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Container Mixture Replacement

CAT 2022 Slot 2 · Quantitative Ability · Medium · Arithmetic

This is a medium Quantitative Ability question from the CAT 2022 Slot 2 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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There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is

  1. A.

    5 : 6

  2. B.

    5 : 4

  3. C.

    6 : 5

  4. D.

    4 : 5

Answer

A

Explanation

Let total capacity of each container be 8 units. Initially: Container 1: 4 units Sugar Syrup (S), 0 Milk (M). Container 2: 0 S, 4 M. Step 1: Half of C1 (2 units S) transferred to C2. Now C1: 2 S, 0 M. C2: 2 S, 4 M (total 6 units). Step 2: Half of C2 (1 S, 2 M) transferred back to C1. Now C1: 3 S, 2 M. C2: 1 S, 2 M (total 3 units). Step 3: Half of C1 (1.5 S, 1 M) transferred back to C2. Now C2 has: Sugar Syrup = 1+1.5=2.51 + 1.5 = 2.5 units. Milk = 2+1=32 + 1 = 3 units. Ratio of S to M in C2 = 2.5:3=5:62.5 : 3 = 5 : 6.

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