Purity mixing via alligation: Two solutions, one of 90% purity and another of 97% purity, are mixed to get 21 litres of a 94% pure mixture. How many litres of the 90% solution were used?

Introduction / Context:
We are mixing two purity solutions to reach a target purity. This can be handled either by a direct equation on pure content or by the alligation rule. Both give the same result quickly.

Given Data / Assumptions:

• Total mixture = 21 L.
• Purities: 90% and 97%; target = 94%.

Concept / Approach:
Let x be the volume from the 90% solution. Then (21 − x) comes from the 97% solution. Equate total pure content to the pure content in the final mixture and solve for x.

Step-by-Step Solution:
0.90x + 0.97(21 − x) = 0.94 * 21.0.90x + 20.37 − 0.97x = 19.74 ⇒ −0.07x = −0.63 ⇒ x = 9.

Verification / Alternative check:
Alligation differences: (97 − 94) : (94 − 90) = 3 : 4. Therefore, volumes are in ratio 3 (from 90%) to 4 (from 97%). For 21 L total, 3 + 4 = 7 parts → each part 3 L → 90% share = 3 parts = 9 L, matching the equation method.

Why Other Options Are Wrong:

• 12 L, 15 L, and 6 L do not satisfy the purity balance for a 21 L mixture at 94%.

Common Pitfalls:

• Swapping the alligation differences, which inverts the component volumes.

Final Answer:
9 litres