But if that question had asked, cost per liter of the solution then answer would be A. because, in that case, sprit in solution A is 1/2 and spirit in solution B 1/3. But here it's talking about the total cost. so C

The problems says that cost per liter is directly proportional to the spirit by volume. Directly proportional means \(y = k*x\), with \(k\) being a constant.

Setting up an equation, we have

\(\frac{cost}{liter} = \frac{total spirit}{total volume} * k\)

We also know that

\(\frac{cost}{liter} = \frac{total cost}{total volume}\)

So setting the two equations equal, we get

\(\frac{total cost}{total volume} = \frac{total spirit}{total volume} * k\)

\(total cost = total spirit * k\)

Because there is 1 liter of sprit, total cost = k units for both quantities.

Solution:

Let the Cost be C and the volume of spirit be Vs

Thus formulating the above info in to a eqn gives us
c∝\(\frac{ k}{Vs}\)
Qty A: x= \(\frac{k}{1}\)
Thus x=k

Qty B: y=\(\frac{k}{1}\)
y=k

At this point it might seem that x and y could be anything. But notice, there is a k there as well, which is common in both the quantities.

Therefore k=x=y

IMO C

Hope this helps

can someone pls explain why the equation isn't Cost = k*s/(s+w) where k is a constant, s is the solution and w is water?