Teas worth Rs. 100 per kg and Rs. 120 per kg are mixed with a third variety in the ratio of 1 : 1 : 2. If the mixture is worth Rs. 133 per kg, then find the price of the third variety per kg.Choices:- Rs. 156 Rs. 154 Rs.150 Rs.152
Question
Teas worth Rs. 100 per kg and Rs. 120 per kg are mixed with a third variety in the ratio of 1 : 1 : 2. If the mixture is worth Rs. 133 per kg, then find the price of the third variety per kg.Choices:- Rs. 156 Rs. 154 Rs.150 Rs.152
Solution
To solve this problem, we can use the concept of weighted averages.
Step 1: Identify the weights and values of the first two teas. The first tea is worth Rs. 100 per kg and the second tea is worth Rs. 120 per kg. They are mixed in the ratio 1:1, so their weights are equal.
Step 2: The mixture is worth Rs. 133 per kg. This is the weighted average of the three teas.
Step 3: We can set up the equation for the weighted average as follows:
(Weight1 * Value1 + Weight2 * Value2 + Weight3 * Value3) / (Weight1 + Weight2 + Weight3) = Average Value
Substituting the given values into the equation, we get:
(1 * 100 + 1 * 120 + 2 * Value3) / (1 + 1 + 2) = 133
Step 4: Simplify the equation to find the value of Value3.
(100 + 120 + 2 * Value3) / 4 = 133
220 + 2 * Value3 = 532
2 * Value3 = 532 - 220
2 * Value3 = 312
Value3 = 312 / 2
Value3 = Rs. 156
So, the price of the third variety of tea per kg is Rs. 156. Therefore, the correct choice is Rs. 156.
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