All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic > Weights and Scales
Three Jar Trial (Posted on 2016-01-25) Difficulty: 3 of 5
Consider three jars, labelled Jar 1, Jar 2 and Jar 3.

Jar 1 contains four liters of a solution that is 45% acid.
Jar 2 contains five liters of a solution that is 48% acid.
Jar 3 contains one liter of a solution that is n% acid.

From jar 3, x/y liters of the solution is added to jar 1, and the remainder of the solution in jar 3 is added to jar 2, where x and y are relatively prime positive integers.

At the end, each jar 1 and jar 2 contain solutions that are 50% acid.

Determine n+x+y.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 4
Each of the three jars has a Volume, Acid Content, and Concentration to keep track of.

Before distributing Jar 3:
       | Volume | Acid Content | Concentration
-------+--------+--------------+---------------
Jar 1  |    4   |      1.8     |     0.45
Jar 2  |    5   |      2.4     |     0.48
Jar 3  |    1   |       N      |       N

After distributing Jar 3: (Letting Z=x/y)
       | Volume | Acid Content | Concentration
-------+--------+--------------+---------------
Jar 1  |   4+Z  |    1.8+Z*N   |     0.5
Jar 2  |   6-Z  |  2.4+(1-Z)*N |     0.5

Then two equations can be formed:
(1.8+Z*N)/(4+Z) = 1/2
(2.4+(1-Z)*N)/(6-Z) = 1/2

Each equation can be solved for N:
N = (Z+0.4)/(2Z)
N = (1.2-Z)/(2-2Z)

Equating these two expressions yields Z=2/3, and therefore N=80%.  The value of N+X+Y is 85.

  Posted by Brian Smith on 2016-01-25 12:00:55
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information