Let’s solve each question step-by-step.

Question 11

Problem: A mixture of 40 liters of milk and water contains 10% water. How much water should be added so that water may be 20% in the new mixture?

1. Initial water amount: 10% of 40 liters = 0.1 * 40 = 4 liters.
2. Amount of milk: 40 - 4 = 36 liters.
3. Let $x$ be the additional water to be added. In the new mixture, total water will be $4 + x$, and total volume will be $40 + x$.
4. Setting up the equation for 20% water in the new mixture: $\frac{4 + x}{40 + x} = 0.2$
5. Solving for $x$: $4 + x = 0.2(40 + x)$ $4 + x = 8 + 0.2x$ $0.8x = 4$ $x = 5$

Answer: $b. \, 5$

Question 12

Problem: One liter of water is evaporated from 6 liters of a solution containing 5% salt. The percentage of salt in the remaining solution is:

1. Initial salt amount: 5% of 6 liters = 0.05 * 6 = 0.3 liters.
2. New volume after evaporation: 6 - 1 = 5 liters.
3. New salt percentage: $\frac{0.3}{5} \times 100 = 6\%$

Answer: $c. \, 6$

Question 13

Problem: To a sugar solution of 3 liters containing 40% sugar, one liter of water is added. The percentage of sugar in the solution is:

1. Initial sugar amount: 40% of 3 liters = 0.4 * 3 = 1.2 liters.
2. New total volume: 3 + 1 = 4 liters.
3. New sugar percentage: $\frac{1.2}{4} \times 100 = 30\%$

Answer: $c. \, 30$

Question 14

Problem: The quantity of water (in ml) needed to reduce 9 ml shaving lotion containing 50% alcohol to a lotion containing 30% alcohol is:

1. Initial alcohol amount: 50% of 9 ml = 0.5 * 9 = 4.5 ml.
2. Let $x$ be the amount of water to be added. New total volume will be $9 + x$.
3. Setting up the equation for 30% alcohol in the new mixture: $\frac{4.5}{9 + x} = 0.3$
4. Solving for $x$: $4.5 = 0.3(9 + x)$ $4.5 = 2.7 + 0.3x$ $1.8 = 0.3x$ $x = 6$

Answer: $c. \, 6$

Would you like further clarification on any question? Here are five additional related questions to practice:

1. If 50 liters of a solution has 30% acid, how much water should be added to reduce the concentration to 20%?
2. A 10-liter solution has 2 liters of salt. What percentage of the solution is salt?
3. How much pure alcohol should be added to 20 liters of a 40% alcohol solution to make it 50%?
4. If 5 liters of a 60% sugar solution is diluted by adding 2 liters of water, what is the new percentage of sugar?
5. A 15-liter solution has 10% alcohol. If 3 liters evaporate, what is the percentage of alcohol in the remaining solution?

Tip: To solve problems involving mixture percentages, carefully set up equations based on initial and final concentrations and solve for the unknown.