Q. A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litres of a 40% acid solution?

The correct answer is (C) 6 litres of 50% and 4 litres of 25%

Explanation:

To solve this problem, we use the concept of mixture and alligation. Let’s break it down step by step:

Step 1: Define the variables
Let the amount of the 50% acid solution be x litres.
Then, the amount of the 25% acid solution will be (10 – x) litres, since the total mixture is 10 litres.

Step 2: Write the equation for the total acid content
The total acid content in the mixture is given by:
(Acid from 50% solution) + (Acid from 25% solution) = (Acid in 40% solution).

This can be written as:
0.50x + 0.25(10 – x) = 0.40(10)

Step 3: Simplify the equation
Expand and simplify:
0.50x + 2.5 – 0.25x = 4
0.25x + 2.5 = 4
0.25x = 4 – 2.5
0.25x = 1.5
x = 1.5 ÷ 0.25
x = 6

Step 4: Interpret the result
The amount of the 50% acid solution is 6 litres.
The amount of the 25% acid solution is 10 – 6 = 4 litres.

Final Answer: The correct option is (C) 6 litres of 50% and 4 litres of 25%.