Percentage Increase and Decrease in Word Problems
Percentage increase and decrease in word problems means applying a percentage change to a real-life situation, such as a price rise, a discount, a population change or interest on savings, and includes questions with successive changes such as a rise followed by a fall. It builds directly on core percentage skills but focuses on setting up the right calculation from a worded scenario, including the common trap that a percentage increase followed by an equal decrease does not return to the original amount.
Method
- Read the problem carefully to identify whether the amount is increasing or decreasing, and by what percentage.
- Decide whether to find the change amount separately and add or subtract it, or use a single multiplier, such as x1.15 for a 15% increase.
- For successive percentage changes, such as a rise then a fall, apply each multiplier in turn to the running total, never by adding the percentages together.
- Remember that increasing an amount by a percentage and then decreasing the new amount by the same percentage does not return you to the original value.
- Underline exactly what the question asks for at the end, since word problems often ask for the amount of change itself, not the new total, or the other way round.
- Check the answer's direction matches the context: an increase should give a bigger number, and a decrease should give a smaller one.
Worked example
A gym membership costs 40 pounds a month. The gym increases the price by 15%, then six months later decreases the new price by 10%. Work out the final monthly price.
- Find the price after the 15% increase using the multiplier 1.15: 40 x 1.15 = 46.
- Find the price after the 10% decrease using the multiplier 0.90, applied to the new price of 46: 46 x 0.90.
- Work out the multiplication: 46 x 0.90 = 41.40.
- Final answer: the final monthly price is 41.40 pounds.
Practice questions
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Q1A town's population of 8000 increases by 5%. Work out the new population.Show answer
Answer: 8400 (8000 x 1.05)
Q2A car worth 12,000 pounds decreases in value by 25%. Work out its new value.Show answer
Answer: 9000 pounds (12,000 x 0.75)
Q3A 60-pound coat has its price increased by 30%, then the new price is reduced by 30%. Work out the final price, and state whether it is the same as the original 60 pounds.Show answer
Answer: 54.60 pounds (60 x 1.3 = 78, then 78 x 0.7 = 54.60); it is not the same as the original 60 pounds
Q4A savings account of 500 pounds earns 4% interest in a year. Work out the amount in the account after one year.Show answer
Answer: 520 pounds (500 x 1.04)
Q5A company's profit falls from 250,000 pounds to 220,000 pounds. Express the fall as a percentage decrease of the original profit.Show answer
Answer: 12% (a fall of 30,000, and 30,000 / 250,000 = 0.12)
Q6True or False: increasing an amount by 50% and then decreasing the result by 50% returns you to the original amount.Show answer
Answer: False
Q7Explain why a 20% increase followed by a 20% decrease does not return an amount to its original value.Show answer
Answer: The second percentage change, the 20% decrease, is calculated on the new, larger amount rather than on the original amount, so a bigger absolute amount is taken away than was added, leaving a final value lower than the starting amount.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A laptop's price of 720 pounds is reduced by 15% in a sale. Calculate the sale price.
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In January, a small business had 40,000 pounds in revenue. Revenue increased by 25% in February, then fell by 10% in March. (a) Calculate the revenue in February. (b) Calculate the revenue in March. (c) Calculate the overall percentage change from January to March.
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Free printable worksheet
Want more practice on paper? Download the percentage increase and decrease in word problems worksheet pack - 4 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 44 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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