Question : Rice worth Rs.126 per kg and Rs.135 per kg are mixed with a third variety in the ratio of 1 : 1 : 2. If the mixture is worth Rs.153 per kg, then the price of the third variety per kg (in Rs.) is:
Option 1: 182.5
Option 2: 195.5
Option 3: 133.5
Option 4: 175.5
Correct Answer: 175.5
Solution :
The first and second varieties are mixed in equal proportions.
Their average price = $\frac{126 + 135}{2}$ = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at Rs.$x$ per kg, in the ratio 2 : 2 = 1 : 1.
By the rule of allegation, we have,
Ratio = (Higher value – Mean value) : (Mean value – Lower value)
⇒ $\frac{1}{1} = \frac{x – 153}{153 - 130.5}$
⇒ $1 = \frac{x – 153}{22.5}$
⇒ $x = 153 + 22.5$
$\therefore x = 175.5$
Hence, the correct answer is 175.5.
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