A storage tank is completely filled with 150 liters of a solution containing Compounds X, … — GMAT

A storage tank is completely filled with $150$ liters of a solution containing Compounds X, Y, and Water in a ratio of $2:3:5$ by volume. First, $30$ liters of the mixture are drained and replaced with $30$ liters of a liquid mixture that is $20\%$ Compound Y by volume. Next, $50$ liters of the resulting mixture are drained and replaced with $50$ liters of another liquid mixture that is $70\%$ Compound Y by volume. What is the percentage of Compound Y, by volume, in the final mixture?

Cevap: 42 %

Cevap

The final mixture contains 42% of Compound Y by volume.

To find the final concentration, track the exact volume of Compound Y through both stages. Initially, the tank holds

150 \times \frac{3}{10} = 45

liters of Y. In the first replacement, draining

30

liters (

20\%

of the tank) leaves

80\%

of Y, which is

36

liters; adding

30

liters of

20\%

Y mixture adds

6

liters, bringing Y to

42

liters. In the second replacement, draining

50

liters (

\frac{1}{3}

of the tank) leaves

\frac{2}{3}

of Y, which is

28

liters; adding

50

liters of

70\%

Y mixture adds

35

liters, yielding

63

liters of Y. The final concentration is

\frac{63}{150} \times 100\% = 42\%

Adım Adım Çözüm

Calculate initial volume of Compound Y in the tank

Initial Y volume = 45 liters

The ratio X:Y:Water is 2:3:5, giving a total of 2 + 3 + 5 = 10 parts. The fraction of Y is 3/10. For a 150-liter tank, Y = 150 * (3/10) = 45 liters.

Calculate Compound Y after the first draining and replacement cycle

Compound Y volume after first replacement = 42 liters

Draining 30 liters removes 30 / 150 = 1/5 of the mixture. Y remaining = 45 * (1 - 1/5) = 36 liters. Replacing with 30 liters of 20% Y adds 30 * 0.20 = 6 liters of Y. Total Y = 36 + 6 = 42 liters.

Calculate Compound Y after the second draining and replacement cycle

Compound Y volume after second replacement = 63 liters

Draining 50 liters removes 50 / 150 = 1/3 of the current mixture. Y remaining = 42 * (1 - 1/3) = 28 liters. Replacing with 50 liters of 70% Y adds 50 * 0.70 = 35 liters of Y. Total Y = 28 + 35 = 63 liters.

Compute final percentage of Compound Y

42%

The final volume of the tank remains 150 liters. Percentage of Y = (63 / 150) * 100% = 42%.

Anahtar Kavram

Multi-Stage Mixture Removal and Replacement

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