Aptitude:Mixture and Alligation

(11) A baker has two types of flour: one that costs $2 per kilogram and another that costs $3 per kilogram. In what ratio should these flours be mixed to get a blend costing $2.40 per kilogram?

• (a) 3:2
• (b) 2:3
• (c) 4:1
• (d) 1:4

Answer

Correct Answer: (c) 4:1
Let \( x \) be the amount of the $2 per kilogram flour and \( y \) be the amount of the $3 per kilogram flour. The equation based on cost is:
<br /> 2x + 3y = 2.40(x + y) \\<br /> 2x + 3y = 2.40x + 2.40y \\<br /> 0.60y = 0.40x \\<br /> 3y = 2x \\<br /> y = \frac{2}{3}x<br />
The ratio of \( x \) to \( y \) is 1:4, which simplifies to 4:1.

(12) A jeweler has two types of gold: one that is 18 karats and another that is 24 karats. How many grams of each type of gold should be mixed to obtain 30 grams of gold that is 20 karats?

• (a) 12g of 18 karats and 18g of 24 karats
• (b) 15g of 18 karats and 15g of 24 karats
• (c) 9g of 18 karats and 21g of 24 karats
• (d) 10g of 18 karats and 20g of 24 karats

Answer

Correct Answer: (c) 9g of 18 karats and 21g of 24 karats
Let \( x \) grams be the amount of 18 karats gold and \( 30 – x \) grams be the amount of 24 karats gold. The equation based on karats is:
<br /> \frac{18}{20}x + \frac{24}{20}(30 - x) = 20 \\<br /> \frac{18}{20}x + \frac{720 - 24x}{20} = 20 \\<br /> 18x + 720 - 24x = 400 \\<br /> -6x = -320 \\<br /> x = 53.\overline{3}<br />
Therefore, 9 grams of 18 karats gold and 21 grams of 24 karats gold are needed.

(13) A car rental company has two types of cars: economy cars and luxury cars. The rental cost for an economy car is $30 per day, and for a luxury car is $80 per day. How many days should a customer rent each type of car to spend a total of $200 on rental costs for 5 days?

• (a) 3 days of economy and 2 days of luxury
• (b) 4 days of economy and 1 day of luxury
• (c) 2 days of economy and 3 days of luxury
• (d) 5 days of economy and 0 days of luxury

Answer

Correct Answer: (b) 4 days of economy and 1 day of luxury
Let \( x \) be the number of days for an economy car and \( y \) be the number of days for a luxury car. The equation based on total cost is:
<br /> 30x + 80y = 200 \\<br /> 3x + 8y = 20<br />
One possible solution is \( x = 4 \) and \( y = 1 \), which corresponds to renting an economy car for 4 days and a luxury car for 1 day, totaling $200 in rental costs for 5 days.

(14) A chef has two types of spices: one that is 10% salt and another that is 40% salt. How many grams of each type of spice should be mixed to obtain 200 grams of a spice blend that is 20% salt?

• (a) 80g of 10% and 120g of 40%
• (b) 100g of 10% and 100g of 40%
• (c) 120g of 10% and 80g of 40%
• (d) 60g of 10% and 140g of 40%

Answer

Correct Answer: (b) 100g of 10% and 100g of 40%
Let \( x \) grams be the amount of 10% spice and \( 200 – x \) grams be the amount of 40% spice. The equation based on salt content is:
<br /> 0.10x + 0.40(200 - x) = 0.20 \times 200 \\<br /> 0.10x + 80 - 0.40x = 40 \\<br /> -0.30x = -40 \\<br /> x = 100<br />
Therefore, 100 grams of 10% spice and 100 grams of 40% spice are needed.

(15) A coffee shop has two types of coffee beans: one that costs $6 per pound and another that costs $12 per pound. In what ratio should these beans be mixed to create a blend costing $9 per pound?

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

Answer

Correct Answer: (c) 1:1
Let \( x \) be the amount of $6 per pound coffee beans and \( y \) be the amount of $12 per pound coffee beans. The equation based on cost is:
<br /> 6x + 12y = 9(x + y) \\<br /> 6x + 12y = 9x + 9y \\<br /> 3y = 3x \\<br /> y = x<br />
The ratio of \( x \) to \( y \) is 1:1.