30 litre of solution contains alcohol and water in the ratio 2:3. How much alcohol must be added to the solution to make a solution containing 60% of alcohol?a)10b)12c)14d)15e)None of theseCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Problem: To make a 60% alcohol solution, we need to add alcohol to a given solution containing alcohol and water in the ratio 2:3. We need to find the amount of alcohol to be added.

Given: 30 litres of solution containing alcohol and water in the ratio 2:3.

Let's assume the amount of alcohol in the given solution is 2x litres and the amount of water is 3x litres.

Then, according to the question, we can write:

Amount of alcohol in the given solution = 2x litres
Amount of water in the given solution = 3x litres
Total amount of solution = 30 litres

Now, we need to find the amount of alcohol to be added to make a 60% alcohol solution. Let's assume we need to add y litres of alcohol.

Then, the amount of alcohol in the final solution will be (2x + y) litres and the amount of water will still be 3x litres.

According to the question, the final solution should be a 60% alcohol solution. This means that:

(2x + y) / (2x + y + 3x) = 0.6

Simplifying the above equation, we get:

2x + y = 18x + 0.6y
0.4y = 16x
y = 40x/3

Therefore, we need to add 40x/3 litres of alcohol to the given solution to make a 60% alcohol solution.

Now, we know that the total amount of solution is 30 litres. So,

2x + 3x = 30
5x = 30
x = 6

Therefore, the amount of alcohol in the given solution is 2x = 12 litres and the amount of water is 3x = 18 litres.

Substituting the value of x in the equation for y, we get:

y = 40x/3 = 40*6/3 = 80/3

Therefore, we need to add 80/3 litres of alcohol to the given solution to make a 60% alcohol solution.

Hence, the correct answer is option (d) 15.

Answer

The initial solution contains 30 liters, with alcohol and water in the ratio 2:3.

The amount of alcohol in the solution is:

The amount of water in the solution is:

We need to add some amount of alcohol (let it be x) to make the alcohol content 60% of the total solution.

After adding x liters of alcohol, the new total volume of the solution will be 30 + x liters, and the amount of alcohol will be 12 + x liters.

The concentration of alcohol should be 60%, so:

Solving the equation:

Thus, 15 liters of alcohol must be added to the solution.

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