6 Percentage Decrease Problems
6 Percentage Decrease Problems
Problem 1: Price Decrease
Problem: The price of a laptop is $1200. If it decreases by 15%, find the new price.
Solution:
- Identify the given values:
- Original Price = $1200
- Percentage Decrease = 15%
- Calculate New Price:
- New Price = Original Price × (1 - Decrease%/100)
- New Price = 1200 × (1 - 15/100)
- New Price = 1200 × 0.85 = $1020
Answer:
- New Price = $1020
Explanation:
- A percentage decrease reduces the original value by a fraction.
- The multiplier (1 - Decrease%/100) accounts for the remaining value after the decrease.
Problem 2: Population Decline
Problem: A city’s population is 50,000. It decreases by 10% due to migration. Find the new population.
Solution:
- Identify the given values:
- Original Population = 50,000
- Percentage Decrease = 10%
- Calculate New Population:
- New Population = Original Population × (1 - Decrease%/100)
- New Population = 50,000 × (1 - 10/100)
- New Population = 50,000 × 0.9 = 45,000
Answer:
- New Population = 45,000
Explanation:
- The population decreases by 10% of its original size, calculated using the percentage decrease formula.
- The result is the new population after the decline.
Problem 3: Salary Reduction
Problem: An employee’s salary is $3000 per month. Due to budget cuts, it decreases by 8%. Find the new salary.
Solution:
- Identify the given values:
- Original Salary = $3000
- Percentage Decrease = 8%
- Calculate New Salary:
- New Salary = Original Salary × (1 - Decrease%/100)
- New Salary = 3000 × (1 - 8/100)
- New Salary = 3000 × 0.92 = $2760
Answer:
- New Salary = $2760
Explanation:
- The salary reduction is calculated by multiplying the original salary by (1 - Decrease%/100).
- This gives the new salary after the cut.
Problem 4: Find Original Value
Problem: After a 20% decrease, the price of a phone is $80. Find the original price.
Solution:
- Identify the given values:
- New Price = $80
- Percentage Decrease = 20%
- Relate New Price to Original Price:
- New Price = Original Price × (1 - Decrease%/100)
- 80 = Original Price × (1 - 20/100)
- 80 = Original Price × 0.8
- Solve for Original Price:
- Original Price = 80 / 0.8
- Original Price = $100
Answer:
- Original Price = $100
Explanation:
- The new price is 80% of the original price. Divide by 0.8 to find the original price.
- This reverses the percentage decrease.
Problem 5: Calculate Percentage Decrease
Problem: The weight of a person decreased from 80 kg to 72 kg. Find the percentage decrease.
Solution:
- Identify the given values:
- Original Weight = 80 kg
- New Weight = 72 kg
- Calculate Decrease:
- Decrease = Original Weight - New Weight
- Decrease = 80 - 72 = 8 kg
- Calculate Percentage Decrease:
- Percentage Decrease = (Decrease / Original Weight) × 100
- Percentage Decrease = (8 / 80) × 100 = 10%
Answer:
- Percentage Decrease = 10%
Explanation:
- The percentage decrease is the decrease divided by the original value, expressed as a percentage.
- This shows the relative change in weight.
Problem 16: Successive Decreases
Problem: A product’s price is $200. It decreases by 10% in the first month and 5% in the second month. Find the final price.
Solution:
- Identify the given values:
- Original Price = $200
- First Decrease = 10%
- Second Decrease = 5%
- Calculate Price after First Decrease:
- Price after first decrease = 200 × (1 - 10/100)
- = 200 × 0.9 = $180
- Calculate Price after Second Decrease:
- Final Price = 180 × (1 - 5/100)
- = 180 × 0.95 = $171
Alternative Method:
- Final Price = Original Price × (1 - First Decrease%/100) × (1 - Second Decrease%/100)
- = 200 × 0.9 × 0.95 = $171
Answer:
- Final Price = $171
Explanation:
- Successive percentage decreases are applied sequentially, multiplying by each decrease factor.
