A mixture of 125 gallons of wine and water contains 20% water .How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture. a 10 gals b 8.5 gals c 8 gals d 6.66 gals e 8.33 gals

Two ways to solve this: Method 1: 125 gallons of solution has 25 gallons of water (20%). Let's add x gallons of water to the solution to bump the concentration to 25%. So, the new concentration is: (25 + x)/(125+x) = 25/100. Solve for x. x = 25/3 or 8.33 gallons. Method 2: You are adding solution which is 100% concentrated water (pure water, of course). Resulting solution is 25%. If you are adding x gallons of 100% concentrated water, (125*20 + x*100)/(125+x) = 25 => 125*20 + x*100 = 125*25 + x*25 => 75*x = 125*5 => x = 25/3 or 8.33 gallons

ankurmit wrote:A mixture of 125 gallons of wine and water contains 20% water .How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture. a 10 gals b 8.5 gals c 8 gals d 6.66 gals e 8.33 gals Wine = .8*125 = 100 gallons. The amount of wine is not changing and must be 75% of the new mixture: 100 = .75x x = 100/.75 = 133.33 gallons. Since the volume of the new mixture is 133.33 gallons, the amount of water that must be added = 133.33-125 = 8.33 gallons. The correct answer is E.

vkb001 wrote: Method 2: You are adding solution which is 100% concentrated water (pure water, of course). Resulting solution is 25%. If you are adding x gallons of 100% concentrated water, (125*20 + x*100)/(125+x) = 25 => 125*20 + x*100 = 125*25 + x*25 => 75*x = 125*5 => x = 25/3 or 8.33 gallons Thanks dear..i was looking out this method only. Thank you Mitch

Mitch great understandng of the underlying concept Thanks GMATGuruNY wrote:ankurmit wrote:A mixture of 125 gallons of wine and water contains 20% water .How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture. a 10 gals b 8.5 gals c 8 gals d 6.66 gals e 8.33 gals Wine = .8*125 = 100 gallons. The amount of wine is not changing and must be 75% of the new mixture: 100 = .75x x = 100/.75 = 133.33 gallons. Since the volume of the new mixture is 133.33 gallons, the amount of water that must be added = 133.33-125 = 8.33 gallons. The correct answer is E.