Ratio & Proportion Questions for SSC CGL

Fundamentals: Ratio vs Proportion

A ratio is a comparison of two quantities using division (a:b means a/b). A proportion is an equation stating two ratios are equal (a:b = c:d, or a/b = c/d). In SSC exams, you'll rarely see pure definition questions; instead, ratios hide inside word problems about money distribution, mixture problems, or speed comparisons. The key skill is recognizing when to set up a ratio and when to use the proportionality rule (cross-multiply).

• Ratio a:b can be written as a/b; simplify by dividing both by their GCD
• Proportion a:b = c:d means ad = bc (cross-multiplication rule — use this constantly)
• If a:b = c:d, then a+c : b+d is also equal to the ratio (componendo rule)
• Inverse ratio: if a:b, then b:a is the inverse
• Compound ratio: (a:b) × (c:d) = ac : bd (multiply term-by-term)

Direct and Inverse Proportions

Direct proportion: as one quantity increases, the other increases at the same rate (y = kx, where k is constant). Inverse proportion: as one increases, the other decreases proportionally (y = k/x). SSC loves these in speed-distance-time, work-rate, and price-quantity contexts. The trap: students confuse which is which, especially in multi-step problems.

• Direct: more workers => more work done in same time; more time => more work done
• Inverse: more workers => less time to finish same work; higher speed => less time to cover distance
• Always identify the constant (k) first, then use it to find unknowns
• In compound scenarios (e.g., work), multiply ratios of all variables involved

Ratio in Mixtures and Alligation

Mixture problems ask: if you combine two substances in a certain ratio, what's the resulting concentration or average? Alligation is the reverse: given a final mixture, find the ratio of components. This is a high-frequency SSC topic disguised as 'ratio'. The method is visual and algebraic: set up the ratio, use the mean-weighted formula, or draw the alligation grid.

• Mixture ratio a:b means for every a parts of substance A, there are b parts of B
• Average/mean of mixture = (a×value_A + b×value_B) / (a+b)
• Alligation rule: (Price_A - Mean) : (Mean - Price_B) = Ratio of B : Ratio of A (note the flip)
• In successive dilution, apply the ratio formula repeatedly

Ratio in Profit-Loss and Partnership

When two partners invest capital for different periods, their profit share is in the ratio of (capital × time). This combines ratio with business math. SSC often sets up a scenario with unequal investments and time periods, then asks for profit split. The formula is straightforward but requires careful reading.

• Profit ratio = (Capital_A × Time_A) : (Capital_B × Time_B)
• If time is equal, profit ratio = capital ratio
• If capital is equal, profit ratio = time ratio
• Always simplify the final ratio by dividing by GCD

Ratio in Speed-Distance-Time

When comparing journeys, speeds, or times, ratios simplify complex scenarios. If two people travel the same distance at different speeds, their times are inversely proportional to speeds. If they travel for the same time at different speeds, distances are directly proportional. SSC uses this to test both ratio logic and mental arithmetic speed.

• Same distance, different speeds: time ratio is inverse of speed ratio
• Same time, different speeds: distance ratio equals speed ratio
• For relative speed (two objects moving toward/away): add speeds if opposite, subtract if same direction

• Confusing direct and inverse proportion: students multiply when they should divide, especially in work and time problems. Always ask: does the unknown increase or decrease?
• Forgetting to simplify ratios: leaving 60:40 instead of 3:2 wastes time and invites arithmetic errors in follow-up calculations.
• Misapplying componendo/dividendo: these rules only work when ratios are equal; students apply them blindly to unrelated numbers.
• In alligation, flipping the ratio: the rule is (Price_A - Mean) : (Mean - Price_B) = Qty_B : Qty_A. The quantities are reversed relative to prices. Memorize this or draw the grid every time.
• Ignoring units and context: a ratio of 2:3 for money is different from 2:3 for time; students mix them up in partnership and mixture problems.

• RATIO RULE: 'Cross-multiply for proportion' — if a/b = c/d, then ad = bc. Say this aloud when you see two ratios.
• DIRECT vs INVERSE: 'More workers, less time' (inverse). 'More hours, more pay' (direct). Use real-life analogies.
• ALLIGATION GRID: Draw a triangle with prices at corners and mean in middle. Differences on diagonals give ratio (flipped). Visual beats formula.
• PARTNERSHIP: 'Capital times Time' — multiply both before comparing. C×T is your mantra.

• Ratio questions in SSC CGL Tier-1 are usually 2-3 questions, often bundled with other topics (mixture + ratio, partnership + profit, speed + ratio). Expect 1-2 minutes per question if you're fluent.
• Watch for 'hidden' ratio questions: a problem about distributing money or combining substances is a ratio problem in disguise. Read carefully.
• Mental arithmetic is critical: you'll need to simplify ratios quickly. Practice dividing by 2, 5, and 10 without a calculator.
• In Tier-2 (descriptive), ratio may appear in a 5-mark problem combining two concepts (e.g., mixture + profit). Alligation grid method is fastest here.
• Recent papers (2022-2024) show increasing use of compound ratios and inverse proportion in work-rate contexts. Be extra sharp on these.