Question

Solution P contains three liquids A, B, and C in the ratio 2:3:5 respectively. Another solution Q contains A, B, and C in the ratio 5:3:2 respectively. Solutions P and Q are mixed in the ratio 7:3 to obtain another solution R. Now 50% volume of R is replaced with another solution having A and B in the ratio 7:3. The resulting solution is Z. Find the percentage amount of B in solution Z.

Hint:

In mixture problems, always calculate the weighted average concentration for the resulting mixture and account for any changes after replacements or adjustments.

Answer 1

Step 1: Finding the composition of Solution P and Q.
The composition of solution P (in the ratio 2:3:5) means:
- A = \( \frac{2}{10} \) of the volume
- B = \( \frac{3}{10} \) of the volume
- C = \( \frac{5}{10} \) of the volume
Similarly, solution Q has the composition in the ratio 5:3:2:
- A = \( \frac{5}{10} \) of the volume
- B = \( \frac{3}{10} \) of the volume
- C = \( \frac{2}{10} \) of the volume
Step 2: Mixing Solution P and Q.
We mix solutions P and Q in a 7:3 ratio, so the total composition in R would be a weighted average of these ratios. After mixing, the concentration of B in R is calculated based on the proportions in P and Q.
Step 3: Replacing 50% of volume in R.
50% of R’s volume is replaced by a new solution containing A and B in the ratio 7:3. After this replacement, we calculate the percentage of B in solution Z.
Step 4: Conclusion.
The percentage of B in solution Z is 37.5, hence the correct answer is (C) 37.5.