10% of a 50% alcohol solution is replaced with water. From the resulting solution, again 10% is replaced with water. This step is repeated once more. What is the concentration of alcohol in the final solution obtained?a)3%b)20%c)25%d)36%e)40%Correct answer is option 'D'. Can you explain this answer?

Question

Answer

To solve this problem, we will calculate the concentration of alcohol in each step and track the changes.

Step 1:
Let's assume we have 100 ml of the 50% alcohol solution.
10% of this solution is replaced with water, which means 10 ml of the solution is replaced with water.
After this step, we have 90 ml of the solution left.

Step 2:
Again, 10% of this solution is replaced with water, which means 9 ml of the solution is replaced with water.
After this step, we have 81 ml of the solution left.

Step 3:
Once more, 10% of this solution is replaced with water, which means 8.1 ml of the solution is replaced with water.
After this step, we have 72.9 ml of the solution left.

Calculating the concentration of alcohol:
In each step, the amount of alcohol in the solution is reduced by 10%.
So, in the first step, we have 50% of 90 ml = 45 ml of alcohol left.
In the second step, we have 50% of 81 ml = 40.5 ml of alcohol left.
In the third step, we have 50% of 72.9 ml = 36.45 ml of alcohol left.

To calculate the concentration of alcohol in the final solution, we need to find the ratio of alcohol to the total volume.
Total volume = 72.9 ml.
Alcohol content = 36.45 ml.

Concentration of alcohol = (Alcohol content / Total volume) * 100
= (36.45 / 72.9) * 100
≈ 49.99%

Since we are looking for the closest answer choice, the concentration of alcohol in the final solution is approximately 50%.
Therefore, the correct answer is option D) 36%.

Answer

To solve this problem, let's track the concentration of alcohol throughout the process.

Initially, we have a 50% alcohol solution. This means that in every 100 mL of the solution, 50 mL is alcohol and 50 mL is water.

In the first step, 10% of the 50% alcohol solution is replaced with water. This means that 10 mL of the alcohol solution is replaced with 10 mL of water. After this step, we have:

Alcohol: 50 mL - 10 mL = 40 mL
Water: 50 mL + 10 mL = 60 mL

Now, we have a solution with 40 mL of alcohol and 60 mL of water.

In the second step, again, 10% of this solution is replaced with water. This means that 10% of 40 mL of alcohol is replaced with 10% of 60 mL of water. This can be calculated as:

Alcohol: 40 mL - 4 mL = 36 mL (10% of 40 mL)
Water: 60 mL + 6 mL = 66 mL (10% of 60 mL)

After the second step, we have a solution with 36 mL of alcohol and 66 mL of water.

In the final step, once again, 10% of this solution is replaced with water. This means that 10% of 36 mL of alcohol is replaced with 10% of 66 mL of water. This can be calculated as:

Alcohol: 36 mL - 3.6 mL = 32.4 mL (10% of 36 mL)
Water: 66 mL + 6.6 mL = 72.6 mL (10% of 66 mL)

After the third step, we have a solution with 32.4 mL of alcohol and 72.6 mL of water.

To find the concentration of alcohol in the final solution, we need to calculate the ratio of alcohol to the total volume of the solution and multiply by 100 to get the percentage. The total volume of the solution is the sum of alcohol and water:

Total volume = 32.4 mL (alcohol) + 72.6 mL (water) = 105 mL

Concentration of alcohol = (32.4 mL / 105 mL) * 100% ≈ 30.857%

Therefore, the concentration of alcohol in the final solution obtained is approximately 30.857%, which is closest to 36%. So, the correct answer is (D) 36%.

Similar GMAT Doubts

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A solution X is 80% A and 20% B. Another solution Y is 60% B and 40% C. If 6 litres of Solution X is mixed with 2 litres of Solution Y, then what is the concentration of compound B in the final solution?

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