There are three varieties of tea – I, II, III – available in the market. Mani bought a certain quantity of each variety. The average cost per kg of varieties I and II for the quantities he bought worked out to be ₹50. The same for varieties II and III is ₹60 and that for varieties I and III is ₹68. Which of the following cannot be the average cost per kg of all the three varieties of tea that he bought?
Question
There are three varieties of tea – I, II, III – available in the market. Mani bought a certain quantity of each variety. The average cost per kg of varieties I and II for the quantities he bought worked out to be ₹50. The same for varieties II and III is ₹60 and that for varieties I and III is ₹68. Which of the following cannot be the average cost per kg of all the three varieties of tea that he bought?
Solution
The problem can be solved by using the concept of averages.
Let's denote the average cost per kg of tea varieties I, II, and III as A, B, and C respectively.
From the problem, we know that:
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The average cost of varieties I and II is ₹50. Therefore, (A + B)/2 = 50. We can simplify this to A + B = 100.
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The average cost of varieties II and III is ₹60. Therefore, (B + C)/2 = 60. We can simplify this to B + C = 120.
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The average cost of varieties I and III is ₹68. Therefore, (A + C)/2 = 68. We can simplify this to A + C = 136.
Now, we can add the three equations together:
A + B + B + C + A + C = 100 + 120 + 136 2A + 2B + 2C = 356 A + B + C = 178
So, the average cost per kg of all three varieties of tea that Mani bought is ₹178.
Therefore, any value that is not ₹178 cannot be the average cost per kg of all the three varieties of tea that he bought.
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