The ratio of water and ammonia in solution A is 1 : 4; the ratio of

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

When a question asks a ratio, if one condition is about a ratio and the other condition is just a number, then the condition about a ratio would be sufficient. Thus A could be the answer most likely for this quesiton.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.
We can modify the original condition and question as follows.

Assume \(Aw\) and \(Aa\) are amounts of water and ammonia in Solution A and \(Bw\) and \(Ba\) are assumed in the similar way.

\(Aw : Aa = 1:4\) => \(Aw = x\) and \(Aa = 4\)x
\(Bw : Ba = 3:1\) => \(Bw = 3y\) and \(Ba = y\)

Assume \(a\) and \(b\) are amounts of solutions A and B, respectively.
\(a = 5x\) and \(b = 4y\)

The question asks \(( a*Aw + b*Bw ) / (a*Aa + b*Ba) = (ax + by) / ( 3ax + 3by ) = ( 5x^2 + 4y^2 ) / ( 15x^2 + 12y^2 )\).

Condition 1)
\(a : b = 2 : 3\)
\(5x : 4y = 2 : 3\)
\(15x = 8y\)
\(x/y = 8/15\)

\(( 5x^2 + 4y^2 ) / ( 15x^2 + 12y^2 )\)
\(= ( 5(x/y)^2 + 4 ) / ( 15(x/y)^2 + 12 )\)
\(= ( 5(8/15)^2 + 4 ) / ( 15(8/15)^2 + 12\)).
This is sufficient.

Condition 2)
\(a = 20\)
\(x = 4\)
Since we don't know b or y, this is not sufficient.

Then answer is A