Two bottles are partially filled with water. The larger bottle currently holds \(\frac{1}{3}\) of its capacity. The smaller bottle, which has \(\frac{2}{3}\) of the capacity of the larger bottle, currently holds \(\frac{3}{4}\) of its capacity.If the contents of the smaller bottle are poured into the larger bottle, the larger bottle will be filled to what fraction of its
capacity?

A. \(\frac{5}{6}\)

B. \(\frac{3}{4}\)

C. \(\frac{2}{3}\)

D. \(\frac{7}{12}\)

E. \(\frac{1}{2}\)
_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Let \(L\) be the capacity of the larger bottle
Let \(l\) be the current capacity of the larger bottle. \(l = \frac{1}{3}L\)
Let \(S\) be the capacity of the smaller bottle. \(S = \frac{2}{3}L\)
Let \(s\) be the current capacity of the smaller bottle. \(s = \frac{3}{4}S\)

Question: What is \(l + s\)

First get \(s\) in terms of \(L\)

\(s = \frac{3}{4} \times \frac{2}{3}L = \frac{1}{2}L\)

\(s + l = (\frac{1}{2} + \frac{1}{3})L = \frac{5}{6}L\)


_________________

Please press +1 Kudos if this post helps.

Take larger bottle (L) to have capacity 9 L and since smaller bottle(S) has 2/3rd the larger bottles capacity, S = 6 L capacity.

Now we are told that L is filled up to 1/3rd its capacity i.e 3 L.

S is filled up to 3/4th its capacity i.e 4.5 L.

when we add 4.5 L to 3 L we get 7.5 L.

7.5/9 = 75/90 = 15/18 = 5/6
Hence answer is A.
_________________

Please press Kudos if this helped

“Going in one more round when you don't think you can, that's what makes all the difference in your life.”