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About Ratio & Proportion — Class 7 ICSE

Apply ratio and proportion concepts to solve real-world problems including direct and inverse variation. This topic is part of the ICSE Class 7 mathematics syllabus (chapter: Chapter 7). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Ratio & Proportion

  • Understanding Ratios
  • Proportion
  • Direct Proportion
  • Inverse Proportion
  • Unitary Method & Word Problems

Interactive lesson · about 20 minutes · checkpoint question after every unit

Ratio & Proportion — solved examples for Class 7 ICSE

Example 1easy

What is the ratio of 4 to 8?
  1. A)1 : 2
  2. B)2 : 1
  3. C)1 : 4
  4. D)4 : 1

Step-by-step solution

  1. The ratio of 4 to 8 is written as 4 : 8.
  2. Divide both by HCF (4):
    4:8=4/4:8/4=1:24 : 8 = 4/4 : 8/4 = 1 : 2

Answer: 1 : 2

Example 2medium

The ratio of two numbers is 5 : 8 and their sum is 78. Find the two numbers.
  1. A)30 and 48
  2. B)35 and 43
  3. C)25 and 53
  4. D)40 and 38

Step-by-step solution

  1. Total parts = 5 + 8 = 13
  2. One part = 78 / 13 = 6
  3. First number = 5 x 6 = 30
    First=5x6=30First = 5 x 6 = 30
  4. Second number = 8 x 6 = 48
    Second=8x6=48Second = 8 x 6 = 48

Answer: 30 and 48

Example 3hard

The ratio of two numbers is 3 : 5. If 8 is added to each number, the new ratio becomes 13 : 19. Find the original numbers.
  1. A)18 and 30
  2. B)15 and 25
  3. C)9 and 15
  4. D)12 and 20

Step-by-step solution

  1. Let the numbers be 3k and 5k.
  2. After adding 8:
    (3k+8)/(5k+8)=13/19(3k + 8) / (5k + 8) = 13 / 19
  3. Cross multiply:
    19(3k+8)=13(5k+8)19(3k + 8) = 13(5k + 8)
  4. 57k + 152 = 65k + 104, so 48 = 8k, giving k = 6
  5. Numbers: 3 x 6 = 18 and 5 x 6 = 30. Verify: (18+8)/(30+8) = 26/38 = 13/19
    Numbers=18and30Numbers = 18 and 30

Answer: 18 and 30

Practice questions on Ratio & Proportion

  1. Q1.easy

    Express the ratio 15 : 25 in its simplest form.
    1. A)3 : 5
    2. B)5 : 3
    3. C)1 : 5
    4. D)15 : 25
    Show answer

    Answer: 3 : 5

    Hint: Find the HCF of 15 and 25 first.

  2. Q2.easy

    There are 12 boys and 18 girls in a class. What is the ratio of boys to girls in simplest form?
    1. A)2 : 3
    2. B)3 : 2
    3. C)12 : 18
    4. D)4 : 6
    Show answer

    Answer: 2 : 3

    Hint: Write the ratio as 12 : 18 and then simplify by dividing by the HCF.

  3. Q3.easy

    Which of the following ratios is equivalent to 2 : 5?
    1. A)4 : 10
    2. B)3 : 6
    3. C)5 : 2
    4. D)6 : 12
    Show answer

    Answer: 4 : 10

    Hint: Multiply both parts of 2 : 5 by the same number to get an equivalent ratio.

  4. Q4.medium

    Find the mean proportion between 4 and 16.
    1. A)8
    2. B)10
    3. C)6
    4. D)12
    Show answer

    Answer: 8

    Hint: The mean proportion of a and c is the number b such that a : b = b : c, so b = sqrt(a x c).

  5. Q5.medium

    If 12 workers can build a wall in 10 days, how many days will 15 workers take to build the same wall?
    1. A)8 days
    2. B)12 days
    3. C)6 days
    4. D)9 days
    Show answer

    Answer: 8 days

    Hint: More workers means fewer days. Total work = 12 x 10 = 120 worker-days.

  6. Q6.medium

    Rs 560 is divided among three friends A, B, and C in the ratio 2 : 3 : 3. How much does B receive?
    1. A)Rs 210
    2. B)Rs 140
    3. C)Rs 200
    4. D)Rs 180
    Show answer

    Answer: Rs 210

    Hint: Total parts = 2 + 3 + 3 = 8. Find one part first.

  7. Q7.hard

    Rs 3600 is to be divided among A, B, and C such that A gets twice as much as B and B gets three times as much as C. How much does A get?
    1. A)Rs 2160
    2. B)Rs 1080
    3. C)Rs 360
    4. D)Rs 1800
    Show answer

    Answer: Rs 2160

    Hint: Express everything in terms of C. If C = x, then B = 3x and A = 6x.

  8. Q8.hard

    The ratio of pocket money of Sita and Gita is 4 : 5. If Sita gets Rs 80 more, the ratio becomes 6 : 5. Find the original pocket money of each.
    1. A)Sita: Rs 160, Gita: Rs 200
    2. B)Sita: Rs 200, Gita: Rs 250
    3. C)Sita: Rs 240, Gita: Rs 300
    4. D)Sita: Rs 120, Gita: Rs 150
    Show answer

    Answer: Sita: Rs 160, Gita: Rs 200

    Hint: Let Sita = 4k and Gita = 5k. After increase: (4k + 80) / 5k = 6/5.

  9. Q9.hard

    Find the mean proportion between 9 and 25.
    1. A)15
    2. B)17
    3. C)12
    4. D)20
    Show answer

    Answer: 15

    Hint: Mean proportion of a and c is sqrt(a x c).

These are 9 of the 60 questions available for Ratio & Proportion. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.