MA Practice SET – 1
Mixture & Alligation: Level 1
1.
A trail mix contains raisins, peanuts, and chocolate chips in the ratio 3:2:1 by weight. If the total weight of the mix is 12 pounds, how many pounds of peanuts are there?
Solution (C):
Total parts = \(3 + 2 + 1 = 6\) parts.
Value of one part = \(12 \div 6 = 2\) pounds.
Peanuts are 2 parts: \(2 \times 2 = 4\) pounds.
2.
A 50-liter solution contains 20% alcohol. How many liters of pure alcohol are in the solution?
Solution (B):
Amount = \(20\% \text{ of } 50 = 0.2 \times 50 = 10\) liters.
3.
If you mix 3 liters of water with 12 liters of milk, what is the percentage of water in the final mixture?
Solution (D):
Total volume = \(3 + 12 = 15\) liters.
Percent Water = \(\frac{3}{15} \times 100\% = \frac{1}{5} \times 100\% = 20\%\).
4.
A grocer mixes 2 kg of coffee costing $10/kg with 3 kg of coffee costing $15/kg. What is the cost per kg of the mixture?
Solution (A):
Total cost = \((2 \times 10) + (3 \times 15) = 20 + 45 = 65\).
Total weight = \(2 + 3 = 5\) kg.
Average cost = \(65 / 5 = \$13\).
5.
To make a certain shade of purple paint, you mix red and blue paint in the ratio 3:4. If you use 12 gallons of blue paint, how many gallons of red paint do you need?
Solution (C):
\(\frac{\text{Red}}{\text{Blue}} = \frac{3}{4}\).
\(\frac{R}{12} = \frac{3}{4} \implies R = \frac{3}{4} \times 12 = 9\) gallons.
6.
A salt solution contains 5 grams of salt in 45 grams of water. What is the concentration of salt by weight?
Solution (E):
Total weight = \(5 + 45 = 50\) grams.
Concentration = \(\frac{5}{50} \times 100\% = \frac{1}{10} \times 100\% = 10\%\).
7.
How many liters of water must be added to 10 liters of pure juice to make a mixture that is 50% juice?
Solution (B):
Juice = 10L.
To be 50%, total volume must be such that \(10 / \text{Total} = 0.5\).
Total = 20L.
Water needed = \(20 – 10 = 10\) liters.
8.
A metal alloy consists of Copper and Zinc in a 7:3 ratio. If the total weight is 50 kg, what is the weight of Zinc?
Solution (C):
Total parts = 10. Zinc is 3 parts.
Zinc = \(\frac{3}{10} \times 50 = 3 \times 5 = 15\) kg.
9.
Two liquids A and B are mixed in equal amounts. Liquid A costs $4/liter and Liquid B costs $6/liter. What is the cost per liter of the mixture?
Solution (A):
Since amounts are equal, simple average applies: \(\frac{4+6}{2} = 5\).
10.
If a mixture is 4 parts water and 1 part syrup, what fraction of the mixture is syrup?
Solution (D):
Total = \(4 + 1 = 5\) parts.
Syrup fraction = \(1/5\).
Score: 0 / 0