Percentages: Practice Set 4
Percentages: Practice Set 4 focuses on reverse percentage problems, where a final amount after a percentage change is given and the original amount must be found, together with percentage profit and loss questions from a shop or business context. It follows on from Percentages: Practice Set 3 and leads towards combined percentage and ratio problems.
Method
- For a reverse percentage problem, first identify what percentage of the original amount the given final amount represents, remembering that an increase gives more than 100% and a decrease gives less than 100%.
- Divide the given final amount by that percentage to find the value of 1%, then multiply by 100 to find the original amount.
- For a profit or loss question, find the profit or loss first by subtracting the cost price from the selling price, or the selling price from the cost price for a loss.
- To find percentage profit or loss, write the profit or loss as a fraction of the original cost price, then convert that fraction to a percentage.
- Be careful that percentage profit and loss are always calculated as a percentage of the cost price, not the selling price, unless the question states otherwise.
- Check a reverse percentage answer by applying the original percentage change to it and confirming you get back to the amount given in the question.
Worked example
A shop buys a bicycle for 120 pounds and sells it for 156 pounds. Calculate the percentage profit.
- Find the profit: selling price minus cost price, 156 - 120 = 36 pounds.
- Write the profit as a fraction of the cost price: 36/120.
- Convert this fraction to a percentage by multiplying by 100: 36/120 x 100.
- Work out 36/120 x 100 = 30.
- The percentage profit is 30%.
Practice questions
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Q1A shop buys a lamp for 40 pounds and sells it for 52 pounds. Find the percentage profit.Show answer
Answer: 30% (profit = 12 pounds, 12/40 x 100 = 30)
Q2A jacket bought for 80 pounds is sold at a loss for 68 pounds. Find the percentage loss.Show answer
Answer: 15% (loss = 12 pounds, 12/80 x 100 = 15)
Q3After a 20% increase, a number becomes 108. Find the original number.Show answer
Answer: 90 (108 / 1.2)
Q4After a 30% decrease, a price becomes 42 pounds. Find the original price.Show answer
Answer: 60 pounds (42 / 0.7)
Q5A trader buys a batch of toys for 250 pounds in total and sells them all for 325 pounds. Find the percentage profit.Show answer
Answer: 30% (profit = 75 pounds, 75/250 x 100 = 30)
Q6A television is reduced in a sale to 340 pounds after a 15% discount. Find the original price.Show answer
Answer: 400 pounds (340 / 0.85)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A shop buys a set of headphones for 24 pounds and sells them for 33.60 pounds. Calculate the percentage profit.
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After a 12% increase, a price becomes 78.40 pounds. (a) Calculate the original price. (b) Calculate the amount of the increase, in pounds.
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A market trader buys 50 identical scarves for a total of 300 pounds. She sells 30 of them at 9 pounds each, and the remaining 20 at 7.50 pounds each. (a) Calculate her total sales revenue. (b) Calculate her total profit. (c) Calculate her percentage profit, based on the total cost of 300 pounds.
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Free printable worksheet
Want more practice on paper? Download the percentages: practice set 4 worksheet pack - 9 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 36 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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