Ratio & Proportion Tests — Pick a Level and Start
Tap a level to see every test in it. Level 1 is set at real SSC CGL difficulty — start there the day you finish the concept. Level 2 is pitched above the exam, to push accuracy under pressure.
Level 1 SSC CGL Level Checking… View tests
Same difficulty as the real SSC CGL paper — one idea per question. Dividing a total and reading off one share; joining two or three ratios into a single chain; a term found from one known member; a constant added to or taken away from both terms; two groups changing by different amounts; ratios written as fractions; mean, third and fourth proportional; continued proportion; componendo and dividendo; duplicate, sub-duplicate and compound ratios; direct, inverse and joint variation; ratios of areas and volumes; coins of three denominations; income, expenditure and savings; mixtures; transfers between two groups; and groups split two ways at once. A steady score here means the chapter is exam-ready.
Level 2 Above SSC CGL Level Checking… View tests
Harder than the exam asks, because every question chains two ideas or runs one backwards. A mean proportional that hands over the product while the stem hands over the sum; componendo and dividendo that returns 3a : 2b with the coefficients still to be stripped off; two savings running on two unrelated multipliers; a duplicate ratio that has to be built before a chain can be joined; a mixture combined and then diluted, or drawn off and replaced; a value ratio taken through a square or a cube; a chain fixed by a gap between its end terms; and a swap of two quantities that moves a bill by a stated fraction. Clear these and the real paper feels easy.
A ratio compares two quantities of the same kind and carries no units, which is why it travels so far in this syllabus. Write the quantities as 3k and 5k and a ratio stops being a comparison and becomes arithmetic: one unknown, one equation, and every share in the question expressed in the same part. A proportion is the statement that two ratios are equal, and it hands over exactly one usable fact — ad = bc, the product of the extremes equals the product of the means. Mean proportional, third proportional and fourth proportional are that one fact with a different term missing.
The marks go on two habits. The first is reading part to part correctly: 3 : 2 means 3 out of every 5, not 3 out of every 2, and the commonest lost mark in the chapter is a part-to-part ratio used as a fraction of the whole. The second is knowing what survives a change — multiplying every term by the same number leaves a ratio alone, while adding or subtracting the same amount from every term does not. Each test puts twenty-five ratio questions in front of you in one sitting, which is what makes those recurring shapes visible.
How Many Ratio and Proportion Questions Are Asked in SSC CGL?
Ratio is a near-certain question in both tiers, and its real weight is larger than its own count: partnership, average and mixture questions are all solved by turning the words into a ratio first.
| Chapter | Tier I (out of 25) | Tier II Paper I (out of 30) |
|---|---|---|
| Ratio & Proportion | 1–2 | 2–3 |
| Partnership | 0–1 | 1 |
| Average | 1–2 | 1–2 |
| Mixture & Alligation | 1 | 1–2 |
Counts vary by shift. A question that shares profit in the ratio of capital, or splits a total back out of an average, is counted in its own chapter above — but it is a ratio question in everything except its wording, which is why this chapter is worth clearing early.
What You Will Practice in the Ratio and Proportion Chapter
Core topics
- Dividing a total in a two-term or three-term ratio, and reading off one share or the gap between two
- Joining two or three ratios into one chain by matching the shared term
- Finding every member when one of them is known, or when a stated difference is given
- The same constant added to, or taken from, both terms of a ratio
- Two groups changing by different amounts — some joining, some leaving
- Ratios written as fractions or decimals, and clearing them to whole numbers
- Each term multiplied by its own factor, and the ratio of the reciprocals
- Mean proportional, third proportional and fourth proportional
- Continued proportion in three and four terms
- Componendo, dividendo, alternendo, invertendo and addendo
- Duplicate, sub-duplicate, triplicate and sub-triplicate ratios, and compound ratio
- Direct variation, inverse variation and joint variation, including squares and cubes
- A value that varies as the square or the cube of a weight, and what a break costs
- Ratios of areas, volumes, radii and heights in mensuration
- Coins of two or three denominations, by count and by value
- Income, expenditure and savings for one person or two
- Mixtures: combining two vessels, adding one ingredient, and drawing off and replacing
- Transfers and interchanges between two groups, and bills that move when quantities are swapped
- Groups classified two ways at once — sex against faculty, skill against grade
Formulas worth memorising
| Situation | Formula |
|---|---|
Dividing a total in a : b : c | one part = Total / (a + b + c) |
| A term's share of the whole | a / (a + b + c) of the total |
Proportion a : b = c : d | ad = bc — extremes = means |
Mean proportional between a and b | √(ab) |
Third proportional to a and b | b² / a |
Fourth proportional to a, b, c | bc / a |
Continued proportion a : b = b : c | b² = ac |
An opening ratio a : b continued | a² : ab : b² |
| Componendo & dividendo | (p+q)/(p−q) = m/n → p/q = (m+n)/(m−n) |
| Alternendo / invertendo | a:c = b:d / b:a = d:c |
| Addendo | a/b = c/d = (a+c)/(b+d) |
| Duplicate / sub-duplicate ratio | a² : b² / √a : √b |
| Triplicate / sub-triplicate ratio | a³ : b³ / ∛a : ∛b |
Compound ratio of a:b and c:d | ac : bd |
| Direct variation | y = kx, so y₁/x₁ = y₂/x₂ |
| Inverse variation | xy = k, so x₁y₁ = x₂y₂ |
| Joint variation | A = kB/C or A = kBC |
| Sum and difference given | larger = (S+D)/2, smaller = (S−D)/2 |
| Two numbers from a ratio and a difference | one part = D / (a − b) |
The middle rows are the ones to hold on to. Mean, third and fourth proportional are not three formulas but one — ad = bc with a different term missing each time — and every componendo question is that same equation rearranged.
