Ratio Problems: Sharing, Changing and Combining · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Sharing by ratio

Mathematics · Ratio & Proportion · ages 14-15
Name ______________________   Date ____________

  1. Three friends share £90 in the ratio 1:2:3. What is the largest share in pounds?

    Answer: ______________

  2. Two people share money in the ratio 2:3 and the smaller share is £24. What is the total?

    • £60
    • £36
    • £48
    • £72

  3. Two people share money in ratio 2 to 3 and the smaller share is 24 pounds. What is the total?

    • 60 pounds
    • 48 pounds
    • 72 pounds

  4. Three friends share 90 pounds in ratio 1 to 2 to 3. What is the largest share in pounds?

    Answer: ______________

  5. You know a:b = 1:2 and b:c = 3:4. If b = 6, what is a + c?

    Answer: ______________

  6. Two friends share in ratio 3 to 2 and the larger share is 36 pounds. What is the smaller share?

    • 18 pounds
    • 24 pounds
    • 30 pounds

  7. You know a:b = 2:3 and b:c = 4:5. What is the combined ratio a:b:c?

    • 2:3:5
    • 6:9:10
    • 2:7:5
    • 8:12:15

  8. Combining a:b = 2:3 with b:c = 4:5 gives a:b:c = 2:3:5 by copying the numbers across. Is this right?

    Circle one:   True   False

  9. A 3 to 2 split of 50 pounds gives 30 and 20. The first person receives 10 more from outside. What is the new ratio?

    • 3 to 2
    • 4 to 3
    • 2 to 1

  10. A paint mix uses red and white in the ratio 2:5. If it uses 14 litres of red, how many litres of white does it use?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Sharing by ratio W1-mt_vJelayH4uv-s1

  1. 45 · 6 parts share £90, so one part is £15, and 3 parts make £45.
  2. £60 · One part is £24 / 2 = £12, and 5 parts make £60.
  3. 60 pounds · One part is 12 pounds, and 5 parts make 60.
  4. 45 · Six parts share 90, so one part is 15 and three parts make 45.
  5. 11 · a is half of b (3) and c is 4/3 of b (8), so a + c = 11.
  6. 24 pounds · One part is 12 pounds, and 2 parts make 24.
  7. 8:12:15 · Scale so b matches: b needs 12, giving a = 8 and c = 15.
  8. False · It is wrong: b must match in both, and 3 does not equal 4, so scaling to 8:12:15 is needed.
  9. 2 to 1 · The shares become 40 and 20, which simplifies to 2 to 1.
  10. 35 · One part is 14/2 = 7 litres, and 5 parts make 35 litres.
Worksheet · LightMySky