Measurement, Money and Time Depth Set 2
Measurement, Money and Time Depth Set 2 continues to combine measures, money and time in harder multi-step problems, including best-buy comparisons between different pack sizes, timetable problems that cross midnight, and problems that combine a percentage change with a measurement or price. It follows on from Measurement, Money and Time Depth.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a best-buy comparison, convert every option to the same unit price, such as cost per kilogram or cost per litre, before comparing.
- For timetable and duration problems, work in minutes throughout a calculation and only convert back to hours and minutes at the very end.
- When a problem combines measures, money and time in one scenario, identify which quantity the question is actually asking for and work towards only that, ignoring irrelevant information.
- For a percentage applied to a measurement or price, find the percentage of the amount first using the standard percentage method, then add or subtract it as required.
- Break the problem into a numbered sequence of smaller calculations, completing them strictly in order since later steps usually depend on earlier results.
- Sense-check your final answer against the scale of the numbers in the question, and make sure it carries the correct unit (minutes, pounds, litres, and so on).
Worked example
Shop A sells a 750 g bag of rice for 2.40 pounds. Shop B sells a 1.2 kg bag of the same rice for 3.60 pounds. Which shop offers the better value per kilogram?
- Convert Shop A's mass to kilograms: 750 g = 0.75 kg.
- Find Shop A's price per kilogram: 2.40 / 0.75 = 3.20 pounds per kg.
- Find Shop B's price per kilogram: 3.60 / 1.2 = 3.00 pounds per kg.
- Compare the two prices per kilogram: 3.00 pounds is less than 3.20 pounds.
- Shop B offers the better value, since its rice costs less per kilogram.
Practice questions
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Q1A 500 ml bottle of juice costs 1.20 pounds. A 2 litre bottle costs 4.00 pounds. Which is better value per litre?Show answer
Answer: The 2 litre bottle (2.00 pounds per litre, compared with 2.40 pounds per litre for the 500 ml bottle)
Q2A train departs at 22:40 and the journey takes 1 hour 35 minutes. What time does it arrive?Show answer
Answer: 00:15 the next day
Q3A price of 84 pounds is increased by 15%, then the new price is reduced by 10%. Find the final price.Show answer
Answer: 86.94 pounds (84 x 1.15 = 96.60, then 96.60 x 0.9 = 86.94)
Q4A parking charge is 45p for every 20 minutes. A driver parks for 3 hours. Calculate the total cost using the 20-minute rate, and state whether it would have been cheaper to pay a 3.50 pound flat fee for the day.Show answer
Answer: 4.05 pounds using the 20-minute rate (9 x 45p); the 3.50 pound flat fee would have been cheaper
Q5A recipe for 4 people needs 300 g of pasta. How much pasta, in kg, is needed for 10 people, keeping the ratio the same?Show answer
Answer: 0.75 kg (300 / 4 = 75 g per person, then 75 x 10 = 750 g)
Q6A cinema screening starts at 19:50 and the film plus adverts last 2 hours 25 minutes. If the last bus home leaves at 22:30, does the person miss the bus?Show answer
Answer: No; the screening ends at 22:15, which is before the bus leaves at 22:30
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A 400 g jar of coffee costs 5.60 pounds. A 650 g jar of the same coffee costs 8.45 pounds. Which jar offers better value per 100 g, and by how much?
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A coach leaves the school at 07:55 and the journey to the museum takes 1 hour 48 minutes, including a 15-minute stop at a service station. (a) Calculate the coach's actual driving time, excluding the stop. (b) Calculate the time the coach arrives at the museum.
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Amir earns 8.40 pounds per hour. He works 6 hours on Saturday and receives a 20% bonus on his usual rate for working a bank holiday on Monday, also for 6 hours. (a) Calculate his pay for working on Saturday. (b) Calculate his hourly rate on the bank holiday, including the bonus. (c) Calculate his total pay for both days.
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Free printable worksheet
Want more practice on paper? Download the measurement, money and time depth set 2 worksheet pack - 11 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 11 of 11+ Maths Workbook 3, the whole course as one free printable PDF.
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