Coffee worth Tk. 200 per kg and Tk. 240 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 260 per kg, the price of the third variety per kg will be:

Question: Coffee worth Tk. 200 per kg and Tk. 240 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 260 per kg, the price of the third variety per kg will be:

Solution:
Let,
the quantities of the three varieties be 1 kg, 2 kg, and 2 kg respectively.
Total mixture = 1 + 2 + 2 = 5 kg.
1 kg mixture value = Tk. 260
∴ 5 kg or Total value of the mixture = 5 × 260 = Tk. 1300.

Value of first variety = 1 kg × Tk. 200 = Tk. 200.
Value of second variety = 2 kg × Tk. 240 = Tk. 480.
Total value of the first two varieties = Tk. 200 + Tk. 480 = Tk. 680.

Value of the third variety (2 kg) = 1300 - 680 = Tk. 620.
∴ Price per kg of the third variety = Tk. 620/2 kg = Tk. 310.