Ratio and Proportion for SSC CGL: The Short Answer
A ratio compares two quantities of the same kind by division (a : b = a/b), and a proportion says two ratios are equal (a : b = c : d, so a × d = b × c). For SSC CGL, almost every ratio question is solved by writing the quantities as multiples of one unknown (3k and 5k), forming one equation, and solving for k. The four ideas you need are: dividing in a ratio, combining ratios (A:B:C), proportionals (fourth, third, mean), and "add or subtract the same number" questions.
Key takeaway for SSC: Ratio and proportion gives about 1 to 2 direct questions in SSC CGL Tier 1, and the same method drives partnership, mixture, ages, income-expenditure and coin questions. Learn the formula table, the A:B:C trick and the "k method". Every answer in this note was checked in Python.
Ratio work feeds directly into our mixture and alligation and partnership notes, so it is worth getting this foundation right.
What Is Ratio and Proportion? (Meaning with Examples)
- Ratio: a : b, where a is the antecedent and b is the consequent. Both quantities must be in the same unit. 50 paise : ₹2 = 50 : 200 = 1 : 4.
- Proportion: a : b :: c : d. Here a and d are the extremes, b and c are the means. Product of extremes = product of means.
- Continued proportion: a : b = b : c, so b² = a × c.
A ratio does not change if both terms are multiplied or divided by the same non-zero number: 6 : 9 = 2 : 3 = 10 : 15.
Ratio and Proportion Formulas for SSC CGL (Complete List)
| Concept | Formula / rule |
|---|---|
| Divide N in ratio a : b | First = N × a/(a + b), second = N × b/(a + b) |
| Divide N in ratio a : b : c | Each = N × part/(a + b + c) |
| Proportion a : b :: c : d | a × d = b × c |
| Fourth proportional to a, b, c | d = (b × c)/a |
| Third proportional to a, b | c = b²/a |
| Mean proportional between a, b | √(a × b) |
| Compounded ratio of a : b and c : d | ac : bd |
| Duplicate ratio of a : b | a² : b² |
| Sub-duplicate ratio of a : b | √a : √b |
| Triplicate ratio of a : b | a³ : b³ |
| Sub-triplicate ratio of a : b | ∛a : ∛b |
| Inverse (reciprocal) ratio of a : b | b : a (or 1/a : 1/b) |
| A : B = a : b and B : C = c : d | A : B : C = ac : bc : bd |
| Componendo–dividendo | If a/b = c/d, then (a + b)/(a − b) = (c + d)/(c − d) |
Ratio and Proportion Tricks for SSC CGL (with Solved Examples)
Trick 1: Dividing an amount in a ratio
Q. Divide ₹1,560 between Asha and Bina in the ratio 5 : 7. Total parts = 12; one part = 130. Asha = ₹650, Bina = ₹910.
Q. Two numbers are in the ratio 3 : 4 and their sum is 84. Find them. One part = 84 ÷ 7 = 12. Numbers = 36 and 48.
Trick 2: Combining ratios (A : B : C)
If A : B = 2 : 3 and B : C = 4 : 5, make B equal in both. Multiply the first ratio by 4 and the second by 3: A : B = 8 : 12 and B : C = 12 : 15, so A : B : C = 8 : 12 : 15.
Quick pattern: write the ratios one under the other and cross-multiply.
| A | B | C | |
|---|---|---|---|
| A : B | 2 | 3 | |
| B : C | 4 | 5 | |
| Result | 2 × 4 = 8 | 3 × 4 = 12 | 3 × 5 = 15 |
Trick 3: Fourth, third and mean proportional
- Fourth proportional to 4, 10, 6: d = (10 × 6)/4 = 15.
- Third proportional to 9 and 12: c = 12²/9 = 16.
- Mean proportional between 9 and 16: √(9 × 16) = 12.
Notice 9, 12, 16 are in continued proportion (9 : 12 = 12 : 16 = 3 : 4).
Trick 4: Adding or subtracting the same number
Q. What number must be added to both terms of 5 : 9 to make it 3 : 4? (5 + x)/(9 + x) = 3/4 → 20 + 4x = 27 + 3x → x = 7. Option check is often faster: try each option in (5 + x) : (9 + x) and see which gives 3 : 4. With x = 7: 12 : 16 = 3 : 4. ✔
Trick 5: Compound, duplicate and sub-duplicate ratios
- Compounded ratio of 2 : 3 and 4 : 5 = 8 : 15.
