Mixture Problems

swerve wrote: ↑

Fri May 22, 2020 10:08 am

A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?

A. 1:1
B. 2:3
C. 3:2
D. 9:4
E. 27:8

The OA is E

Solution:

We are given that in a bottled solution, the ratio of water to soap is 3 : 2. Since the ratio of soap to salt is three times this ratio, the ratio of soap to salt is 9 : 2. We see the number for soap in the first ratio is 2 while that in the second is 9. We can make them the same number by using their LCM. Since the LCM of 2 and 9 is 18, we can say the ratio of water to soap is 27 : 18 and the ratio of soap to salt is 18 : 4. Thus:
water : soap : salt = 27 : 18 : 4
If the ratio of water to soap is halved by water evaporation, the new ratio of water to soap is 13.5 : 18 and the new ratio of water : soap : salt is 13.5 : 18 : 4. Thus, the ratio of water to salt after water evaporation is 13.5 : 4 or 27 : 8.

Answer: E