Math Is Fun Forum

Two identical glasses, one filled two thirds with water and the other filled completely with a mixed solution of 60% alcohol and 40% water.

One third of the mixed solution in the second glass is then poured into the first glass. After mixing, a third of the content of the first glass is poured into the second glass.

What is the concentration of the alcohol in the second glass now?

A Crime Story
An elementary school teacher had her purse stolen. The thief had to be Lilian, Judy , David, Theo, or Margaret. When questioned, each child made three statements :

Lilian :
(1)    I didn’t take the purse.
(2)    I have never in my life stolen anything.
(3)    Theo did it.

Judy :
(4)    I didn’t take the purse
(5)    My daddy is rich enough, and I have a purse of my own.
(6)    Margaret knows who did it.

David:
(7)    I didn’t take the purse.
(8)    I didn’t know Margaret before I enrolled in this school.
(9)    Theo did it.

Theo :
(10)    I am not guilty.
(11)    Margaret did it.
(12)    Lilian is lying when she says I stole the purse.

Margaret:
(13)    I didn’t take the teacher’s purse.
(14)    Judy is guilty.
(15)    David can vouch for me because he knows me since I was born.

Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?

How to solve this Question?
:

1/z+ 1/y+ 1/x + 1/w + 1/v + 1/t + 1/s = 1

1/z means 1 over z a fraction.
The letters can be any number.
How to find seven numbers that fit into the equation?

(the numerator is always 1)

What if its 8 sets of fraction? is there any technique?