Mixture Problem

[vabrol]

If a scientist has x liters of a ethanol and benzene solution that is 15% benezene. if he wants to nake te solution 10% benzene,how many of liters must he add?
1) 3x/2
2) 5x/4
3) 2x/3
4)x/2
5)x/4

Official Answer:

SPOILER: 4

[sdasar]

Currently it has 0.85x of ethanol and 0.15x of Benzene (total = x liters).

Let us say we add y liters of ethanol to make the mixture 10% benzene. The total mixture is now x+y liters.

Therefore
0.15 x / ( x + y) = 0.10; 0.15 x = 0.10 x + 0.10 y;
y= (0.05x)/ 0.10; y = x/2;

The answer is 4.

[Goma]

Solution using alligator method
Current % Ethanal Pure Ethanol to be added
85 100

90 (% of ethanol in the resulting solution)

10 (100-90) 5 (90-85) (cross difference)
2 1 (proportion)
1 (1/2)
X X/2