Mixures tough PS

[satishchandra]

A container has 3L of pure wine. 1L from the container is taken out and 2L water is added.The process is repeated several times. After 19 such operations, qty of wine in mixture is

[HSPA]

I guess it is going as 1 -> 1/2 -->1/4-->1/8 till 19 terms

t19 = a x r ^ (n-1)
= 1 x 1/2 ^ 18
= 1/250 mL

[shankar.ashwin]

Found this wonderful explanation

https://www.gmatquantum.com/shared-posts ... stion.html

But its beyond scope of the GMAT IMO. Couldn't solve it in < 2mins..

[user123321]

initially let x litres of wine is present

1) after first operation we will have
x-(x/x) = (x-1)x/x litres of wine & total solution = x+1
2) after second operation we will have
(x-1)-(x-1)/(x+1) = (x-1)x/(x+1) & total solution = x+2
3) after third operation we will have
((x-1)x/(x+1)) - ((x-1)x/(x+1))/(x+2) = (x-1)x/(x+2) & total solution = x+3
.
.
at this step i can see the pattern
so at 19th step
19)(x-1)x/(x+18)
since x = 3 => 2*3/21 = 2/7

nice problem

user123321