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Q69·CSAT · Prelims 2022

Evaluating final mixture ratios after two-way liquid transfers

NumericalMixtures & AlligationsFactual singleMedium

Question

There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?

Options

a

m = n

Answer
b

m > n

c

m < n

d

Cannot be determined due to insufficient data

Explanation

Trace the fluid volumes step by step. Start: X = 100M, Y = 100W.

Step 1: Move 20 ml from X to Y.

Container X now holds: 80M.
Container Y now holds: 100W + 20M (Total volume = 120 ml).

Step 2: Move 20 ml of the mixed Y back to X. The fraction being moved is 20/120 = 1/6 of the container Y.

Water moved to X = 1/6 × 100W = 100/6 W.
Milk moved back to X = 1/6 × 20M = 20/6 M.

Final State Calculation:

Final X: Milk = 80M + 20/6M = 500/6 M. Total volume is back to 100 ml.
Final Y: Water = 100W - 100/6W = 500/6 W. Total volume is back to 100 ml.

Calculate the final proportions: m (milk in X) = (500/6) / 100 = 5/6. n (water in Y) = (500/6) / 100 = 5/6. The proportions are perfectly identical: ⟨MATH⟩m = n⟨/MATH⟩.

A classic closed-loop mixture principle dictates that if equal volumes are exchanged back and forth between two pure substances, the final concentration of liquid A in the first container will identically match the concentration of liquid B in the second.

Answer: (a).

Question details

Year

2022

Paper

CSAT

Question

Q69

Section

Numerical Ability

Sub-topic

Mixtures & Alligations

Type

Factual single

Difficulty

Medium

Source hint

Containers X and Y, milk and water transfers

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