Word Problems
(Mixture)
Practice Exercise
Very Easy (Difficulty Level-1):
1. How many gallons of a 7% saline solution must be added to 4 gallons of a 25% saline solution so that the resulting mixture is a 15% saline solution?
A. 1
B. 4
C. 5
D. 9
E. 10
2. A scientist created a mixture of 3 parts acid and 5 parts ammonia to make a 16-ounce solution. If she wants the solution to be 50 percent acid, how much acid should the scientist add?
A. 4 ounces
B. 3 ounces
C. 2 ounces
D. 1 ounce
E. 0.5 ounces
3. How many liters of water must be added to a 20 liter solution of water and acid, which is 24% acid, to make a solution that is 8% acid?
A. 20
B. 40
C. 48
D. 60
E. 170
4. A chemist mixes a 12-ounce solution that is 45% acid with 8 ounces of solution that is 70% acid. What percent of acid is in the mixture?
A. 11
B. 20
C. 37.5
D. 55
E. 57.5
Easy (Difficulty Level-2):
5. A flask contains 160 ml of solution that is 25% alcohol by volume. How much pure alcohol must be added to the flask so that the resulting solution is 60% alcohol by volume?
6. One cup of nuts that contains exactly half peanuts and half cashews is added to a bowl of nuts that is exactly one-third peanuts, one third cashews, and one third almonds. This results in a three-cup mixture of nuts. What fraction of the new nut mixture is peanuts?
7. Eight liters of a 45% saline solution is left in the sun. Water evaporates from the solution leaving a 60% saline solution. Approximately how much water evaporated from the solution?
A. 1.2 liters
B. 2.0 liters
C. 2.1 liters
D. 6.0 liters
E. 7.0 liters
Medium (Difficulty Level-3):
8. Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. How many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume?
9. If 3 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?
10. Graham crackers cost $0.25 per pound and marshmallows cost $0.85 per pound. How many pounds of graham crackers must be added to 25 pounds of marshmallows to arrive at a mixture worth $0.45 a pound?
A. 170
B. 100
C. 60
D. 50
E. 20
11. Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?
A. 10
B. 5
C. 4
D. 2
E. 1
12. A chemist has 10 liters of a solution that is 10 percent nitric acid by volume. He wants to dilute the solution to 4 percent strength by adding water. How many liters of water must he add?
(A) 15
(B) 18
(C) 20
(D) 25
(E) 26
13. Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
A) 18
B) 20
C) 24
D) 36
E) 42
Hard (Difficulty Level-4):
14. Solution X is 30% salt by volume and Solution Y is 70% salt by volume. If 300 milliliters of solution X is combines with 200 ml of solution Y, the resulting solution will be what percent salt?
15. A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is three times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
A. 1:1
B. 2:3
C. 3:2
D. 9:4
E. 27:8
16. Two solutions of 90% and 97% purity are mixed resulting in 21 litres of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?
(A) 15 litres
(B) 12 litres
(C) 9 litres
(D) 6 litres
(E) 4 litres
17. Joseph brought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each. He mixed them in some ratio. Then he sold the mixture at 7 cents per ounce, making a profit of 20%. What was the ratio of the mixture?
(A) 1 : 10
(B) 1 : 5
(C) 2 : 7
(D) 3 : 8
(E) 5 : 7
18. A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?
19. Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X?
Very Hard & Tricky (Difficulty Level-5):
20. Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid X?
21. A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
22. There are 2 bars of gold-silver alloy; one piece has 2 parts of gold to 3 parts of silver and another has 3 parts of gold to 7 parts of silver. If both bars are melted into 8 kg bar with the final gold to silver ratio of 5:11. What was the weight of the first bar?
23. A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit’s diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture.
24. Some part of the 50% solution of acid was replaced with the equal amount of 30% solution of acid. As a result, 40% solution of acid was obtained. What part of the original solution was replaced?
25. Two alloys A and B are composed of two basic elements. The ratio of the components of the two basic elements are 5 : 3 and 1 : 2 respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in the alloy X?
(A) 1 : 1
(B) 2 : 3
(C) 5 : 2
(D) 4 : 3
(E) 7 : 9
Answer Sheet:
1. C
2. A
3. B
4. D
5. 140
6. 7⁄18
7. B
8. 450
9. (3x + 2y)⁄5
10. D
11. B
12. A
13. E
14. 46
15. E
16. C
17. B
18. 800 units
19. 33.33%
20. 37.5%
21. 1⁄3
22. 1Kg
23. 140
24. 1⁄2
25. A