- Duplicate ratio of 3 : 4 = 9 : 16.
- Sub-duplicate ratio of 25 : 36 = 5 : 6.
- Triplicate ratio of 2 : 3 = 8 : 27.
Trick 6: Fractional ratios
To divide in the ratio 1/2 : 1/3 : 1/4, multiply by the LCM of the denominators (12): 6 : 4 : 3.
Q. Divide ₹2,600 among A, B and C in the ratio 1/2 : 1/3 : 1/4. 6 : 4 : 3 → 13 parts, one part = 200. A = ₹1,200, B = ₹800, C = ₹600.
Income and Expenditure Ratio Questions (SSC CGL Favourite)
Write Income − Expenditure = Savings for each person using k-multiples.
Q. The incomes of Ravi and Sohan are in the ratio 4 : 5 and their expenditures are in the ratio 3 : 4. Each saves ₹6,000. Find their incomes. Let incomes be 4x and 5x, expenditures 3y and 4y. 4x − 3y = 6,000 and 5x − 4y = 6,000. Subtracting: x − y = 0, so x = y. Then 4x − 3x = 6,000 → x = 6,000. Incomes = ₹24,000 and ₹30,000 (expenditures ₹18,000 and ₹24,000).
Q. The salaries of A and B are in the ratio 3 : 5. Each gets an increment of ₹4,000 and the ratio becomes 2 : 3. Find their salaries. (3k + 4,000)/(5k + 4,000) = 2/3 → 9k + 12,000 = 10k + 8,000 → k = 4,000. Salaries = ₹12,000 and ₹20,000.
Coins Ratio Questions (₹1, 50 paise, 25 paise)
Multiply the number ratio by the value of each coin to get the value ratio.
Q. A bag has ₹1, 50 paise and 25 paise coins in the ratio 3 : 4 : 8. The total value is ₹168. How many coins of each type are there? Value of one "set" = 3 × 1 + 4 × 0.5 + 8 × 0.25 = 3 + 2 + 2 = ₹7. Number of sets = 168 ÷ 7 = 24. Coins = 3 × 24 = 72 coins of ₹1, 4 × 24 = 96 coins of 50 paise, 8 × 24 = 192 coins of 25 paise.
Ages in Ratio Questions (Past and Future Ratios)
Ages questions are ratio questions in disguise: the difference between two ages never changes, so write both ages as multiples of k and shift both by the same number of years.
Q. The ages of Meera and her brother are in the ratio 5 : 3. After 6 years the ratio will be 7 : 5. Find their present ages. (5k + 6)/(3k + 6) = 7/5 → 25k + 30 = 21k + 42 → 4k = 12 → k = 3. Present ages = 15 years and 9 years. Check: after 6 years, 21 : 15 = 7 : 5. ✔
Shortcut: the difference in ratio terms must match. Now the difference is 5 − 3 = 2 parts; later it is 7 − 5 = 2 parts. Since the differences are already equal, one part means the same in both ratios. Each term grows by 2 parts (5 → 7 and 3 → 5), so 2 parts = 6 years, one part = 3 years, ages = 15 and 9. This "equal difference" trick works whenever the two ratio differences are equal; if they are not, scale one ratio first.
Mixture Ratio Questions (Adding Water or Milk)
The quantity you do not add stays constant. Use it as the anchor.
Q. 40 litres of a mixture has milk and water in the ratio 7 : 3. How much water must be added to make the ratio 7 : 5? Milk = 28 L, water = 12 L. Milk stays 28, so the new water must be 20 L. Water to add = 8 litres.
For replacement and alligation problems, use the method in our mixture and alligation note.
How to Solve Ratio and Proportion Questions Quickly (Step-by-Step Method)
- Convert units so both terms are in the same unit (paise and rupees, minutes and hours).
- Write each quantity as a multiple of k (3k, 5k).
- Form one equation from the extra condition (sum, difference, new ratio after change).
- Solve for k and multiply back.
- Use option testing for "add or subtract the same number" questions; it is usually faster than algebra.
- Anchor the unchanged quantity in mixture and income questions.
