Ratio Proportion Questions for IBPS CLERK

What is a Ratio

A ratio compares two quantities of the same kind. If there are 3 apples and 5 oranges, the ratio of apples to oranges is 3:5. The first number is called the antecedent and the second is the consequent. Always simplify a ratio to its lowest form first — this saves calculation time in exams. Ratios have no units; they are pure numbers.

• Ratio a:b means a divided by b. It is NOT the same as b:a.
• Always simplify using HCF before doing anything else.
• Duplicate ratio of a:b is a squared : b squared.
• Sub-duplicate ratio of a:b is root(a) : root(b).
• Compound ratio: multiply antecedents together and consequents together. (a:b) and (c:d) gives ac:bd.
• Inverse ratio of a:b is b:a.

Proportion — The Core Rule

Proportion means two ratios are equal. If a:b = c:d, then a, b, c, d are in proportion. The key rule is called Cross Multiplication or the Means-Extremes rule: product of extremes equals product of means. This is the engine behind almost every proportion problem in IBPS Clerk. Fourth proportional, third proportional, and mean proportional are common direct question types.

• If a:b = c:d, then ad = bc (cross multiply always).
• Fourth proportional to a, b, c is x where a:b = c:x, so x = bc/a.
• Third proportional to a, b is x where a:b = b:x, so x = b squared / a.
• Mean proportional between a and b is root(ab).
• Continued proportion: a:b = b:c means b squared = ac.

Dividing a Quantity in a Given Ratio

This is the most practical application in IBPS Clerk. A total amount is shared among people in a given ratio. The trick: add all parts of the ratio to find the total parts, then each person gets their share proportionally. This pattern appears in partnership problems, salary division, and DI tables.

• If total is T and ratio is a:b:c, then shares are T x a/(a+b+c), T x b/(a+b+c), T x c/(a+b+c).
• Always add ratio parts first — this is the denominator.
• If one share is given and you need to find total or another share, use unitary method.
• Ratio can be extended: 3 persons in ratio 2:3:5 means out of 10 equal parts, they get 2, 3, 5 respectively.

Ratio Changes — When One Quantity Changes

A common IBPS question type: a ratio is given, then one or both quantities change (by adding or subtracting a number), and you need to find the new ratio or the original values. Set up the problem with variables. If A:B = 3:5, let A = 3k and B = 5k. Then apply the change condition. Solving for k gives you actual values.

• Always express ratio as multiples of k. A:B = 3:5 means A=3k, B=5k.
• Form an equation from the condition given and solve for k.
• Once k is known, find any value by substituting back.
• If a number is added to both, the ratio changes — don't assume it stays the same.

• Not simplifying the ratio before solving — leads to messy large numbers and calculation errors under time pressure.
• Confusing third proportional with mean proportional. Third proportional uses b squared / a. Mean proportional uses square root of ab.
• In ratio change problems, adding or subtracting a number from both sides and assuming the ratio stays proportional — it does NOT, that is the whole point of the problem.
• Forgetting that a:b is NOT equal to b:a. Order matters. Antecedent comes first. Getting this reversed in word problems about income or expenditure is a classic trap.
• In compound ratio, multiplying only the antecedents and forgetting the consequents, or mixing up which is antecedent and which is consequent in each ratio.

• FM-4T rule for proportional types: Fourth = bc/a, Mean = root(ab), Third = b2/a. Remember FM-4T like an FM radio station at 4T frequency.
• For dividing in ratio: ADD then DIVIDE. Add all ratio parts to get denominator, then divide total by it, then multiply each part. The three steps are ADD, FIND UNIT, MULTIPLY.
• Cross multiplication visual: draw a cross between the two fractions. The numbers at the ends of each diagonal multiply together and must be equal. Looks like an X — so remember X means CROSS MULTIPLY.
• Variable k is your best friend — any ratio problem without actual values, immediately write A = mk and B = nk. This converts ratio language into algebra and almost always cracks the problem.

• IBPS Clerk Prelims usually has 1-2 direct ratio questions like finding fourth proportional or dividing a sum. These are easy 30-second questions if formulas are memorized — never skip these.
• Ratio appears inside Age Problems heavily in both Prelims and Mains. The pattern is almost always: current ratio given, future or past ratio given, find current ages using the k method.
• In Mains, DI sets often have a ratio column in tables. You may need to find actual values from ratios given total is mentioned elsewhere. Practice reading such tables carefully.
• Time-saving tip: In most division problems, do NOT convert to decimals. Keep fractions till the final step. Decimals slow you down and cause rounding errors.
• If a question mentions sub-duplicate or triplicate ratio in the options, do not panic — these are just square roots and cubes of the original ratio respectively. Duplicate = square, Sub-duplicate = square root, Triplicate = cube.