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

Answer: (D)

Rs. 600

Answer 2

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.