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Ratio and proportion for RRB Group D

Sharing money in a ratio, joining two ratios, finding a fourth or mean proportional, coins in a bag. Ratio questions in RRB Group D follow simple patterns. Think in "parts" and they become easy. Methods, worked examples and practice with solutions.

27 Sept 2026 6 min read

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In this guide
  1. Ratio basics
  2. Dividing an amount in a ratio
  3. Combining two ratios
  4. Proportion and proportionals
  5. Worked examples
  6. Common mistakes
  7. Practice set
  8. What to do next

A ratio compares two amounts of the same kind. The most useful way to think about it is as parts. In the ratio 3 : 5, one person has 3 parts and the other has 5 parts, so there are 8 parts in all. Once you know what one part is worth, every ratio question is just multiplication.

Ratio shows up on its own and inside other topics: ages, partnerships, mixtures, speeds and work. If you can find "one part" quickly, all of these become easier.

Ratio basics

  • A ratio a : b can be written as the fraction a/b.
  • Multiplying or dividing both terms by the same number does not change it. 12 : 18 = 2 : 3.
  • Both amounts must be in the same unit before you compare them. 50 paise : ₹2 is 50 : 200 = 1 : 4, not 50 : 2.
  • To compare two ratios, write them as fractions and cross-multiply. 3 : 4 and 5 : 7: 3 × 7 = 21 and 4 × 5 = 20, so 3 : 4 is bigger.

Dividing an amount in a ratio

To share an amount in the ratio a : b : c:

  1. Add the parts: a + b + c.
  2. One part = amount ÷ total parts.
  3. Multiply one part by each term.

Always check that the shares add back to the full amount.

Combining two ratios

If you know A : B and B : C, make the B numbers the same, then join them.

A : B = 3 : 4 and B : C = 2 : 5. Multiply the second ratio by 2 so B becomes 4: B : C = 4 : 10. Now A : B : C = 3 : 4 : 10.

When the B numbers don't divide into each other, multiply each ratio by the other's B term. The LCM and HCF guide helps here.

Proportion and proportionals

Four numbers a, b, c, d are in proportion when a : b = c : d. Then a × d = b × c (product of the outer terms = product of the inner terms).

TermMeaningFormula
Fourth proportional to a, b, ca : b = c : xx = b × c ÷ a
Third proportional to a, ba : b = b : xx = b² ÷ a
Mean proportional of a and ba : x = x : bx = √(a × b)

A few other terms that appear in options:

  • Duplicate ratio of a : b is a² : b².
  • Sub-duplicate ratio of a : b is √a : √b.
  • Inverse ratio of a : b is b : a.

Worked examples

Example 1: Share ₹2,400 in the ratio 5 : 3.

  • 5 + 3 = 8 parts; one part = 2,400 ÷ 8 = 300.
  • Shares: 5 × 300 = ₹1,500 and 3 × 300 = ₹900. Check: 1,500 + 900 = 2,400.

Example 2: A : B = 3 : 4 and B : C = 2 : 5. Find A : B : C.

  • Make B equal to 4: B : C = 4 : 10.
  • A : B : C = 3 : 4 : 10.

Example 3: Find the fourth proportional to 3, 5 and 12.

  • 5 × 12 ÷ 3 = 20. Check: 3 : 5 = 12 : 20, since 3 × 20 = 5 × 12 = 60.

Example 4: Find the mean proportional of 4 and 9.

  • √(4 × 9) = √36 = 6. Check: 4 : 6 = 6 : 9.

Example 5: What number must be added to both 5 and 9 so that the ratio becomes 3 : 4?

  • (5 + x) ÷ (9 + x) = 3 ÷ 4.
  • 4(5 + x) = 3(9 + x), so 20 + 4x = 27 + 3x, and x = 7.
  • Check: 12 : 16 = 3 : 4.

Example 6: A bag has ₹1, 50-paise and 25-paise coins in the ratio 1 : 2 : 4. The total value is ₹60. How many coins of each kind are there?

  • Take one "set" of 1, 2 and 4 coins. Its value = 1 × ₹1 + 2 × ₹0.50 + 4 × ₹0.25 = ₹3.
  • Number of sets = 60 ÷ 3 = 20.
  • Coins: 20 of ₹1, 40 of 50 paise, 80 of 25 paise.

Common mistakes

  • Dividing by the wrong number of parts (using 5 instead of 5 + 3 = 8).
  • Joining two ratios without making the middle term equal.
  • Comparing amounts in different units.
  • Mixing up the third and fourth proportionals.
  • Forgetting to give the actual amounts after finding "x".

Practice set

  1. Share ₹1,000 in the ratio 2 : 3.
  2. A : B = 2 : 3 and B : C = 4 : 5. Find A : B : C.
  3. Find the third proportional to 3 and 6.
  4. Find the mean proportional of 9 and 25.
  5. Two numbers are in the ratio 4 : 5 and add up to 270. Find them.
  6. Divide ₹3,600 among A, B and C in the ratio 2 : 3 : 4.
  7. What number must be subtracted from both 15 and 23 so that the ratio becomes 1 : 3?
  8. If A : B = 3 : 4, find (2A + B) : (A + 2B).

Answers:

  1. ₹400 and ₹600. 5 parts; one part = 200.
  2. 8 : 12 : 15. Make B = 12: A : B = 8 : 12 and B : C = 12 : 15.
  3. 12. 6² ÷ 3 = 36 ÷ 3.
  4. 15. √(9 × 25) = √225.
  5. 120 and 150. 9 parts; one part = 30.
  6. ₹800, ₹1,200 and ₹1,600. 9 parts; one part = 400.
  7. 11. (15 − x) ÷ (23 − x) = 1/3, so 45 − 3x = 23 − x and x = 11. Check: 4 : 12 = 1 : 3.
  8. 10 : 11. Put A = 3 and B = 4: (6 + 4) : (3 + 8).

What to do next

  • Solve ten "share in a ratio" questions and check each by adding the shares.
  • Practise five three-term ratio joins until you do them without writing.
  • Learn the proportionals table and test yourself on third versus fourth.
  • Use ratio again in problems on ages and averages.

A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Railway Recruitment Boards website .

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