Question

Mrs. Biswah bought two types of walnuts from a wholesale shop, where the cost of the second type is 33.33% of that of the first type. She then mixed both the types of walnuts and sold them for Rs. 520/kg and made a profit of 30%. If the quantity of the first type of walnut is 20% of that of the second type, then find the average of the cost prices of both types of walnut per kg.

• A. Rs. 550
• B. Rs. 580
• C. Rs. 720
• D. Rs. 600
• E. Rs. 660

Answer 1

The Correct Option is D

Let the cost of the first type of walnut be Rs. \(3x\) per kg.
So, the cost of the second type of walnut is Rs. \(x\) per kg.
Cost of the mixture = \(\frac{110}{130} \times 520\) = Rs. \(400\)/Kg
Quantity of the first type of walnut = \(\frac{1}{5}\) of quantity of the second type
Let the quantity of the first type = \(k\) kg.
So, the quantity of the second type = \(5k\) kg.
So, total cost = \(3x \times k + x \times 5k = 8kx\)
Also, total cost = \(400(k + 5k) = 2400k\)
So, \(8kx = 2400k\)
or, \(x = 300\)
So, the prices of the first and the second type = \(900\) and \(300\) respectively.
So, the average of the prices of both types = \(\frac{900+300}{2}\) = Rs. \(600\)
Alternately, we can use alligation method also:
\(1^{st }\) type \(2^{nd}\) type
\(3x \;x\)
\(400\)
\(1 : 5\)

\(\Rightarrow \frac{400-x}{3x-400} = \frac{1}{5}\)

\(⇒ 2000 - 5x = 3x - 400\)

\(⇒ 2400 = 8x\)

\(⇒ x = 300\)

Hence, option D is the correct answer.