Question

A trader mixes three varieties of groundnuts 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 these

Answer 1

Hint: The cost per kg of the first variety, second variety, and the third variety of groundnuts is Rs 50, Rs. 20, and Rs. 30. Assume the ratio in x. The weight of the first variety, second variety, and a third variety of groundnuts is \[2x\] kg, \[4x\] kg, and \[3x\] kg. Now, calculate the total cost price of the mixture of groundnuts. The selling price per kg of the mixture is Rs. 33 and the total weight of the mixture is \[9x\] kg. Calculate the total selling price of the mixture. At last, use the formulas, Profit = Selling price – Cost price and Profit percentage = \[\dfrac{\text{profit}}{\text{cost}\,\text{price}}\times 100\] .

Complete step by step answer:
According to the question, we are given that a trader mixes three varieties of groundnuts.
The cost per kg of the first variety of groundnuts = Rs. 50 ………………………………………. (1)
The cost per kg of the second variety of groundnuts = Rs. 20 ………………………………………. (2)
The cost per kg of the third variety of groundnuts = Rs. 30 ……………………………………….(3)
The ratio in which all three varieties are mixed in terms of weight = 2: 4: 3 ……………………………………….(4)
Let the ratio be in x.
The weight of the first variety of groundnuts = \[2x\] kg …………………………………………(5)
The weight of the second variety of groundnuts = \[4x\] kg …………………………………………(6)
The weight of the third variety of groundnuts = \[3x\] kg …………………………………………(7)
Now, from equation (1) and equation (5), we get
The cost of first variety of groundnuts = Rs. \[50\times 2x\] = Rs. \[100x\] ……………………………………….(8)
Similarly, from equation (2) and equation (6), we get
The cost of second variety of groundnuts = Rs. \[20\times 4x\] = Rs. \[80x\] ……………………………………….(9)
Similarly, from equation (3) and equation (7), we get
The cost of third variety of groundnuts = Rs. \[30\times 3x\] = Rs. \[90x\] ……………………………………….(10)
Now, from equation (8), equation (9), and equation (10), we have
The total cost price of mixture of groundnuts = Rs. \[100x+80x+90x\] = Rs. \[270x\] …………………………………….(11)
Now, from equation (5), equation (6), and equation (7), we have
The total weight of the mixture of the groundnuts = \[2x+4x+3x\] kg = \[9x\] kg …………………………………….(12)
It is also given in the question that the cost of selling per kg of the mixture is Rs. 33 …………………………………………(13)
From equation (12) and equation (13), we get
The total cost of selling the mixture = Rs. \[33\times 9x\] = Rs. \[297x\] ……………………………………(14)
We know the formula, Profit = Selling price – Cost price ………………………………..(15)
Now, from equation (11), equation (14), and equation (15), we get
Profit = Rs. \[297x-270x\] = Rs. \[27x\] ………………………………………..(16)
We also know the formula, Profit percentage = \[\dfrac{\text{profit}}{\text{cost}\,\text{price}}\times 100\] ……………………………….(17)
Now, from equation (11), equation (16), and equation (17), we get
 Profit percentage = \[\dfrac{27x}{270x}\times 100=\dfrac{100}{10}\] = 10.
Therefore, the profit percentage is 10%.
Hence, the correct option is C.

Note:
 Whenever this type of question appears where we are given the cost price of some items which are mixed in a defined ratio by weight and we are asked to calculate the profit or loss while selling those mixtures at a certain price. Always approach this type of question by assuming the ratio in x. Now, the weight of all items can be calculated, and multiplying it with the cost price, the total cost price of the mixture can be calculated in terms of x. Now, the selling price can be calculated. At last, use the formula, Profit = Selling price – Cost price and Profit percentage = \[\dfrac{\text{profit}}{\text{cost}\,\text{price}}\times 100\] .