AQA · Mathematics · 8300

GCSE Maths: Ratio: solving problems 1

Ratio & Proportion · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Ratio: solving problems 1 (Corbettmaths Video 271), 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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  1. A triangle has interior angles in the ratio 1:3:8. What is the size of the largest angle?

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    120°. The angles sum to 180°, so 1+3+8 = 12 parts. Each part is 15°, and the largest angle is 8 × 15° = 120°.

  2. There are between 30 and 40 sweets shared in the ratio 4:5 with none remaining. How many sweets are there?

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    36 sweets. The ratio 4:5 means 9 parts total; the only multiple of 9 between 30 and 40 is 36.

  3. Victoria receives £6.60 from money shared in the ratio 2:5 (Isaac:Victoria). How much does Isaac receive?

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    £2.64. Victoria's 5 parts equal £6.60, so one part is £1.32. Isaac's 2 parts equal 2 × £1.32 = £2.64.

  4. The ratio children:adults visiting a library is 1:4, with 1,935 total visitors. How many more adults than children visited?

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    1,161 more adults. 5 parts total; each part is 387. Children = 387, adults = 1,548. Difference = 1,161.

  5. A pentagon has interior angles in the ratio 1:2:5:5:7. What is the size of the largest angle?

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    189°. Interior angles of a pentagon sum to 540°. Total parts = 20, so each part is 27°. Largest angle = 7 × 27° = 189°.

  6. Two numbers are in the ratio 3:7 and one number is 42. What are the two possible values for the other number?

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    18 and 98. If 42 is the larger part (7 parts), each part is 6, so the other is 3 × 6 = 18. If 42 is the smaller part (3 parts), each part is 14, so the other is 7 × 14 = 98.

  7. Copper and zinc are mixed in the ratio 4:1 to make brass. If copper costs £5/kg and zinc costs £3.20/kg, what is the cost of 7 kg of brass?

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    £32.48. For 5 parts total: 4 kg copper costs £20, 1 kg zinc costs £3.20; 5 kg brass costs £23.20. 7 kg costs (7/5) × £23.20 = £32.48.

  8. The ratio 25,000,000,000 : 500 can be written as n : 1. What is n in standard form?

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    5 × 10⁷. Divide both sides by 500: n = 25,000,000,000 ÷ 500 = 50,000,000 = 5 × 10⁷.

  9. Point N divides line AB in the ratio AN:NB = 2:1, where A is (3, 20) and B is (15, 2). What are the coordinates of N?

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    (11, 8). N is 2/3 of the way from A to B. x = 3 + (2/3)(15-3) = 3 + 8 = 11; y = 20 + (2/3)(2-20) = 20 - 12 = 8.

  10. A cone has radius 4 cm and height 9 cm; a sphere has radius 6 cm. What is the ratio of the cone's volume to the sphere's volume in simplest form?

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    1:6. Cone volume = (1/3)πr²h = (1/3)π(16)(9) = 48π. Sphere volume = (4/3)πr³ = (4/3)π(216) = 288π. Ratio = 48π:288π = 1:6.

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