Arithmetic

Mixture & Alligation

Medium

Two alcohol solutions, $A$ and $B$ , are mixed in the proportion $1:3$ by volume. The volume of the mixture is then doubled by adding solution $A$ such that the resulting mixture has $72 \%$ alcohol. If solution $A$ has $60 \%$ alcohol, then the percentage of alcohol in solution $B$ is

$90\%$

$92\%$

$94\%$

$89\%$

✅ Correct Option: 2

We have two alcohol solutions mixed in a specific ratio, then more solution is added. Let's break this down to find the alcohol percentage in solution $B$ .

Since we're dealing with ratios and percentages, we can choose convenient numbers that maintain the given proportion. This makes calculations easier without affecting the final answer.

Let's say initially:

Volume of solution $A = 1$ liter

Volume of solution $B = 3$ liters

This gives us the required $1:3$ ratio by volume.

The problem states that the mixture volume is doubled by adding solution $A$ .

Initial mixture volume $= 1 + 3 = 4$ liters

When doubled, final mixture volume $= 8$ liters

Since we started with $4$ liters and end with $8$ liters, we added $4$ liters of solution $A$ .

Final composition:

Solution $A$ : $1 + 4 = 5$ liters

Solution $B$ : $3$ liters (unchanged)

Total: $8$ liters

Now we'll use the fact that alcohol content is conserved - the total amount of pure alcohol before and after mixing remains the same.

Let the percentage of alcohol in solution $B = p\%$

Total alcohol in final mixture:

From solution $A$ : $5$ liters $\times 60\% = 5 \times 0.6 = 3$ liters of pure alcohol

From solution $B$ : $3$ liters $\times p\% = 3 \times \frac{p}{100}$ liters of pure alcohol

Total pure alcohol $= 3 + \frac{3p}{100}$ liters

Alternatively, the final mixture has $72\%$ alcohol in $8$ liters:

Total pure alcohol $= 8 \times 72\% = 8 \times 0.72 = 5.76$ liters

Since both expressions represent the same quantity:

$3 + \frac{3p}{100} = 5.76$

$\frac{3p}{100} = 5.76 - 3$

$\frac{3p}{100} = 2.76$

$3p = 2.76 \times 100$

$3p = 276$

$p = \frac{276}{3} = 92$

Therefore, solution $B$ contains $92\%$ alcohol.

Key Learning: In mixture problems, we focus on conserving the actual amount of the substance (here, pure alcohol) rather than just the percentages. This approach makes the problem much more manageable!

CAT 2021 Slot 3

If a certain weight of an alloy of silver and copper is mixed with $3$ kg of pure silver, the resulting alloy will have $90\%$ silver by weight. If the same weight of the initial alloy is mixed with $2$ kg of another alloy which has $90\%$ silver by weight, the resulting alloy will have $84\%$ silver by weight. Then, the weight of the initial alloy, in kg, is

CAT 2021 Slot 1

The strength of an indigo solution in percentage is equal to the amount of indigo in grams per $100 \mathrm{cc}$ of water. Two $800 \mathrm{cc}$ bottles are filled with indigo solutions of strengths $33 \%$ and $17 \%$ , respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to $21 \%$ then the volume, in cc, of the solution left in the second bottle is

CAT 2023 Slot 3

Anil mixes cocoa with sugar in the ratio $3: 2$ to prepare mixture $A$ , and coffee with sugar in the ratio $7: 3$ to prepare mixture $B$ . He combines mixtures $A$ and $B$ in the ratio $2: 3$ to make a new mixture $C$ . If he mixes $C$ with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be

CAT 2017 Slot 2

Bottle $1$ contains a mixture of milk and water in $7: 2$ ratio and Bottle $2$ contains a mixture of milk and water in $9: 4$ ratio. In what ratio of volumes should the liquids in Bottle $1$ and Bottle $2$ be combined to obtain a mixture of milk and water in $3: 1$ ratio?

CAT 2018 Slot 2

There are two drums, each containing a mixture of paints $A$ and $B$ . In drum $1, \mathrm{~A}$ and B are in the ratio $18: 7$ . The mixtures from drums $1$ and $2$ are mixed in the ratio $3: 4$ and in this final mixture, $A$ and $B$ are in the ratio $13: 7$ . In drum $2$ , then $A$ and $B$ were in the ratio

CAT 2022 Slot 2

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

Two alcohol solutions, AAA and BBB, are mixed in the proportion 1:31:31:3 by volume. The volume of the mixture is then doubled by adding solution AAA such that the resulting mixture has 72%72 \%72% alcohol. If solution AAA has 60%60 \%60% alcohol, then the percentage of alcohol in solution BBB is

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)

Two alcohol solutions, $A$ and $B$ , are mixed in the proportion $1:3$ by volume. The volume of the mixture is then doubled by adding solution $A$ such that the resulting mixture has $72 \%$ alcohol. If solution $A$ has $60 \%$ alcohol, then the percentage of alcohol in solution $B$ is