Aptitude:Mixture and Alligation

(26) A perfume maker has two types of scents: one that is 15% floral and another that is 25% floral. How many milliliters of each type of scent should be mixed to obtain 40 milliliters of perfume that is 20% floral?

• (a) 20 mL of 15% and 20 mL of 25%
• (b) 15 mL of 15% and 25 mL of 25%
• (c) 10 mL of 15% and 30 mL of 25%
• (d) 25 mL of 15% and 15 mL of 25%

Answer

Correct Answer: (c) 10 mL of 15% and 30 mL of 25%
Let \( x \) milliliters be the amount of 15% floral scent and \( 40 – x \) milliliters be the amount of 25% floral scent. The equation based on floral content is:
<br /> 0.15x + 0.25(40 - x) = 0.20 \times 40 \\<br /> 0.15x + 10 - 0.25x = 8 \\<br /> -0.10x = -2 \\<br /> x = 20<br />
Therefore, 10 milliliters of 15% floral scent and 30 milliliters of 25% floral scent are needed.

(27) A chemist has two types of acids: one that is 10% sulfuric acid and another that is 30% sulfuric acid. How many liters of each type of acid should be mixed to obtain 15 liters of acid that is 20% sulfuric acid?

• (a) 10 liters of 10% and 5 liters of 30%
• (b) 6 liters of 10% and 9 liters of 30%
• (c) 8 liters of 10% and 7 liters of 30%
• (d) 12 liters of 10% and 3 liters of 30%

Answer

Correct Answer: (b) 6 liters of 10% and 9 liters of 30%
Let \( x \) liters be the amount of 10% sulfuric acid and \( 15 – x \) liters be the amount of 30% sulfuric acid. The equation based on sulfuric acid content is:
<br /> 0.10x + 0.30(15 - x) = 0.20 \times 15 \\<br /> 0.10x + 4.5 - 0.30x = 3 \\<br /> -0.20x = -1.5 \\<br /> x = 7.5<br />
Therefore, 6 liters of 10% sulfuric acid and 9 liters of 30% sulfuric acid are needed.

(28) A restaurant has two types of soups: one that is 15% salt and another that is 25% salt. How many liters of each type of soup should be mixed to obtain 8 liters of soup that is 20% salt?

• (a) 3 liters of 15% and 5 liters of 25%
• (b) 2 liters of 15% and 6 liters of 25%
• (c) 4 liters of 15% and 4 liters of 25%
• (d) 5 liters of 15% and 3 liters of 25%

Answer

Correct Answer: (c) 4 liters of 15% and 4 liters of 25%
Let \( x \) liters be the amount of 15% soup and \( 8 – x \) liters be the amount of 25% soup. The equation based on salt content is:
<br /> 0.15x + 0.25(8 - x) = 0.20 \times 8 \\<br /> 0.15x + 2 - 0.25x = 1.6 \\<br /> -0.10x = -0.4 \\<br /> x = 4<br />
Therefore, 4 liters of 15% soup and 4 liters of 25% soup are needed.

(29) A paint store has two types of paint: one that is 20% white and another that is 40% white. How many gallons of each type of paint should be mixed to obtain 5 gallons of paint that is 30% white?

• (a) 2 gallons of 20% and 3 gallons of 40%
• (b) 1 gallon of 20% and 4 gallons of 40%
• (c) 3 gallons of 20% and 2 gallons of 40%
• (d) 4 gallons of 20% and 1 gallon of 40%

Answer

Correct Answer: (c) 3 gallons of 20% and 2 gallons of 40%
Let \( x \) gallons be the amount of 20% paint and \( 5 – x \) gallons be the amount of 40% paint. The equation based on white content is:
<br /> 0.20x + 0.40(5 - x) = 0.30 \times 5 \\<br /> 0.20x + 2 - 0.40x = 1.5 \\<br /> -0.20x = -0.5 \\<br /> x = 2.5<br />
Therefore, 3 gallons of 20% paint and 2 gallons of 40% paint are needed.

(30) A farmer has two types of animal feed: one that is 10% protein and another that is 20% protein. How many kilograms of each type of feed should be mixed to obtain 15 kilograms of feed that is 15% protein?

• (a) 7.5 kg of 10% and 7.5 kg of 20%
• (b) 5 kg of 10% and 10 kg of 20%
• (c) 6 kg of 10% and 9 kg of 20%
• (d) 8 kg of 10% and 7 kg of 20%

Answer

Correct Answer: (c) 6 kg of 10% and 9 kg of 20%
Let \( x \) kilograms be the amount of 10% feed and \( 15 – x \) kilograms be the amount of 20% feed. The equation based on protein content is:
<br /> 0.10x + 0.20(15 - x) = 0.15 \times 15 \\<br /> 0.10x + 3 - 0.20x = 2.25 \\<br /> -0.10x = -0.75 \\<br /> x = 7.5<br />
Therefore, 6 kilograms of 10% feed and 9 kilograms of 20% feed are needed.