Aptitude:Mixture and Alligation

(21) A chemist has two types of chemicals: one that is 25% acidic and another that is 35% acidic. How many milliliters of each type of chemical should be mixed to obtain 50 milliliters of a solution that is 30% acidic?

• (a) 30 mL of 25% and 20 mL of 35%
• (b) 20 mL of 25% and 30 mL of 35%
• (c) 25 mL of 25% and 25 mL of 35%
• (d) 15 mL of 25% and 35 mL of 35%

Answer

Correct Answer: (b) 20 mL of 25% and 30 mL of 35%
Let \( x \) milliliters be the amount of 25% acidic chemical and \( 50 – x \) milliliters be the amount of 35% acidic chemical. The equation based on acidity content is:
<br /> 0.25x + 0.35(50 - x) = 0.30 \times 50 \\<br /> 0.25x + 17.5 - 0.35x = 15 \\<br /> -0.10x = -2.5 \\<br /> x = 25<br />
Therefore, 20 milliliters of 25% acidic chemical and 30 milliliters of 35% acidic chemical should be mixed to obtain 50 milliliters of a solution that is 30% acidic.

(22) A car rental agency offers two types of cars for rent: compact cars for $40 per day and SUVs for $80 per day. How many days should a customer rent each type of car to spend a total of $240 on rental costs for 3 days?

• (a) 1 day of compact and 2 days of SUV
• (b) 2 days of compact and 1 day of SUV
• (c) 3 days of compact and 0 days of SUV
• (d) 0 days of compact and 3 days of SUV

Answer

Correct Answer: (b) 2 days of compact and 1 day of SUV
Let \( x \) be the number of days for a compact car and \( y \) be the number of days for an SUV. The equation based on total cost is:
<br /> 40x + 80y = 240 \\<br /> 2x + 4y = 12<br />
One possible solution is \( x = 2 \) and \( y = 1 \), which corresponds to renting a compact car for 2 days and an SUV for 1 day, totaling $240 for 3 days.

(23) A chef has two types of flour: one that is 15% gluten and another that is 30% gluten. How many kilograms of each type of flour should be mixed to obtain 10 kilograms of flour that is 20% gluten?

• (a) 2 kg of 15% and 8 kg of 30%
• (b) 3 kg of 15% and 7 kg of 30%
• (c) 4 kg of 15% and 6 kg of 30%
• (d) 5 kg of 15% and 5 kg of 30%

Answer

Correct Answer: (c) 4 kg of 15% and 6 kg of 30%
Let \( x \) kilograms be the amount of 15% gluten flour and \( 10 – x \) kilograms be the amount of 30% gluten flour. The equation based on gluten content is:
<br /> 0.15x + 0.30(10 - x) = 0.20 \times 10 \\<br /> 0.15x + 3 - 0.30x = 2 \\<br /> -0.15x = -1 \\<br /> x = 6<br />
Therefore, 4 kilograms of 15% gluten flour and 6 kilograms of 30% gluten flour are needed.

(24) A school cafeteria offers two types of milk: one that is 2% fat and another that is 4% fat. How many liters of each type of milk should be mixed to obtain 8 liters of milk that is 3% fat?

• (a) 4 liters of 2% and 4 liters of 4%
• (b) 3 liters of 2% and 5 liters of 4%
• (c) 2 liters of 2% and 6 liters of 4%
• (d) 5 liters of 2% and 3 liters of 4%

Answer

Correct Answer: (b) 3 liters of 2% and 5 liters of 4%
Let \( x \) liters be the amount of 2% fat milk and \( 8 – x \) liters be the amount of 4% fat milk. The equation based on fat content is:
<br /> 0.02x + 0.04(8 - x) = 0.03 \times 8 \\<br /> 0.02x + 0.32 - 0.04x = 0.24 \\<br /> -0.02x = -0.08 \\<br /> x = 4<br />
Therefore, 3 liters of 2% fat milk and 5 liters of 4% fat milk are needed.

(25) A hardware store has two types of nails: one that is 2 inches long and another that is 3 inches long. How many pounds of each type of nail should be mixed to obtain 10 pounds of nails with an average length of 2.4 inches?

• (a) 4 pounds of 2 inches and 6 pounds of 3 inches
• (b) 3 pounds of 2 inches and 7 pounds of 3 inches
• (c) 5 pounds of 2 inches and 5 pounds of 3 inches
• (d) 6 pounds of 2 inches and 4 pounds of 3 inches

Answer

Correct Answer: (c) 5 pounds of 2 inches and 5 pounds of 3 inches
Let \( x \) pounds be the amount of 2-inch nails and \( 10 – x \) pounds be the amount of 3-inch nails. The equation based on average length is:
<br /> (2x) + (3(10 - x)) = 2.4 \times 10 \\<br /> 2x + 30 - 3x = 24 \\<br /> -x = -6 \\<br /> x = 6<br />
Therefore, 5 pounds of 2-inch nails and 5 pounds of 3-inch nails are needed.