Ratio and Proportion Questions for SSC CGL

Basic Ratio Concepts

A ratio a:b means for every a parts of one quantity, there are b parts of another. Ratios are always dimensionless — both quantities must be in the same unit before comparing. Always simplify a ratio to its lowest terms by dividing both parts by their HCF. Think of ratio as a fraction: a:b = a/b.

• Ratio a:b is read as a is to b; it equals the fraction a/b
• To compare two ratios, convert to fractions and cross-multiply: a/b vs c/d → compare ad vs bc
• Duplicate ratio of a:b is a²:b²; Triplicate ratio is a³:b³
• Sub-duplicate ratio of a:b is √a:√b
• Compounded ratio: multiply numerators together and denominators together — (a/b) x (c/d) = ac/bd

Proportion — Types and Rules

Proportion means two ratios are equal: a:b = c:d, written as a/b = c/d. Here a and d are called extremes, b and c are called means. The golden rule — product of extremes equals product of means. This single rule solves most proportion problems. There are three types tested: Direct, Inverse, and Continued proportion.

• Direct proportion: if a increases, b increases — a/b = constant (k)
• Inverse proportion: if a increases, b decreases — a x b = constant
• Continued proportion: a:b = b:c, so b² = ac (b is the geometric mean)
• Fourth proportional: if a:b = c:x, then x = bc/a
• Third proportional: if a:b = b:x, then x = b²/a
• Mean proportional between a and b = √(ab)

Dividing a Quantity in a Given Ratio

SSC CGL loves questions where a total amount is split among people or parts in a given ratio. The trick: treat each ratio unit as one share. Add all parts to get total shares, then find each persons share by multiplying their ratio part by (Total / Sum of ratio parts). This technique works for 2-way, 3-way, or even 4-way splits.

• If total T is divided in ratio a:b, first part = T x a/(a+b), second part = T x b/(a+b)
• For ratio a:b:c, sum of parts = a+b+c; each part = (their share / total) x T
• If ratio changes in steps (A:B = 2:3 and B:C = 4:5), make B equal before combining
• To combine A:B and B:C into A:B:C, multiply to equalize B's value in both ratios

Variation — Direct and Inverse

Variation is proportion in disguise. Direct variation: y = kx (graph is a straight line through origin). Inverse variation: y = k/x. SSC CGL often wraps these in word problems about workers, time, pipes, or wages. Identify the type of variation first, then apply the ratio.

• Direct: more workers, more work done (in same time) — ratio stays same
• Inverse: more workers, less time to finish — product stays same
• Joint variation: z varies directly as x and inversely as y → z = kx/y
• Always set up as: (old values ratio) = (new values ratio) for direct; product = product for inverse

• Forgetting to bring both quantities to the same unit before forming a ratio — e.g., comparing 500g and 2kg without converting kg to grams first
• Confusing third proportional (a:b = b:x) with fourth proportional (a:b = c:x) — third uses b twice, fourth uses four different values
• While combining ratios like A:B and B:C, students forget to equalize B's value by multiplying — they just write A:B:C by stacking, which is wrong when B values differ
• In inverse proportion problems, students apply the direct proportion formula (ratio = ratio) instead of the product = product rule
• When a ratio is given as a fraction (e.g., A/B = 3/5), students solve for A and B as 3 and 5 exactly — the actual values are 3k and 5k; the multiplier k matters when a sum or difference is also given

• FEES rule for proportion: Fourth = Extremes Equal product of means, i.e., ad = bc always
• For combining ratios: EQUALIZE THE BRIDGE — the shared middle term (B in A:B:C) must be the same number in both ratios before you write the combined ratio
• Direct = Same Direction = Division rule (ratio = ratio). Inverse = Opposite Direction = Multiplication rule (product = product). Remember D-D-D and I-O-M
• Mean proportional between a and b: think GEOMETRIC MEAN — it always equals square root of their product, just like GM in statistics

• SSC CGL Tier 1 typically has 1-2 direct ratio/proportion questions plus 2-3 indirect ones hidden in partnership, mixture, and age problems — so mastering this topic has a multiplier effect
• Questions on fourth proportional and mean proportional appear almost every year — memorize those two formulas cold, they take under 30 seconds each
• Combining two ratios into a three-way ratio (A:B:C type) is a high-frequency question format; practice equalizing the middle term quickly by LCM
• For Tier 2, ratio questions get clubbed with data interpretation — you may need to calculate percentage change using ratios across tables, so practice converting between ratio form and percentage form
• When numbers look messy in a ratio problem, immediately check if you can assign a variable k (the multiplier) and use the sum or difference condition to find k — this avoids simultaneous equations and saves 40-50 seconds