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CAT 2022 Slot 2 — QA Question 4

MixturesEasy

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

Answer & solution

  • 5 : 6

  • B

    4 : 5

  • C

    5 : 4

  • D

    6 : 5

Solution

Easy

Pick a convenient starting amount and just track the two ingredients through each transfer. Take container A with 100100 units of sugar syrup and B with 100100 units of milk. "Half the content" of a container is half of whatever it currently holds.

Start: A =100=100 syrup; B =100=100 milk.

1

Move half of A (5050 syrup) into B.

A=50 syrupB=50 syrup+100 milk=150 (ratio 1:2)\begin{aligned} &\text{A}=50\ \text{syrup}\\ &\text{B}=50\ \text{syrup}+100\ \text{milk}=150\ \text{(ratio }1:2) \end{aligned}
2

Move half of B (7575 units) back to A. B is 1:21:2, so 7575 units carry 2525 syrup and 5050 milk.

A=(50+25) syrup+50 milk=75 syrup+50 milk=125B=25 syrup+50 milk=75\begin{aligned} &\text{A}=(50+25)\ \text{syrup}+50\ \text{milk}=75\ \text{syrup}+50\ \text{milk}=125\\ &\text{B}=25\ \text{syrup}+50\ \text{milk}=75 \end{aligned}
3

Move half of A (62.562.5 units) into B. A is 75:50=3:275:50=3:2, so 62.562.5 units carry 37.537.5 syrup and 2525 milk.

B=(25+37.5) syrup+(50+25) milk=62.5 syrup+75 milk\text{B}=(25+37.5)\ \text{syrup}+(50+25)\ \text{milk}=62.5\ \text{syrup}+75\ \text{milk}
4

Final ratio in B:

62.5:75=625:750=5:662.5:75=625:750=5:6

Sugar syrup : milk =5:6=\mathbf{5:6} — option (a).

CAT 2022 Slot 2 QA Q4: There are two containers of the same volume, first container half-filled with sugar syrup and the second conta — Solution | TheCATExam