- The alternative method combines both decreases in one step.
Problem 7: Decrease to Match a Target
Problem: A retailer wants to decrease the price of an item from $150 to $120. Find the percentage decrease required.
Solution:
- Identify the given values:
- Original Price = $150
- New Price = $120
- Calculate Decrease:
- Decrease = Original Price - New Price
- Decrease = 150 - 120 = $30
- Calculate Percentage Decrease:
- Percentage Decrease = (Decrease / Original Price) × 100
- Percentage Decrease = (30 / 150) × 100 = 20%
Answer:
- Percentage Decrease = 20%
Explanation:
- The percentage decrease is calculated to determine how much the original price must fall to reach the target.
- The formula gives the relative decrease needed.
Problem 8: Decrease in Area
Problem: The side of a square is decreased by 10%. Find the percentage decrease in its area.
Solution:
- Identify the given values:
- Percentage Decrease in Side = 10%
- Relate Side Decrease to Area:
- Let original side = s
- Original Area = s²
- New Side = s × (1 - 10/100) = s × 0.9
- New Area = (0.9s)² = 0.81s²
- Calculate Percentage Decrease in Area:
- Decrease in Area = Original Area - New Area = s² - 0.81s² = 0.19s²
- Percentage Decrease = (Decrease / Original Area) × 100
- = (0.19s² / s²) × 100 = 19%
Answer:
- Percentage Decrease in Area = 19%
Explanation:
- The area of a square is proportional to the square of its side. A 10% decrease in side results in a (0.9)² = 0.81 factor decrease in area.
- The percentage decrease is calculated relative to the original area.
Problem 9: Decrease with Fractional Percentage
Problem: A stock price of $500 decreases by 12.5%. Find the new stock price.
Solution:
- Identify the given values:
- Original Price = $500
- Percentage Decrease = 12.5%
- Calculate New Price:
- New Price = Original Price × (1 - Decrease%/100)
- New Price = 500 × (1 - 12.5/100)
- New Price = 500 × 0.875 = $437.50
Answer:
- New Stock Price = $437.50
Explanation:
- Fractional percentages are handled the same way as whole percentages in the formula.
- The new price reflects the original price minus the decrease.
Problem 10: Repeated Decrease
Problem: A value of 200 decreases by 10% each year for 2 years. Find the final value.
Solution:
- Identify the given values:
- Original Value = 200
- Percentage Decrease per Year = 10%
- Time = 2 years
- Calculate Value after First Year:
- Value after Year 1 = 200 × (1 - 10/100)
- = 200 × 0.9 = 180
- Calculate Value after Second Year:
- Final Value = 180 × (1 - 10/100)
- = 180 × 0.9 = 162
Alternative Method:
- Final Value = Original Value × (1 - Decrease%/100)^n
- = 200 × (0.9)^2
- = 200 × 0.81 = 162
Answer:
- Final Value = 162
Explanation:
- Repeated percentage decreases are compounded, similar to compound interest but with a reduction factor.
- The formula (1 - Decrease%/100)^n accounts for multiple decreases.
Key Concepts Summary:
- Percentage Increase:
- New Value = Original Value × (1 + Increase%/100)
- Percentage Increase = [(New Value - Original Value) / Original Value] × 100
- Used for price hikes, population growth, salary raises, etc.
- Percentage Decrease:
- New Value = Original Value × (1 - Decrease%/100)
- Percentage Decrease = [(Original Value - New Value) / Original Value] × 100
- Used for discounts, population decline, salary cuts, etc.
- Successive Changes: Multiply factors (1 ± %/100) for each change.
- Area Changes: For squares, % change in area = [(1 ± %/100)^2 - 1] × 100.
- Finding Original Value: Divide new value by (1 ± %/100).
- Fractional Percentages: Treat as decimals (e.g., 7.5% = 0.075).
Comments
Post a Comment