A ratio is simply a comparison between two quantities of the same kind. When you say the ratio of boys to girls in a class is 3:5, you mean for every 3 boys there are 5 girls — not that there are exactly 3 and 5 of them. The actual numbers could be 6 and 10, or 30 and 50, or any multiple of 3 and 5.
Think of ratio as a recipe. If a dal recipe uses 2 cups of lentils for every 1 cup of onion, the ratio is 2:1. Whether you cook for 2 people or 20, the ratio stays fixed — only the actual quantities scale up.
Proportion is the statement that two ratios are equal. If A:B = C:D, you have a proportion. In everyday terms: if 4 workers finish a wall in 6 days, and 8 workers finish the same wall in 3 days, the work-output ratio is proportional.
Two types matter most for SSC GD:
Partnership is an application of ratio. When two or more people invest capital in a business and share the profit, they split it in the ratio of their investments (adjusted for time if investments are for different durations). If A invests ₹6000 for 12 months and B invests ₹4000 for 12 months, their profit ratio is 6:4 = 3:2. If the durations differ, multiply capital × time to get the effective investment.
The unifying idea across all three: ratios let you work with parts rather than absolute numbers. Most SSC GD questions give you ratios and one absolute number, and ask you to find another absolute number. Your job is to assign a variable to the "unit" and solve.
If A:B = m:n, then actual values are A = mk and B = nk for some constant k.
Finding k: SSC GD will always give you enough information to pin down k. It might say "the difference between A and B is 20" — then mk - nk = 20, so k(m - n) = 20, giving k = 20/(m-n).
Compound Ratio: Multiply corresponding terms.
Compound ratio of a:b and c:d = ac:bd.
Example: Ratio of 2:3 and 4:5 compounded = 8:15.
Duplicate Ratio: Square each term. Duplicate of a:b = a²:b².
Sub-duplicate Ratio: Square root each term. Sub-duplicate of a²:b² = a:b.
Triplicate Ratio: Cube each term.
When you have A:B = 2:3 and B:C = 5:8, to combine them, make B the same in both.
LCM of 3 and 5 is 15. Scale up:
A:B = 2:3 = 10:15B:C = 5:8 = 15:24So A:B:C = 10:15:24.
This is the bread-and-butter technique for three-number problems. Practice it until it takes under 30 seconds.
If a/b = c/d (i.e., a:b :: c:d), then:
a:c :: b:db:a :: d:c(a+b):b :: (c+d):d(a-b):b :: (c-d):d(a+b):(a-b) :: (c+d):(c-d) — this one appears in SSC GD surprisingly often.You do not need to memorize names. Recognize the pattern and apply it.
If original ratio is a:b:c and increments are p%, q%, r% respectively:
New ratio = a(100+p) : b(100+q) : c(100+r)
Divide by 100 mentally or keep as-is and simplify. You will see this pattern in the salary increment PYQ below.
When "quantity ratio" is p:q:r and "rate ratio" is x:y:z, the income ratio = px:qy:rz. Add up to get total income units, then use proportionality to find each class's income.
Equal time period: Profit ratio = Capital ratio.
Unequal time period: Profit ratio = Capital₁ × Time₁ : Capital₂ × Time₂.
Example: A invests ₹5000 for 6 months, B invests ₹4000 for 9 months. Effective investment: A = 5000×6 = 30000, B = 4000×9 = 36000. Profit ratio = 30000:36000 = 5:6.
Working partner: A working partner gets a salary component first (deducted from total profit), then remaining profit is split by capital ratio. Read the question carefully — SSC GD occasionally adds this twist.
Whenever a ratio like A:B:C = 5:2:4:3 is given and you're told one actual difference or value, assign 1 unit = x and set up a single equation. For 4-part ratio 5:2:4:3 with "C gets ₹1000 more than D": units are (4-3)x = 1x = ₹1000, so x = 1000. Then B = 2x = ₹2000. Standard method (forming 4 equations): ~60 seconds. This method: ~15 seconds. You read off B's share directly from the unit value.
Given A:B = m:n and B:C = p:q, write them side by side: A = mp, B = np = np, C = nq. Multiply across: A:B:C = mp:np:nq. The middle term (B) is always n×p. This avoids the LCM step entirely when B's two values share a common factor. For A:B=2:3 and B:C=5:8 → A:B:C = 2×5 : 3×5 : 3×8 = 10:15:24. Step count: standard LCM method = 6 steps, this method = 3 steps.
When salaries are in ratio a:b:c and increments are p%, q%, r%, the new ratio is a(100+p) : b(100+q) : c(100+r). No need to assume absolute values. For ratio 2:3:5 with 15%, 10%, 20% increments: new ratio = 2×115 : 3×110 : 5×120 = 230:330:600 = 23:33:60. Standard method (assume salaries ₹200, ₹300, ₹500, then apply percentages): 8 steps. This pattern: 4 steps.
When passenger class ratios and fare ratios are both given, income ratio = product of corresponding terms. For quantity 1:2:7 and rate 5:4:2, income ratio = 1×5 : 2×4 : 7×2 = 5:8:14. Sum = 27 units = ₹54,000, so 1 unit = ₹2,000. AC sleeper = 5 units = ₹10,000. Standard method (assume actual numbers of passengers): ~90 seconds. This merge approach: ~30 seconds.
