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Problem-solving with ratio & algebra practice questions with answers

Foundation and Higher · Grade 6

A second set of problem-solving with ratio & algebra questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

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Question 1 Easy

5 pens and 5 pencils cost £30. A pen costs £2 more than a pencil. Find the cost of a pencil.

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Answer: 2

  1. Five pens add 5 × £2 = £10 extra.
  2. Subtract extra: £30 - £10 = £20 for 10 items, so 20 / 10 = 2.
  • Method (1): Five pens add 5 × £2 = £10 extra.
  • Accuracy (1): Subtract extra: £30 - £10 = £20 for 10 items, so 20 / 10 = 2.

Question 2 Easy

2 pens and 2 pencils cost £10. A pen costs £1 more than a pencil. Find the cost of a pencil.

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Answer: 2

  1. Two pens add 2 × £1 = £2 extra.
  2. Subtract extra: £10 - £2 = £8 for 4 items, so 8 / 4 = 2.
  • Method (1): Two pens add 2 × £1 = £2 extra.
  • Accuracy (1): Subtract extra: £10 - £2 = £8 for 4 items, so 8 / 4 = 2.

Question 3 Medium

Share £60 in the ratio 1:4. Find the larger share.

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Answer: 48

  1. Total parts: 1 + 4 = 5 parts. One part is 60 / 5 = 12.
  2. Larger share is 4 parts: 4 × 12 = 48.
  • Method (1): Total parts: 1 + 4 = 5 parts. One part is 60 / 5 = 12.
  • Accuracy (1): Larger share is 4 parts: 4 × 12 = 48.

Question 4 Medium

Share £45 in the ratio 2:3. Find the larger share.

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Answer: 27

  1. Total parts: 2 + 3 = 5 parts. One part is 45 / 5 = 9.
  2. Larger share is 3 parts: 3 × 9 = 27.
  • Method (1): Total parts: 2 + 3 = 5 parts. One part is 45 / 5 = 9.
  • Accuracy (1): Larger share is 3 parts: 3 × 9 = 27.

Question 5 Hard

3 adults and 2 children cost £31. A child costs £5. Find the cost of an adult ticket.

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Answer: 7

  1. Cost of 2 children: 2 × 5 = £10.
  2. Remaining for 3 adults: 31 - 10 = £21, so 21 / 3 = 7.
  • Method (1): Cost of 2 children: 2 × 5 = £10.
  • Accuracy (1): Remaining for 3 adults: 31 - 10 = £21, so 21 / 3 = 7.

Question 6 Hard

4 adults and 2 children cost £38. A child costs £3. Find the cost of an adult ticket.

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Answer: 8

  1. Cost of 2 children: 2 × 3 = £6.
  2. Remaining for 4 adults: 38 - 6 = £32, so 32 / 4 = 8.
  • Method (1): Cost of 2 children: 2 × 3 = £6.
  • Accuracy (1): Remaining for 4 adults: 38 - 6 = £32, so 32 / 4 = 8.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Share £70 in the ratio 2:5. Work out the larger share.

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Answer: 50

  1. Total parts: 2 + 5 = 7.
  2. One part is 70 / 7 = £10.
  3. Multiply by larger part 5: 10 × 5 = 50.
  4. The larger share is £50.
  • Method (1): One part 70 / 7 = 10
  • Accuracy (1): Larger share 50

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

A pen that costs £1 more is a pencil plus

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A pen that costs £1 more is a pencil plus £1, inside the bill. £1, inside the bill.

Check 2

3 pens and 2 pencils cost £13. A pen costs £1 more. A pencil costs

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Three pens add £3, leaving £10 for 5 items, so £2. £2.

Check 3

4 pens and 4 pencils cost £24. A pen costs £2 more. A pencil costs

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Four pens add £8, leaving £16 for 8 items, so £2. £2, after removing the extra pounds.

Check 4

Bus fare share of £40 in the ratio 3:5. The larger part is

  1. £28
  2. £25
  3. £32
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£25 £25.

Check 5

Prize share of £48 in the ratio 1:2. The larger part is

  1. £25
  2. £32
  3. £28
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£32 £32.

Check 6

Class share of £36 in the ratio 2:7. The larger part is

  1. £32
  2. £28
  3. £25
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£28 £28.

Check 7

Younger of two people totalling 36, one twice the other, is

  1. 13
  2. 12
  3. 36
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12 12.

Check 8

Younger of a pair totalling 45, one twice the other, is

  1. 15
  2. 16
  3. 14
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15 15.

Check 9

Younger child in a total of 24, one twice the other, is

  1. 9
  2. 24
  3. 8
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8 8.

Check 10

Cafe bill: 2 adults and 3 children cost £28. A child costs £4. An adult costs

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3 children cost £12; 28 - 12 = 16; 16 / 2 = £8. £8.

Check 11

Trip bill: 3 adults and 2 children cost £31. A child costs £5. An adult costs

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2 children cost £10; 31 - 10 = 21; 21 / 3 = £7. £7.

Check 12

Add the ratio parts before you

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Add the ratio parts before you split the amount. split the amount.

Check 13

The larger share uses the larger number of

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The larger share uses the larger number of parts. parts.

Check 14

Younger plus twice the younger is three times the

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Younger plus twice the younger is three times the younger age. younger age.

Check 15

Remove the known child costs before you divide by the number of

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Remove the known child costs before you divide by the number of adults. adults.

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