Question

Ram prepares solutions of alcohol in water according to customers’ needs. This morning Ram has prepared 27 litres of a 12% alcohol solution and kept it ready in a 27 litre delivery container to be shipped to the customer. Just before delivery, he finds out that the customer had asked for 27 litres of 21% alcohol solution. To prepare what the customer wants, Ram replaces a portion of 12% solution by 39% solution. How many litres of 12% solution are replaced?

• A. 5
• B. 9
• C. 10
• D. 12
• E. 15

Hint:

- In replacement problems, track the net change in concentration due to removal and addition.
- Keep total volume constant and equate final concentration to required value.
- Always double-check calculations by substituting back into the problem.

Answer 1

The Correct Option is B

Step 1: Define variables.
Let \(x\) litres of 12% solution be replaced with the same amount of 39% solution. Total volume remains 27 litres.
Step 2: Alcohol content before replacement.
In 27 litres of 12% solution:
\[ \text{Alcohol} = 27 \times 0.12 = 3.24 \, \text{litres}. \] Step 3: Alcohol content after replacement.
After removing \(x\) litres of 12% solution, alcohol removed = \(0.12x\).
Adding \(x\) litres of 39% solution, alcohol added = \(0.39x\).
So new alcohol content = \(3.24 - 0.12x + 0.39x = 3.24 + 0.27x\).
Step 4: Required alcohol in 21% solution.
For 27 litres of 21% solution:
\[ \text{Required alcohol} = 27 \times 0.21 = 5.67 \, \text{litres}. \] Step 5: Form equation.
\[ 3.24 + 0.27x = 5.67 \] \[ 0.27x = 2.43 \quad \Rightarrow \quad x = \frac{2.43}{0.27} = 9. \] \[ \boxed{9 \, \text{litres}} \]