Aptitude:Mixture and Alligation

(1) A chemist has a 20% saline solution and a 60% saline solution. How many liters of each solution must be mixed together to make 10 liters of a 40% saline solution?

• (a) 2 liters of 20% and 8 liters of 60%
• (b) 3 liters of 20% and 7 liters of 60%
• (c) 5 liters of 20% and 5 liters of 60%
• (d) 6 liters of 20% and 4 liters of 60%

Answer

Correct Answer: (c) 5 liters of 20% and 5 liters of 60%
Let \( x \) liters be the amount of 20% solution and \( 10 – x \) liters be the amount of 60% solution. The equation based on the concentration of saline is:
0.20x + 0.60(10 - x) = 0.40 \times 10
0.20x + 6 - 0.60x = 4
-0.40x = -2
x = 5
Hence, 5 liters of 20% solution and 5 liters of 60% solution are needed.

(2) A winemaker has two wines: one that is 12% alcohol and another that is 20% alcohol. How much of each type of wine is needed to make 50 liters of a blend that is 16% alcohol?

• (a) 10 liters of 12% and 40 liters of 20%
• (b) 20 liters of 12% and 30 liters of 20%
• (c) 25 liters of 12% and 25 liters of 20%
• (d) 30 liters of 12% and 20 liters of 20%

Answer

Correct Answer: (b) 20 liters of 12% and 30 liters of 20%
Let \( y \) liters be the amount of 12% wine and \( 50 – y \) liters be the amount of 20% wine. The equation based on the alcohol percentage is:
<br /> [latex]0.12y + 0.20(50 - y) = 0.16 \times 50
0.12y + 10 - 0.20y = 8
-0.08y = -2
y = 25<br />
However, this does not match any option, indicating a calculation error. Recalculating:
<br /> 0.08y = 2 \\<br /> y = 25<br />
This suggests an error in the options provided, the correct mixture would be 25 liters of 12% and 25 liters of 20%.

(3) An alloy A is made by mixing two metals in the ratio 5:3 and alloy B is made by mixing the same metals in the ratio 1:2. If equal quantities of both alloys are melted to form a third alloy C, what will be the ratio of the two metals in alloy C?

• (a) 7:7
• (b) 6:8
• (c) 8:6
• (d) 9:5

Answer

Correct Answer: (a) 7:7
For alloy A, the quantity of the first metal for any equal part is 5/8 and for the second metal it is 3/8. For alloy B, the quantities are 1/3 and 2/3 respectively. For equal quantities of A and B, the combined ratio is:
<br /> [latex]\frac{5}{8} + \frac{1}{3} = \frac{15 + 8}{24} = \frac{23}{24}
\frac{3}{8} + \frac{2}{3} = \frac{9 + 16}{24} = \frac{25}{24}
[/latex]
Simplifying the ratio of the first metal to the second in alloy C gives us 23:25. This suggests an error in the options provided, as the correct ratio is not listed.

(4) A trader mixes two types of rice, one costing $3 per kg and the other costing $5 per kg, to create a 10 kg mixture costing $4 per kg. How many kilograms of each type of rice does the trader mix?

• (a) 3 kg of $3 rice and 7 kg of $5 rice
• (b) 5 kg of $3 rice and 5 kg of $5 rice
• (c) 7 kg of $3 rice and 3 kg of $5 rice
• (d) 8 kg of $3 rice and 2 kg of $5 rice

Answer

Correct Answer: (b) 5 kg of $3 rice and 5 kg of $5 rice
Let \( x \) kilograms be the amount of $3 rice and \( 10 - x \) kilograms be the amount of $5 rice. The equation based on the cost is:
<br /> 3x + 5(10 - x) = 4 \times 10 \\<br /> 3x + 50 - 5x = 40 \\<br /> -2x = -10 \\<br /> x = 5<br />
Hence, 5 kg of $3 rice and 5 kg of $5 rice are needed.

(5) A container has 40 liters of milk with 4% fat, and another container has 30 liters of milk with 6% fat. How many liters of each type of milk must be mixed to create a 50-liter mixture with 5% fat?

• (a) 20 liters of 4% fat milk and 30 liters of 6% fat milk
• (b) 24 liters of 4% fat milk and 26 liters of 6% fat milk
• (c) 25 liters of 4% fat milk and 25 liters of 6% fat milk
• (d) 28 liters of 4% fat milk and 22 liters of 6% fat milk

Answer

Correct Answer: (b) 24 liters of 4% fat milk and 26 liters of 6% fat milk
Let \( y \) liters be the amount of 4% fat milk and \( 50 - y \) liters be the amount of 6% fat milk. The equation based on the fat percentage is:
<br /> 0.04y + 0.06(50 - y) = 0.05 \times 50 \\<br /> 0.04y + 3 - 0.06y = 2.5 \\<br /> -0.02y = -0.5 \\<br /> y = 25<br />
Hence, 24 liters of 4% fat milk and 26 liters of 6% fat milk are needed.