Hello,
Let me try helping you with this one.
It is mentioned in the question that the volume of W is 50% larger than the volume of V. Hence, W=\(\frac{3}{2}\)*V
This implies that V=\(\frac{2}{3}\)*W
Now, V is filled with 2/3 with the solution and W is filled 3/4 with the solution.
Half of the solution in V is filled into W. We need to find the fraction of W that is filled. So, we have to express everything in terms of W.
Half of the solution in V in terms of W is 1/3. When we express that in terms of W, it becomes
half the volume of solution in V=\(\frac{1}{3}\)*\(\frac{2}{3}\)*W
This is added to 3/4 of the volume W.
The total volume is (\(\frac{1}{3}\)*\(\frac{2}{3}\)*W)+(\(\frac{3}{4}\)*W)=\(\frac{35}{36}\)*W
Hence, the answer is E.
Hope this helps! Let me know if I could help you any further.
megafan wrote:
Vial V is \(\frac{2}{3}\) full of a certain solution and vial W, which has 50% more capacity than vial V, is \(\frac{3}{4}\) full of the same solution. If half of the solution in vial V is poured into vial W, vial W will be filled to what fraction of its capacity?
(A)\(\frac{27}{36}\)
(B)\(\frac{10}{11}\)
(C)\(\frac{11}{12}\)
(D)\(\frac{23}{24}\)
(E)\(\frac{35}{36}\)
I was able to solve it in under 2 mins, but curious to know if there is a 10-sec approach?