Common Mistakes in Ratio and Proportion Questions
- Comparing quantities in different units (paise vs rupees).
- Combining A : B and B : C without first making B equal.
- In coin questions, using the number ratio as the value ratio.
- Writing the third proportional of a and b as a²/b instead of b²/a.
- Adding the same number to only one term.
- In mixture questions, changing the quantity that was not added.
Quick Revision Table: Ratio and Proportion Shortcuts
| Situation | Shortcut |
|---|---|
| Split N in a : b | N × a/(a + b) |
| A : B and B : C | Equalise B, then join |
| Fourth proportional | bc/a |
| Third proportional | b²/a |
| Mean proportional | √ab |
| Fractional ratio | Multiply by LCM of denominators |
| Same number added | Test options or cross-multiply |
| Coins | Value of one set = Σ (count × coin value) |
| Mixture (add water) | Keep milk fixed |
| Income – expenditure | Income − expense = savings for each |
Ratio and Proportion Questions for SSC CGL (Practice Set with Answers)
- Divide ₹720 in the ratio 4 : 5. Answer: ₹320 and ₹400.
- If A : B = 3 : 4 and B : C = 5 : 6, find A : B : C. Answer: 15 : 20 : 24. Make B = 20 in both.
- Find the fourth proportional to 12, 18 and 27. Answer: 40.5. (18 × 27)/12.
- Find the mean proportional between 16 and 25. Answer: 20. √400.
- What number must be subtracted from both 7 and 11 to make the ratio 3 : 5? Answer: 1. 6 : 10 = 3 : 5.
- Find the third proportional to 5 and 25. Answer: 125. 25²/5.
- A purse has ₹1, 50 paise and 25 paise coins in the ratio 5 : 6 : 8, worth ₹300 in all. How many 25 paise coins are there? Answer: 240. One set = 5 + 3 + 2 = ₹10; 30 sets; 8 × 30 = 240.
- The monthly incomes of two persons are in the ratio 5 : 7. Each pays ₹1,500 as rent and the amounts left are in the ratio 5 : 8. Find their incomes. Answer: ₹4,500 and ₹6,300. (5k − 1,500)/(7k − 1,500) = 5/8 gives k = 900.
- Divide ₹2,600 among three people in the ratio 1/2 : 1/3 : 1/4. What does the second person get? Answer: ₹800. 6 : 4 : 3, one part = 200.
- 60 litres of a mixture has milk and water in the ratio 2 : 1. How much water must be added to make the ratio 1 : 2? Answer: 60 litres. Milk 40 L stays; water must become 80 L, so add 60 L.
Test these patterns under time in the SSC CGL Ratio, Proportion and Mixture Mock Test 01.
Ratio and Proportion FAQs
What is the difference between ratio and proportion?
A ratio compares two quantities (3 : 5). A proportion states that two ratios are equal (3 : 5 :: 6 : 10). In a proportion, the product of the extremes equals the product of the means.
How do you find the mean proportional?
The mean proportional between a and b is √(a × b). For 9 and 16 it is 12.
What is the formula for the third proportional?
The third proportional to a and b is b²/a. For 9 and 12 it is 144/9 = 16.
How do you combine two ratios like A : B and B : C?
Make the common term B equal in both ratios by multiplying, then write A : B : C. For A : B = 2 : 3 and B : C = 4 : 5, the answer is 8 : 12 : 15.
What is the duplicate ratio of 3 : 4?
9 : 16. A duplicate ratio squares both terms; a sub-duplicate ratio takes their square roots.
How many questions come from ratio and proportion in SSC CGL?
Usually 1 to 2 direct questions in SSC CGL Tier 1 quant, plus several questions in other topics (partnership, ages, mixture, time and work) that use the same ratio method.
Practice Next
- Mock tests: SSC CGL Ratio, Proportion and Mixture Mock Test 01, SSC CGL Quant Mini Mock Test 02 and SSC CHSL Quant Mini Mock Test 01.
- Related notes: mixture and alligation questions for bank exams, partnership questions for bank exams, age problems for bank exams and profit and loss tricks for SSC CGL, plus speed time and distance tricks for SSC CGL, LCM and HCF tricks for SSC CGL.
- Exam details: SSC CGL 2026 and SSC CHSL 2026.
- Browse all study notes.