CAT 2022 Slot 2 · Quant · Question 6

CAT 2022 Slot 2 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.

Averages, Mixture and AlligationArithmeticMultiple choiceHard
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
Pick an option, then check.
Answer & solution

Answer: Option A

Take each container's full volume as 16 units, so each starts half-filled with 8 units.

Container 1 holds 8 units of syrup and container 2 holds 8 units of milk.

First transfer: half of container 1, that is 4 units of syrup, moves across.

Container 1 now has 4 syrup; container 2 has 4 syrup and 8 milk, a total of 12 units.

Second transfer: half of container 2, that is 6 units, moves back — and it is a uniform mixture, so it carries syrup and milk in the ratio 4:8.

That means 2 units of syrup and 4 units of milk move back.

Container 1 now holds 4+2=6 syrup and 4 milk, a total of 10 units.

Container 2 is left with 4-2=2 syrup and 8-4=4 milk.

Third transfer: half of container 1, that is 5 units, moves across, carrying syrup and milk in the ratio 6:4.

That means 3 units of syrup and 2 units of milk move across.

Container 2 finally holds 2+3=5 syrup and 4+2=6 milk.

The ratio is 5:6 — the first option.

Shortcut. Choosing 16 as the container volume keeps every transfer a whole number, since the quantities are repeatedly halved. Each transfer is then just "split the current contents in half and move one half", with no fractions at any stage.

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