Two equal vessels contain mixtures of liquids A and B in the ratios 7 : 3 and 4 : 1 respectively. If the quantities of these two…

Question

Two equal vessels contain mixtures of liquids A and B in the ratios 7 : 3 and 4 : 1 respectively. If the quantities of these two mixtures are mixed together in a third vessel, what will be the resulting ratio of liquid A to liquid B?

1. A. 2 : 1
2. B. 3 : 1 (Correct answer)
3. C. 5 : 1
4. D. 4 : 1

Correct Answer

Option B — 3 : 1

Detailed Solution & Explanation

The correct answer is 3 : 1.

Key Points

• Work with equal volumes, taking 1 unit from each vessel and using a common denominator of 10.
• Vessel 1 is A : B = 7 : 3, so it holds 7/10 of A and 3/10 of B.
• Vessel 2 is A : B = 4 : 1 = 8 : 2, so it holds 8/10 of A and 2/10 of B.
• Mixing: A = 7/10 + 8/10 = 15/10, and B = 3/10 + 2/10 = 5/10.
• Ratio A : B = 15 : 5 = 3 : 1.

Additional Information

• Rewriting both ratios over the same denominator (here tenths) is what makes the two mixtures directly addable.
• This shortcut is valid only because the vessels are equal in size; with unequal volumes each mixture must be weighted by its own quantity.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*