The three mistakes that cost the most marks
- Reading a part-to-part ratio as a share of the whole.
3 : 2means 3 out of every 5, not 3 out of every 2;1 : 4means one in five. Almost every cross-classified question — boys and girls inside two faculties, men and women inside two grades — is set to catch exactly this. - Adding ratio terms across two groups of different sizes. If one shop sells 250 items in the ratio
3 : 2and another sells 270 in the ratio5 : 4, the overall ratio is not8 : 6. A part in the first shop is 50 items and a part in the second is 30, so both must become actual counts before anything is added. - Assuming a flat addition leaves a ratio alone. Multiplying every term by the same number keeps a ratio; adding or subtracting the same amount from every term does not. Rs 300 added to shares of
2 : 3 : 4makes them23 : 33 : 43, which is a flatter ratio — a common addition always pulls the terms closer together.
Solved Examples — SSC CGL Ratio and Proportion
A : B = 3 : 4 and B : C = 8 : 9, find A : B : C.A : B = 6 : 8. The chain is then 6 : 8 : 9, and no number divides all three. Hanging the 9 straight onto 3 : 4 to get 3 : 4 : 9 is the slip — the scaling has to happen before anything is attached. Answer: 6 : 8 : 93 : 5. When 10 is added to each, the ratio becomes 5 : 7. Find the smaller number.3k and 5k. Adding a constant changes the numbers but never k, so (3k + 10)/(5k + 10) = 5/7. Cross-multiplying gives 21k + 70 = 25k + 50, so 4k = 20 and k = 5. The numbers are 15 and 25, and adding 10 to each gives 25 and 35, which is 5 : 7. Answer: 15√(8 × 50) = √400 = 20, and it checks out as 8 : 20 = 20 : 50, both sides being 2 : 5. The third proportional is 20²/5 = 80, checking as 5 : 20 = 20 : 80, both 1 : 4. Both come from the same rule, b² = ac — in the first the middle term was missing, in the second an end term was. Answer: 20 and 804 : 5 and their expenditures in the ratio 3 : 4. If each saves ₹4,000, what is the second man's income?4x and 5x, expenditures 3y and 4y. Savings give 4x − 3y = 4000 and 5x − 4y = 4000. Multiplying the first by 4 and the second by 3 and subtracting leaves x = 4000, so the incomes are ₹16,000 and ₹20,000, the expenditures ₹12,000 and ₹16,000. Using one multiplier for both ratios is the mistake here. Answer: ₹20,000How the Ratio and Proportion Chapter Tests Work
- 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Optional 15-minute timer — with the clock to build exam speed, without it while you are still learning the chapter.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare Ratio and Proportion for SSC CGL
- Do percentage first. A percentage is a ratio out of a hundred, and the income–expenditure and fractional-change questions in this chapter read much more easily once percentage is fluent.
- Put every question on one multiplier. Writing the quantities as
3kand5kturns a comparison into one unknown and one equation. Two unconnected ratios in the same question, though, need two multipliers —xandy, neverktwice. - Learn
ad = bcinstead of three formulas. Mean proportional, third proportional and fourth proportional are the same rule with a different term missing, and so is every componendo question. - Say the part-to-whole out loud. Before using
3 : 2, say “three out of five”. That one habit removes the most expensive mistake in the chapter. - Know what survives a change. A common multiplier keeps a ratio; a common addition or subtraction does not. If the question adds a flat amount, the actual numbers must be found first.
