PERCENTAGES. Junior Cert Revision

Transcription

1 PERCENTAGES Junior Cert Revision

2 2016 JCHL Paper 1 Question 1 (a) (i) A bus company increases the price of all of its tickets by 6%. Before the increase, the price of a ticket from Cork to Dublin was Find the price of this ticket after the increase. Find 106% of the price of the bus ticket. Alternate Method: = = Find 6% and add this onto the original price of the bus ticket = (ii) Six months later, the company reduces the price of this ticket back to Find the percentage decrease in the price of this ticket. Give your answer correct to one decimal place. First calculate the decrease needed by subtracting the costs Percentage Decrease = Decrease Original 100 = = 5.7%

3 2015 Sample JCHL Paper 1 Question 5 (a) A meal in a restaurant cost Jerry The price included VAT at 9%. Jerry wanted to know the price of the meal before the VAT was included. He calculated 9% of and subtracted it from the cost of the meal. Explain why Jerry will not get the correct answer using this method. He will not get the correct answer as 9% of the price after VAT is NOT the same as 9% of the price before VAT. Calculate each to illustrate why. Correct Method = 109% 0.28 = 1% = 100% When the price INCLUDES VAT let the price equal 100+VAT%. Then work backwards to find 100% (the price before VAT). 28 is the price before VAT. Jerry s Method = = 27.78

4 2015 Sample JCHL Paper 1 Question 5 (b) Suppose that the rate of VAT was 13.5% instead of 9%. How much would Jerry have paid for the meal in that case? = 109% 0.28 = 1% = 100% When the price INCLUDES VAT let the price equal 100+VAT%. Then work backwards to find 100% (the price before VAT). 28 is the price before VAT. Apply new VAT rate of 13.5% = Alternate Method: Find 13.5% and add this onto the price before VAT = = 31.78

5 2015 JCHL Paper 1 Question 2 (a) David weighs 88 kg. The average male triathlete of his height weighs 83 kg. If David aims to reach this weight, what percentage decrease is required? Give your answer correct to two decimal places. First calculate the decrease needed by subtracting the weights = 5 Percentage Decrease = Decrease Original = 5.68% 88

6 2015 JCHL Paper 1 Question 2 (b) Mary s house was worth Mary increased the value of her house by 15% by building a conservatory. She then increased its value by a further 10% by repaving the driveway. Find the total percentage increase in value = = = Calculate 115% of the value of the house and then 110% of that to see what the house is worth now. Calculate the increase in the value of the house. Percentage Increase = Increase Original = 26.5%

7 2013 JCHL Paper 1 Question 4 (a) The minimum wage per hour for different categories of workers is shown in the table. By law the Under 18 minimum wage is set at 70% of the minimum wage for an experienced adult worker. Verify that this is true for the rates shown in the table on the right = Just calculate 70% of We could multiply by: % Category Min. Wage per hour Experienced adult worker 8.65 Aged under Over 18 in first year of employment 6.92 Over 18 in second year of first employment 7.79 Source:

8 2013 JCHL Paper 1 Question 4 (b) The government has decided that it is going to reduce all minimum wage rates by 6%. Calculate the new minimum wage for an experienced adult worker, correct to two decimal places, after this reduction. Category Min. Wage per hour Experienced adult worker 8.65 Aged under Over 18 in first year of employment 6.92 Over 18 in second year of first employment 7.79 Source: = 8.13 Alternate Method: Find 6% and subtract this from the current minimum wage. Reducing by 6% is the same as finding 94% of the number = = 8.13

9 2013 JCHL Paper 1 Question 4 (c) John is an experienced adult worker. After the reduction he says If the minimum wage were to be increased by 6% then I would be back earning 8.65 per hour. Is John s statement correct? Explain your answer. No = 8.62 This is not as high as the original starting point. 6% of 8.65 is clearly not the same as 6% of 8.13!

10 2012 JCHL Paper 1 Question 3 (a) (i) The value of one euro against other currencies on a particular day is shown in the table below. Mary was going to America for a few months. She changed 1200 into US Dollars using the exchange rate in the table. How many dollars should she receive at this exchange rate? Currency Rate ( ) US Dollar Pound Sterling Lithuanian Litas Latvian Lats Polish Zloty = $ = $ JCHL Paper 1 Question 3 (a) (ii) The bank charged 3% commission on the transaction. How many dollars did she receive? Alternate Method: Find 3% and subtract this from the current minimum wage. $ = $ Subtracting 3% is the same as finding 97% of the number = =

11 2012 JCHL Paper 1 Question 3 (b) On returning to Ireland Mary had $3060. She changed this amount into euro. The bank again charged her 3% commission on the transaction. She received Find the exchange rate on that day, correct to two decimal places = 97% = 1% The amount she received was 97% of the amount that was converted (the bank kept 3%). Use this to try and find 100% (the original amount before commission) = 100% = 100% = 1.45 Exchange Rate = Dollar Amount Euro Amount 1 = $1.45

12 2012 JCHL Paper 1 Question 3 (c) David changed a certain amount of sterling into euro at the exchange rate in the table above. A few days later he again changed the same amount of sterling into euro at a different exchange rate. He received fewer euro this time. No commission was charged on these transactions. Write down one possible value for the exchange rate for the second transaction. 1 = = Anything greater than

13 2013 JCHL Paper 1 Question 1 (a) Adam got 24 marks from a total of 30 marks in a class test. What percentage mark did Adam get? = 80% 30

14 2011 JCHL Paper 1 Question 2 (a) A computer salesperson is paid an annual salary of He is also paid a commission of 4% on sales. Last year the salesperson earned Calculate the value of the sales. Calculate the amount of money that he earned on commission ,000 = 8,000 This amount is 4% of his total sales, so let it equal 4% and find 100%. 8,000 = 4% 8000 = 1% = 100% 4 200,000 = 100% The value of sales was 200,000

15 2010 JCHL Paper 1 Question 1 (a) The price of a litre of petrol on the 1st of August was The price on the 1st September was Calculate the percentage decrease over this period. First calculate the decrease by subtracting the prices = 0.03 Percentage Decrease = Decrease Original = 2.5%

16 2009 JCHL Paper 1 Question 1 (a) In a school library, 28% of the books are classified as fiction and the remainder as non-fiction. There are 3240 non-fiction books in the library. Find the number of books which are classified as fiction. Calculate the % of books that are non-fiction. Alternate Method: = 72% = 1% We can use the fact that 72% of the books is 3240 to find 28% of the books = 100% = 100% 3240 = 72% = 1% = 28% = 28% 1260 of the books are classified as fiction. There are 4500 books in total of the books are classified as fiction.

17 2008 JCHL Paper 1 Question 2 (c) (i) In 2006, the average costs of running a car for the year were as follows: road tax 485, petrol 1440, servicing 650 and insurance 425. What was the total cost of running the car in 2006? Sum all the costs to find the total cost

18 2008 JCHL Paper 1 Question 2 (c) (ii) In 2007, the petrol costs went up by 5%, the cost of servicing went up by 15% and the cost of insurance went down by 10%. Given that the total running costs increased by 4.6% in 2007, calculate the percentage (%) increase in the road tax for 2007, giving your answer correct to one decimal place. Find the new running costs. Petrol = 1512 Servicing = Insurance = Find 104.6% of 3000 for the 2007 running costs = 3138 Subtract the Petrol, Servicing and Insurance to find 2017 Road Tax Find the increase in Road Tax Percentage Increase = Increase Original = 2.3% 485