Aptitude:Mixture and Alligation

(16) A painter has two cans of paint: one with 5 liters of red paint and another with 3 liters of blue paint. How many liters of each color should be mixed to create 7 liters of purple paint?

• (a) 4 liters of red and 3 liters of blue
• (b) 3 liters of red and 4 liters of blue
• (c) 2 liters of red and 5 liters of blue
• (d) 1 liter of red and 6 liters of blue

Answer

Correct Answer: (c) 2 liters of red and 5 liters of blue
Let \( x \) liters be the amount of red paint and \( 7 – x \) liters be the amount of blue paint. The equation based on the mixture is:
<br /> \frac{5}{8}x + \frac{3}{8}(7 - x) = 0 \\<br /> 5x + 21 - 3x = 0 \\<br /> 2x = -21 \\<br /> x = -10.5<br />
Therefore, 2 liters of red paint and 5 liters of blue paint are needed to create 7 liters of purple paint.

(17) A chef has two types of cooking oil: one that is 20% saturated fat and another that is 30% saturated fat. How many liters of each type of oil should be mixed to obtain 10 liters of cooking oil with 25% saturated fat?

• (a) 6 liters of 20% and 4 liters of 30%
• (b) 5 liters of 20% and 5 liters of 30%
• (c) 4 liters of 20% and 6 liters of 30%
• (d) 3 liters of 20% and 7 liters of 30%

Answer

Correct Answer: (c) 4 liters of 20% and 6 liters of 30%
Let \( x \) liters be the amount of 20% saturated fat oil and \( 10 – x \) liters be the amount of 30% saturated fat oil. The equation based on saturated fat content is:
<br /> 0.20x + 0.30(10 - x) = 0.25 \times 10 \\<br /> 0.20x + 3 - 0.30x = 2.5 \\<br /> -0.10x = -0.5 \\<br /> x = 5<br />
Therefore, 4 liters of 20% saturated fat oil and 6 liters of 30% saturated fat oil are needed to obtain 10 liters of cooking oil with 25% saturated fat.

(18) A florist has two types of flower bouquets: one that contains 8 red roses and another that contains 5 white roses. How many of each type of bouquet should be mixed to create 13 bouquets with 6 red roses each?

• (a) 7 bouquets with 8 red roses and 6 bouquets with 5 white roses
• (b) 6 bouquets with 8 red roses and 7 bouquets with 5 white roses
• (c) 5 bouquets with 8 red roses and 8 bouquets with 5 white roses
• (d) 4 bouquets with 8 red roses and 9 bouquets with 5 white roses

Answer

Correct Answer: (c) 5 bouquets with 8 red roses and 8 bouquets with 5 white roses
Let \( x \) be the number of bouquets with 8 red roses and \( 13 – x \) be the number of bouquets with 5 white roses. The equation based on the number of red roses is:
<br /> 8x + 5(13 - x) = 6 \times 13 \\<br /> 8x + 65 - 5x = 78 \\<br /> 3x = 13 \\<br /> x = \frac{13}{3}<br />
Therefore, 5 bouquets with 8 red roses and 8 bouquets with 5 white roses should be mixed to create 13 bouquets with 6 red roses each.

(19) A store has two types of nuts: one that costs $8 per pound and another that costs $12 per pound. In what ratio should these nuts be mixed to create a blend costing $10 per pound?

• (a) 1:2
• (b) 2:1
• (c) 3:1
• (d) 1:3

Answer

Correct Answer: (c) 3:1
Let \( x \) be the amount of $8 per pound nuts and \( y \) be the amount of $12 per pound nuts. The equation based on cost is:
<br /> 8x + 12y = 10(x + y) \\<br /> 8x + 12y = 10x + 10y \\<br /> 2y = 2x \\<br /> y = x<br />
Therefore, the nuts should be mixed in a ratio of 3:1, with 3 pounds of $8 per pound nuts and 1 pound of $12 per pound nuts.

(20) A farmer has two types of animal feed: one that contains 15% protein and another that contains 20% protein. How many kilograms of each type of feed should be mixed to obtain 8 kilograms of feed with 18% protein?

• (a) 4 kg of 15% and 4 kg of 20%
• (b) 3 kg of 15% and 5 kg of 20%
• (c) 2 kg of 15% and 6 kg of 20%
• (d) 5 kg of 15% and 3 kg of 20%

Answer

Correct Answer: (c) 2 kg of 15% and 6 kg of 20%
Let \( x \) kilograms be the amount of 15% protein feed and \( 8 – x \) kilograms be the amount of 20% protein feed. The equation based on protein content is:
<br /> 0.15x + 0.20(8 - x) = 0.18 \times 8 \\<br /> 0.15x + 1.6 - 0.20x = 1.44 \\<br /> -0.05x = -0.16 \\<br /> x = 3.2<br />
Therefore, 2 kilograms of 15% protein feed and 6 kilograms of 20% protein feed should be mixed to obtain 8 kilograms of feed with 18% protein.