AQA · Mathematics · 8300
GCSE Maths: Ratio: sharing the total
Ratio & Proportion · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Ratio: sharing the total (Corbettmaths Video 270), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the first step when sharing a total in a ratio?
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Add the parts of the ratio together to find the total number of parts.
When dividing £700 in the ratio 5:3:2, what is the total number of parts?
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10 parts (5 + 3 + 2 = 10).
When concrete is made by mixing cement, sand and gravel in the ratio 1:2:3, what fraction of the mixture is cement?
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1/6 of the mixture. There are 6 parts total (1+2+3), and cement is 1 part.
If the ratio of boys to girls in a class is 2:3, and Ben claims there are 28 students, why must Ben be wrong?
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Because 28 is not divisible by 5 (the total number of parts: 2+3). The number of students must be a multiple of 5.
If Sophie has 60 pencils and the ratio of sharpened to blunt pencils is 4:1, how many pencils are sharpened?
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48 pencils. There are 5 parts total (4+1), each part = 12 pencils, so sharpened = 4 × 12 = 48.
When dividing money in the ratio 2:3 and Molly receives £240 as the larger share, how much does Chris receive?
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£160. If Molly gets 3 parts = £240, then 1 part = £80, so Chris gets 2 parts = £160.
If Charlene and Danielle share money in ratio 2:3 and Danielle gets £25 more than Charlene, what is the value of one part?
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£25. The difference between 3 parts and 2 parts is 1 part, which equals £25.
If the ratio of girls to boys in a class is 2:3, what fraction of the class are girls?
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2/5 of the class. There are 5 parts total (2+3), and girls represent 2 parts.
If a carpet 240cm long is cut in the ratio 1:2:5, what is the length of the longest piece?
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150cm. There are 8 parts total (1+2+5), each part = 30cm, so the longest piece (5 parts) = 150cm.
If the ratio of boys to girls in a school is 4:5 and there are 220 boys, how many students attend the school?
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495 students. If 4 parts = 220, then 1 part = 55, so total (9 parts) = 495.
If Ed has 30 sweets and the ratio of red to yellow sweets is 2:3, how many red sweets does he have?
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12 red sweets. There are 5 parts total (2+3), each part = 6 sweets, so red = 2 × 6 = 12.
If the angles in a triangle are in the ratio 1 : 2 : 9, what is the size of the largest angle?
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135°. The angles sum to 180°. With ratio 1 : 2 : 9, the parts total 12. Each part is 15°, so the largest angle is 9 × 15° = 135°.
Three angles are in the ratio 2 : 3 : 5 and the smallest angle is 50°. What are the other two angles?
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75° and 125°. If the smallest (2 parts) is 50°, each part is 25°. So the other angles are 3 × 25° = 75° and 5 × 25° = 125°.
When given a ratio and the value of one quantity, what is the first step to find the other quantity?
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Divide the known value by its corresponding number in the ratio to find the value of one part.
A school sends French and German students in the ratio 1 : 3, with 21 German students. What is the total number of students this school sent?
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28 students. French: 7 (1 part), German: 21 (3 parts). Total: 7 + 21 = 28.
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