Aptitude:Mixture and Alligation

(31) A perfume store has two types of fragrances: one that is 15% rose scent and another that is 30% rose scent. How many milliliters of each type of fragrance should be mixed to obtain 40 milliliters of fragrance that is 20% rose scent?

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

Answer

Correct Answer: (b) 20 ml of 15% and 20 ml of 30%
Let \( x \) milliliters be the amount of 15% fragrance and \( 40 – x \) milliliters be the amount of 30% fragrance. The equation based on rose scent content is:
<br /> 0.15x + 0.30(40 - x) = 0.20 \times 40 \\<br /> 0.15x + 12 - 0.30x = 8 \\<br /> -0.15x = -4 \\<br /> x = 20<br />
Therefore, 20 milliliters of 15% fragrance and 20 milliliters of 30% fragrance are needed.

(32) A gardener has two types of soils: one that is 40% clay and another that is 60% clay. How many kilograms of each type of soil should be mixed to obtain 12 kilograms of soil that is 50% clay?

• (a) 6 kg of 40% and 6 kg of 60%
• (b) 5 kg of 40% and 7 kg of 60%
• (c) 4 kg of 40% and 8 kg of 60%
• (d) 7 kg of 40% and 5 kg of 60%

Answer

Correct Answer: (c) 4 kg of 40% and 8 kg of 60%
Let \( x \) kilograms be the amount of 40% soil and \( 12 – x \) kilograms be the amount of 60% soil. The equation based on clay content is:
<br /> 0.40x + 0.60(12 - x) = 0.50 \times 12 \\<br /> 0.40x + 7.2 - 0.60x = 6 \\<br /> -0.20x = -1.2 \\<br /> x = 6<br />
Therefore, 4 kilograms of 40% soil and 8 kilograms of 60% soil are needed.

(33) A perfume store has two types of fragrances: one that is 20% jasmine scent and another that is 40% jasmine scent. How many milliliters of each type of fragrance should be mixed to obtain 60 milliliters of fragrance that is 30% jasmine scent?

• (a) 30 ml of 20% and 30 ml of 40%
• (b) 20 ml of 20% and 40 ml of 40%
• (c) 15 ml of 20% and 45 ml of 40%
• (d) 25 ml of 20% and 35 ml of 40%

Answer

Correct Answer: (c) 15 ml of 20% and 45 ml of 40%
Let \( x \) milliliters be the amount of 20% fragrance and \( 60 – x \) milliliters be the amount of 40% fragrance. The equation based on jasmine scent content is:
<br /> 0.20x + 0.40(60 - x) = 0.30 \times 60 \\<br /> 0.20x + 24 - 0.40x = 18 \\<br /> -0.20x = -6 \\<br /> x = 30<br />
Therefore, 15 milliliters of 20% fragrance and 45 milliliters of 40% fragrance are needed.

(34) A candy store has two types of candies: one that is 30% chocolate and another that is 60% chocolate. How many grams of each type of candy should be mixed to obtain 100 grams of candy that is 40% chocolate?

• (a) 40g of 30% and 60g of 60%
• (b) 50g of 30% and 50g of 60%
• (c) 60g of 30% and 40g of 60%
• (d) 30g of 30% and 70g of 60%

Answer

Correct Answer: (b) 50g of 30% and 50g of 60%
Let \( x \) grams be the amount of 30% candy and \( 100 – x \) grams be the amount of 60% candy. The equation based on chocolate content is:
<br /> 0.30x + 0.60(100 - x) = 0.40 \times 100 \\<br /> 0.30x + 60 - 0.60x = 40 \\<br /> -0.30x = -20 \\<br /> x = 50<br />
Therefore, 50 grams of 30% candy and 50 grams of 60% candy are needed.

(35) A chef has two types of spices: one that is 10% salt and another that is 30% salt. How many grams of each type of spice should be mixed to obtain 120 grams of a spice blend that is 20% salt?

• (a) 40g of 10% and 80g of 30%
• (b) 60g of 10% and 60g of 30%
• (c) 80g of 10% and 40g of 30%
• (d) 30g of 10% and 90g of 30%

Answer

Correct Answer: (b) 60g of 10% and 60g of 30%
Let \( x \) grams be the amount of 10% spice and \( 120 – x \) grams be the amount of 30% spice. The equation based on salt content is:
<br /> 0.10x + 0.30(120 - x) = 0.20 \times 120 \\<br /> 0.10x + 36 - 0.30x = 24 \\<br /> -0.20x = -12 \\<br /> x = 60<br />
Therefore, 60 grams of 10% spice and 60 grams of 30% spice are needed.