CTS Practice Mixtures Problems

Dear Reader, below are three problems from mixtures. These questions are of similar nature and require you to remember a simple equation to solve these.
Question 1
Sharmila Begum, a tea merchant has two varieties of tea one costing Rs.62 per kg. and the other costing Rs.72 per kg. In what ratio she should mix these two varieties such that the mixture is worth Rs.64.50 per kg.
a) 3:1 b) 2:1 c)1:3 d)none of these.
Answer : a) 3 : 1
Solution :
Let us assume that the ratio of new mixture be a : b so that the new price becomes Rs. C. (in our case X = 64.5). Let us assume C1 be the cost per Kg of I variety of tea and C2 be the cost per Kg of the II variety. (In this problem, C1 = 62 and C2 = 72)
Then we have, a.C1 + b.C2 / (a + b) = C
Substituting C1 = 62, C2 = 72 and C = 64.5, we get
62a + 72b / a + b = 64.5 ---- eq 1
Now let us substitute the value of options one by one in this equation to check which one satisfies this equation.
Option I : a = 3, b = 1
Substitute a, b values in eq 1 we get,
62. 3 + 72.1 / 4 = 64.5
Or 258 = 258
Thus, option I satisfies the equation and hence it is the correct answer.