When people leave a party and the ratio changes, start from the new ratio. If the final ratio is 1:3, write ladies = k and gents = 3k after removal. Before removal: ladies = k+2, gents = 3k+2, and their ratio was 1:2. So (k+2)/(3k+2) = 1/2 → 2k+4 = 3k+2 → k = 2. Total before = (k+2)+(3k+2) = 4+8 = 12. Working forward from the original ratio requires setting up two simultaneous equations (~75 seconds). Working backward from the final ratio requires one equation (~20 seconds).
In the exam hall, read the question once and classify it:
Step 1 — Identify question type.
Step 2 — Assign units. Never guess absolute values unless forced. Let each part of the ratio = 1 unit.
Step 3 — Find the unit value. The question always gives you one anchor (a difference, a total, or one person's share). Solve for the unit, then multiply to find the required quantity.
Step 4 — Sanity check in 5 seconds. Does the answer feel proportional? If B's share comes out larger than A's share when B's ratio is smaller, you've made an error. Catch it before moving on.
Why this question: Tests whether you can handle a product of three ratios expressed as fractions — a trap question where panicked students try to multiply everything out.
Solving path: Let A=2k, B=3k, C=4k. Then (A/B)×(B/C)×(C/A) = A/A = 1 (the B and C cancel completely). But the question asks for the ratio A/B : B/C : C/A, meaning the three fractions as separate terms. A/B = 2/3, B/C = 3/4, C/A = 4/2 = 2. LCM of denominators 3, 4, 1 is 12. Multiply each by 12: (2/3)×12 : (3/4)×12 : 2×12 = 8:9:24.
Why this question: Classic unit method — four-part ratio with a difference condition. Tests whether you can find k instantly from the condition "C gets ₹1000 more than D."
Solving path: Ratio is A:B:C:D = 5:2:4:3. Let each part = x. C's share = 4x, D's share = 3x. Given: 4x - 3x = ₹1000, so x = ₹1000. B's share = 2x = 2×1000 = ₹2000.
Why this question: Three numbers linked by two separate ratios — tests the chain-link technique.
Solving path: First:Second = 2:3, Second:Third = 5:8. Make the Second term common. Second is 3 in first ratio and 5 in second. LCM(3,5) = 15. Scale: First:Second = 10:15, Second:Third = 15:24. So First:Second:Third = 10:15:24. Sum of parts = 49 units. Total = 98, so 1 unit = 2. Second number = 15×2 = 30.
Why this question: Ratio with subtraction — people leaving changes the ratio. Classic "work backward" scenario.
Solving path: After 2 ladies and 2 gents leave, ratio is 1:3. Let ladies = k, gents = 3k. Before leaving: ladies = k+2, gents = 3k+2, ratio was 1:2. So (k+2) = (3k+2)/2 → 2k+4 = 3k+2 → k = 2. Total before = (k+2) + (3k+2) = 4 + 8 = 12.
Why this question: Two-layer ratio (son:wife, wife:daughter) — tests building a three-part ratio from two two-part ratios, then using a monetary difference.
Solving path: Son:Wife = 3:1 and Wife:Daughter = 3:1. Wife appears in both. Wife = 3 in second ratio, 1 in first. Scale first ratio so Wife = 3: Son:Wife = 9:3. So Son:Wife:Daughter = 9:3:1. Son's share = 9x, Daughter's share = 1x. Difference = 9x - x = 8x = ₹10,000 → x = ₹1,250. Total = (9+3+1)x = 13×1250 = ₹16,250.
Why this question: Coins of equal count but different denominations — tests converting all denominations to a common unit before summing.
Solving path: Let n coins of each type. Value: n×1 + n×0.50 + n×0.25 = n(1.75) = ₹35. So n = 35/1.75 = 20 coins of each type.
Why this question: Percentage increment applied to a ratio — tests the direct multiplication shortcut.
Solving path: Original ratio 2:3:5, increments 15%, 10%, 20%. New ratio = 2×115 : 3×110 : 5×120 = 230:330:600. Divide each by 10: 23:33:60.
Why this question: Dual ratio (quantity and rate) — tests the income-ratio merge technique.
Solving path: Passenger ratio = 1:2:7, fare ratio = 5:4:2. Income ratio = 1×5 : 2×4 : 7×2 = 5:8:14. Total parts = 27. Total income = ₹54,000. One part = 54,000/27 = ₹2,000. AC sleeper income = 5×2,000 = ₹10,000.
Treating the ratio as the actual number. If A:B = 3:5, A is not 3 — it is 3k. Always work in units, find k, then compute the required value. Students who forget this step pick the wrong answer option.
Forgetting to adjust ratios when linking three-part ratios. In A:B = 2:3 and B:C = 5:8, directly writing A:B:C = 2:3:8 is wrong because the B values (3 and 5) are not the same. You must equalize B first.
Applying percentage increment to the ratio terms as if they're absolute numbers — and then simplifying too early. In the salary increment problem, if you cancel down 230:330:600 to 23:33:60 only at the end, you're fine. If you try to simplify mid-calculation, you can introduce rounding errors with messy numbers.
In partnership problems, ignoring the time factor. If A invests ₹3000 for 6 months and B invests ₹2000 for 9 months, the profit ratio is NOT 3:2. It is 3×6 : 2×9 = 18:18 = 1:1. The time dimension is non-negotiable.
In coin problems, working in mixed units. If some coins are in rupees and some in paise, convert everything to paise (or everything to rupees) before writing the equation. Mixing units gives a nonsensical equation.
In "people leave/join" problems, setting up the equation from the original ratio and writing two variables. This forces a simultaneous equation when one equation (working from the final ratio) is enough. Always set the unknown from the simpler, final ratio.