TheCATExam
Sign in

CAT 2022 Slot 3 — QA Question 21

MixturesEasy

A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio

Answer & solution

  • A

    10 : 13

  • B

    10 : 3

  • C

    3 : 10

  • 1 : 1

Solution

Easy

Just track the milk in each container. A neat symmetry of equal-swap problems makes the final ratio fall out at 1:11:1 — but we verify it by computing the actual amounts.

1

First transfer: 150150 cc milk, glass →\to cup.

Glass: 350 milkCup: 150 milk+500 water=650 cc total\begin{aligned} &\text{Glass: }350\ \text{milk}\\ &\text{Cup: }150\ \text{milk}+500\ \text{water}=650\ \text{cc total} \end{aligned}
2

Second transfer: 150150 cc of cup's mixture back. The cup is 150650\tfrac{150}{650} milk, 500650\tfrac{500}{650} water:

milk moved=150×150650=45013water moved=150×500650=150013\begin{aligned} &\text{milk moved}=150\times\frac{150}{650}=\frac{450}{13}\\ &\text{water moved}=150\times\frac{500}{650}=\frac{1500}{13} \end{aligned}
3

Final amounts. Water now in glass, and milk now in cup:

water in glass=150013milk in cup=150−45013=1950−45013=150013\begin{aligned} &\text{water in glass}=\frac{1500}{13}\\ &\text{milk in cup}=150-\frac{450}{13}=\frac{1950-450}{13}=\frac{1500}{13} \end{aligned}
4

Form the ratio:

1500/131500/13=1:1\frac{1500/13}{1500/13}=1:1

The ratio is 1:1\mathbf{1:1}.

When both containers start with equal volumes and you do an equal-out-then-equal-back swap, the displaced-liquid amounts always match: water in the glass == milk in the cup. The ratio is 1:11:1 without any arithmetic.

CAT 2022 Slot 3 QA Q21: A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transfer — Solution | TheCATExam