Percentage Problems – Civil Service Exam

Percentage Problems - Civil Service Exam

Overview of Solving Percentage Composition Problems

Percentage composition problems are a type of mathematical question where you calculate the proportion of a specific component within a mixture or total, expressed as a percentage. These problems often arise in chemistry, cooking, finance, and other practical fields.

Step-by-Step Guide to Solve Percentage Composition Problems

Identify the Components: Begin by determining the mass, volume, or quantity of each component in the mixture as well as the total mass, volume, or quantity of the mixture.
Write Down the Formula: The basic formula for finding the percentage of a component in a mixture is:
Part: This is the quantity of the component for which you are calculating the percentage.
- Total: This is the total quantity of all components in the mixture.
Substitute the Values: Replace “Part” and “Total” in the formula with the respective values identified in step 1.
Perform the Calculation: Execute the division followed by multiplication by 100 to convert the fraction into a percentage.
Interpret the Result: The result is the percentage that the specific component contributes to the overall mixture, reflecting its proportionate share.

Example Problem and Solution

Problem: A salad mix contains 300 grams of lettuce, 100 grams of tomatoes, and 50 grams of carrots. Calculate the percentage of tomatoes in the salad mix.

Solution:

Total mass of the salad mix:
Mass of tomatoes: 100 grams
Percentage of tomatoes:
$Thus, tomatoes make up about 22.22% of the salad mix.$

Common Mistakes to Avoid

Ignoring or Misidentifying Components: Ensure all components of the mixture are accounted for in the total.
Unit Mismatch: Ensure that all measurements are in the same units (e.g., all in grams or all in liters) before performing calculations.
Calculation Errors: Double-check calculations, especially the order of operations in the percentage formula.

Practice Test on Percentage Problems - Civil Service Exam

Question 1

Question:
A mixture of copper and tin consists of 18 kg of copper and 2 kg of tin. What percent of the mixture, by mass, is tin?

Choice A: 10%
Choice B: 11%
Choice C: 9%
Choice D: 12%
Answer: A
Solution:
Total mass of the mixture = 18 kg + 2 kg = 20 kg.
Percent of tin =

Question 2

Question:
A certain blend of spices contains 4 kg of turmeric and 1 kg of pepper. What percent of the blend, by mass, is pepper?

Choice A: 20%
Choice B: 25%
Choice C: 15%
Choice D: 30%
Answer: A
Solution:
Total mass of the blend = 4 kg + 1 kg = 5 kg.
Percent of pepper =

Question 3

Question:
A bag contains 30 kg of rice and 10 kg of beans. What percent of the bag’s contents, by mass, is beans?

Choice A: 25%
Choice B: 33%
Choice C: 20%
Choice D: 30%
Answer: A
Solution:
Total mass of the contents = 30 kg + 10 kg = 40 kg.
Percent of beans =

Question 4

Question:
A canister of mixed nuts contains 16 kg of almonds and 4 kg of walnuts. What percent of the canister, by mass, is walnuts?

Choice A: 15%
Choice B: 20%
Choice C: 25%
Choice D: 30%
Answer: B
Solution:
Total mass of the mixture = 16 kg + 4 kg = 20 kg.
Percent of walnuts =

Question 5

Question:
A container holds 28 liters of a solution composed of water and glycerin. If the glycerin accounts for 7 liters, what percent of the solution, by volume, is glycerin?

Choice A: 20%
Choice B: 25%
Choice C: 30%
Choice D: 35%
Answer: B
Solution:
Total volume of the solution = 28 liters.
Percent of glycerin =

6. If x is 150% of y, then y is what percent of x+y

Solution: x = 1.5y. y=n(x + y).

y=p(1.5y + y)

y=p(2.5y)

y/2.5y = p

1/2.5 = p

.4 = p

40% = p