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Question 6 :Two types of tea A and B are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices per kg of A and B are in the ratio

  1. 21 : 25
  2. 19 : 24
  3. 18 : 25
  4. 17 : 25

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Explanatory Answer

Method of solving this CAT Question from Ratio and Proportions

Let Tea A and B be sold at Rs.a and Rs.b respectively
When A and B are mixed in the ratio 3 : 2 and sold at a profit of 10% at Rs.40 per Kg
\\frac{3a + 2b}{5}) = \\frac{40}{1.1}) ------(1)
When A and B are mixed in the ratio 2 : 3 and sold at a profit of 5% at Rs.40 per Kg
\\frac{2a + 3b}{5}) = \\frac{40}{1.05}) ------(2)

Solving equations (1) and (2), we get
1.1 × (\\frac{3a + 2b}{5})) = 1.05 × (\\frac{2a + 3b}{5}))
\\frac{11}{10}) × (3a + 2b) = \\frac{21}{20}) × (2a + 3b)
66a + 44b = 42a + 63b
24a = 19b

\\frac{a}{b}) = \\frac{19}{24})
So, the cost prices per Kg of A and B are in the ratio 19 : 24

The question is "Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio"

Hence, the answer is 19 : 24

Choice B is the correct answer.

 

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