Problem Solving

yvonne0923 wrote:Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. jugs X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until Y is filled, what fraction of jug X contains water?
A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

We can let each of the two equally sized jugs be 10 liters (or some unit of capacity). Thus jug X's full capacity is 50 liters (since the 10 liters of water only filled to 1/5 of its capacity) and jug Y's full capacity is 15 liters (since the 10 liters of water only filled to 2/3 of its capacity).

If water is poured from jug X into jug Y until jug Y is filled, we need to pour 5 liters of water from jug X to jug Y to make jug Y filled to its capacity. Thus, we have 5 liters of water left in jug X, whose full capacity is 50 liters, and hence 5/50 = 1/10 of jug X contains water.

Alternate Solution:

Note that the amounts of water in jug X and jug Y are equal (since an equal amount of water was poured into each). If we fill jug Y, which was 2/3 full, to the full capacity, we are increasing the amount of water in jug Y by 50%. Therefore, the amount of water in jug X will be decreased by 50%, in which case, we get (50%)(1/5) = (1/2)(1/5) = 1/10 of jug X filled with water.

Answer: D

yvonne0923 wrote:Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. jugs X is 1/5 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until Y is filled, what fraction of jug X contains water?


A. 0
B. 1/15
C. 2/15
D. 1/10
E. 2/10

We can let each of the two equally sized jugs be 10 liters (or some unit of capacity). Thus jug X's full capacity is 50 liters (since the 10 liters of water only filled the jug to 1/5 of its capacity), and jug Y's full capacity is 15 liters (since the 10 liters of water only filled the jug to 2/3 of its capacity).

If water is poured from jug X into jug Y until jug Y is filled, we need to pour 5 liters of water from jug X to jug Y to make jug Y filled to its capacity. Thus, we have 5 liters of water left in jug X, whose full capacity is 50 liters, and hence 5/50 = 1/10 of jug X contains water.

Alternate Solution:

Note that the amounts of water in jug X and jug Y are equal (since an equal amount of water was poured into each). If we fill jug Y, which was 2/3 full, to the full capacity, we are increasing the amount of water in jug Y by 50%. Therefore, the amount of water in jug X will be decreased by 50%, in which case, we get (50%)(1/5) = (1/2)(1/5) = 1/10 of jug X filled with water.

Answer: D