rs.100 \\
 & {{2}^{nd}}\text{variety}=Rs.20/kg \\
 & \Rightarrow 4kg=20\times 4=Rs.80 \\
 & {{3}^{rd}}\text{variety}=Rs.30/kg \\
 & \Rightarrow 3kg=30\times 3=Rs.90 \\
\end{align}\]
Total cost of all would be
\[\begin{align}
  & \Rightarrow 100+80+90 \\
 & \Rightarrow Rs.270 \\
\end{align}\]
The newly formed mixture is Rs.33 per kg. Since, the ratio of 3 varieties is 2:4:3, so, the total weight of new single variety of groundnut would be
\[\Rightarrow 2+4+3=9kg\]
So, the cost of 9kg new variety groundnut is,
\[33\times 9=Rs.297\]
Now, calculate difference between the initial and final cost of groundnuts, this would give us profit.
\[\text{Profit}=297-270=Rs.27\]
To find the fraction of profit, divide the profit by initial price of groundnuts i.e. Rs.270
\[\Rightarrow \dfrac{27}{270}=0.1\]
To get profit %, we will multiply the above fraction with 100.
\[0.1\times 100=10\%\]
So, our profit percentage comes out to be 10%. The trader would make a total of 10% of profit by selling the mixture at Rs.33 per kg.
Therefore, option C is correct.

Note: We have read that profit is the difference of cost price and selling price of a product, but in this question, there is no mention of any cost price, so, don't get confused and tick the last option D: None of these. After finding the fraction do not forget to multiply the result with 100 because here percentage is required. If there was an option 0.1, you might have chosen that and got it wrong.