Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be-

Question: Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be-Solution:Since first and second varieties are mixed in equal proportions.So, their average price = Tk. (126 + 135)/2 = Tk. 130.50So, the mixture is formed by mixing two varieties, one at Tk. 130.50 per kg and the other at say, Tk. x per kg in the ratio 2 : 2 = 1 : 1. We have to find x.We know,⇒ Quantity of cheaper : Quantity of Dearer = (CP of of Dearer - Mean Price) : (Mean Price - CP of Cheaper)⇒ (CP of of Dearer - Mean Price) : (Mean Price - CP of Cheaper) = Quantity of cheaper : Quantity of Dearer⇒ (x - 153) : (153 - 130.50) = 1 : 1⇒ x - 153 = 153 - 130.50⇒ x = 22.5 + 153∴ x = 175.5