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Mixtures and Replacement Formula

CAT 2023 Slot 1 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2023 Slot 1 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16 : 9, then the ratio of cocoa in mixture P to that in mixture Q is

  1. A.

    4 : 9

  2. B.

    1 : 3

  3. C.

    5 : 9

  4. D.

    1 : 2

Answer

C

Explanation

In mixture Q, coffee : cocoa =16:9= 16 : 9. Fraction of coffee remaining in Q =1625= \frac{16}{25}.

Let the fraction of coffee remaining after one replacement be kk. After two operations, fraction of coffee =k2=1625  ⟹  k=45= k^2 = \frac{16}{25} \implies k = \frac{4}{5}.

In mixture P (after 1 operation):

  • Fraction of coffee =45= \frac{4}{5}
  • Fraction of cocoa =1−45=15=525= 1 - \frac{4}{5} = \frac{1}{5} = \frac{5}{25}

In mixture Q:

  • Fraction of cocoa =925= \frac{9}{25}

Ratio of cocoa in P to Q =525:925=5:9= \frac{5}{25} : \frac{9}{25} = 5 : 9.

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