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Ratio of Cost Prices of Tea Blends

CAT 2019 Slot 1 · Quantitative Ability · Easy · Ratio and Proportions

This is an easy Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Ratio and Proportions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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. A.

    21 : 25

  2. B.

    19 : 24

  3. C.

    18 : 25

  4. D.

    17 : 25

Answer

B

Explanation

Let cost price of A be aa and B be bb. Case 1: Ratio 3 : 2 Average CP = 3a+2b5\frac{3a + 2b}{5} Selling Price = 4040, Profit = 10% ⇒\Rightarrow Average CP = 401.1=40011\frac{40}{1.1} = \frac{400}{11} 3a+2b5=40011⇒3a+2b=200011\frac{3a + 2b}{5} = \frac{400}{11} \Rightarrow 3a + 2b = \frac{2000}{11}

Case 2: Ratio 2 : 3 Average CP = 2a+3b5\frac{2a + 3b}{5} Selling Price = 4040, Profit = 5% ⇒\Rightarrow Average CP = 401.05=80021\frac{40}{1.05} = \frac{800}{21} 2a+3b5=80021⇒2a+3b=400021\frac{2a + 3b}{5} = \frac{800}{21} \Rightarrow 2a + 3b = \frac{4000}{21}

Taking the ratio of equations: 3a+2b2a+3b=2000/114000/21=2122\frac{3a + 2b}{2a + 3b} = \frac{2000/11}{4000/21} = \frac{21}{22} 66a+44b=42a+63b⇒24a=19b⇒ab=192466a + 44b = 42a + 63b \Rightarrow 24a = 19b \Rightarrow \frac{a}{b} = \frac{19}{24}.

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