- Learn the ratio words. Duplicate is squaring, sub-duplicate is the square root, triplicate is cubing, sub-triplicate is the cube root, and compound is
ac : bd. These questions are pure vocabulary — the arithmetic is trivial once the word is read correctly. - For variation, fix the constant first. Write
A = kB/C, findkfrom the complete reading, and only then substitute — whichever letter is the unknown. A factor on a squared quantity enters squared, and on a quantity underneath it inverts. - Do Level 1 untimed, the same day you finish the theory. It is set at real SSC CGL difficulty; the aim is picking the right method, not speed.
- Repeat Level 1 with the 15-minute clock on, then move to Level 2. A Tier I ratio question that takes more than about forty seconds usually means the parts were not set up on one multiplier at the start.
- Verify against a real paper. Once Level 1 is consistent under the clock, attempt a previous year paper and then a full mock test under locked sectional timing.
All SSC CGL Chapter Wise Tests
Every chapter below has its own free Level 1 and Level 2 tests with full solutions.
Browse all 45 chapter tests — Maths (35) · Reasoning (10)
- Number System
- Rule of Divisibility
- Remainder Theorem
- Decimal & Fraction
- LCM & HCF
- Square & Cube Root
- Number Series (AP & GP)
- Power, Indices & Surds
- Algebraic Formula
- Algebraic Result
- Algebraic Expression & Identities
- Percentage
- Profit & Loss
- Discount & Marked Price
- Simple Interest
- Compound Interest
- Ratio & Proportion
- Partnership
- Average
- Problems on Ages
- Mixture & Alligation
- Time & Work
- Pipe and Cistern
- Time, Speed and Distance
- Quadratic Equation
- Boat and Stream
- Races
- Trigonometry
- Heights & Distances
- Geometry
- Mensuration
- Coordinate Geometry
- Probability
- Statistics
- Data Interpretation
- All Maths chapters →
SSC CGL अनुपात और समानुपात (Ratio & Proportion) चैप्टर टेस्ट — हिंदी में
अनुपात एक ही प्रकार की दो राशियों की तुलना है और उसकी कोई इकाई नहीं होती, इसी कारण वह पूरे पाठ्यक्रम में साथ चलता है। राशियों को 3k और 5k लिख देने पर अनुपात तुलना नहीं रहता, गणित बन जाता है — एक अज्ञात, एक समीकरण, और प्रश्न का हर हिस्सा उसी भाग में। समानुपात का अर्थ है दो अनुपातों का बराबर होना, और उससे काम का केवल एक तथ्य मिलता है: ad = bc, अर्थात बाह्य पदों का गुणनफल मध्य पदों के गुणनफल के बराबर। मध्यानुपाती, तृतीयानुपाती और चतुर्थानुपाती इसी एक तथ्य के तीन रूप हैं, जिनमें हर बार कोई एक पद अज्ञात रहता है।
सबसे अधिक अंक दो बातों पर कटते हैं। पहली: भाग-से-भाग अनुपात को पूरे का अंश पढ़ लेना — 3 : 2 का अर्थ हर 5 में से 3 है, हर 2 में से 3 नहीं। दूसरी: यह भूल जाना कि बदलाव के बाद अनुपात बचता है या नहीं — हर पद को एक ही संख्या से गुणा करने पर अनुपात वही रहता है, पर हर पद में एक ही राशि जोड़ने या घटाने पर बदल जाता है। इसलिए जब प्रश्न में सीधी राशि जोड़ी जाए, तो पहले वास्तविक संख्याएँ निकालनी पड़ती हैं।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (SSC CGL के स्तर का) और लेवल 2 (SSC CGL से कठिन)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 15 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।
SSC CGL Ratio and Proportion — Frequently Asked Questions
How many ratio and proportion questions are asked in SSC CGL?
What topics come under ratio and proportion for SSC CGL?
What is the difference between ratio and proportion?
a : b, and it has no units. A proportion is a statement that two ratios are equal, written a : b = c : d, and it gives one usable equation: ad = bc, the product of the extremes equals the product of the means. Every mean, third and fourth proportional question is that one equation with a different term missing.How do I find the mean proportional and the third proportional?
a and b is √(ab), because a : m = m : b gives m² = ab. The third proportional to a and b is b²/a, from a : b = b : c. The fourth proportional to a, b and c is bc/a. All three come from the same rule, so it is worth learning ad = bc rather than three separate formulas. Note that order matters for a third proportional but not for a mean proportional.How many questions are in each ratio and proportion practice test?
Are the ratio and proportion tests available in Hindi?
Are these SSC CGL ratio and proportion tests free?
What does duplicate ratio mean, and how is it different from compound ratio?
a : b is a² : b² — each term squared. Sub-duplicate is the square root of each term, triplicate is each term cubed and sub-triplicate is the cube root. A compound ratio is different: it combines two separate ratios into one by multiplying the first terms together and the second terms together, so a : b compounded with c : d is ac : bd. These questions are mostly vocabulary — the arithmetic is easy once the word is read correctly.