Ratio, Proportion And Partnership Questions for SSC GD

Ratio Basics and Simplification

A ratio is a comparison of two quantities using division. Written as a:b, it means a/b. Ratios must always be in simplest form by dividing both parts by their GCD (Greatest Common Divisor). For example, 15:25 simplifies to 3:5 by dividing both by 5. In SSC GD, you will often see ratios of money, ages, or quantities that need simplification before solving. Always reduce first—it makes calculation faster and reduces errors.

• Ratio a:b means a/b; always simplify using GCD
• Compound ratio: if a:b = 2:3 and b:c = 4:5, then a:b:c = 8:12:15 (multiply to make middle term equal)
• Inverse ratio of a:b is b:a
• Ratio does NOT have units; it is a pure number
• In word problems, identify what is being compared and set up ratio carefully

Proportion and Its Types

Proportion states that two ratios are equal: a:b = c:d, written as a/b = c/d. In direct proportion, as one quantity increases, the other increases proportionally (e.g., more workers = more work done). In inverse proportion, as one increases, the other decreases (e.g., more workers = less time needed). SSC GD frequently tests both types in word problems. Always identify which type before setting up the equation.

• Direct proportion: y = kx (k is constant); if x doubles, y doubles
• Inverse proportion: y = k/x; if x doubles, y becomes half
• In a:b = c:d, the product of means equals product of extremes: b*c = a*d
• Continued proportion: if a:b = b:c, then b is the geometric mean of a and c
• SSC GD loves 'work' problems using inverse proportion (workers and days)

Partnership: Profit Sharing

Partnership questions ask how profit or loss is divided among partners. The key rule: profit is shared in the ratio of capital invested AND time period invested. If two partners invest the same capital for the same time, they get equal profit. If capital or time differs, adjust the ratio accordingly. This is the most common SSC GD partnership question type. Always multiply capital by time to get the effective contribution ratio.

• Profit ratio = (Capital1 * Time1) : (Capital2 * Time2)
• If time is same for all, profit ratio = capital ratio
• If capital is same for all, profit ratio = time ratio
• Total profit is divided in the profit ratio
• Working partner may get extra salary/commission (subtract from total profit first, then divide remainder)

Common Partnership Variations

SSC GD tests partnership in different scenarios. Sometimes a partner joins mid-year (different time periods). Sometimes there is a working partner who gets salary before profit division. Sometimes the question gives profit and asks for capital. Always read carefully and identify: (1) capital amounts, (2) time periods, (3) any salary/commission, (4) total profit. Then apply the formula step by step.

• Mid-year entry: use actual months invested, not full year
• Working partner salary: deduct from total profit first, then divide remainder by ratio
• Sleeping partner: invests capital but does no work, gets only profit share
• If profit is given and capital is unknown, use ratio to set up equation
• Always check: does the question ask for profit share or capital invested?

• Forgetting to simplify ratio before using it in calculations—leads to wrong final answer even if method is correct
• Confusing direct and inverse proportion—read the problem carefully; 'more workers' means LESS time (inverse), not more time
• In partnership, forgetting to multiply capital by time—using only capital ratio when time differs is a major trap
• Not reducing profit ratio to simplest form before dividing profit—causes arithmetic errors
• Misidentifying working partner salary as part of profit—must subtract salary BEFORE dividing profit by ratio
• Assuming all partners invest for full 12 months when the problem says 'mid-year entry'—always check time period carefully

• RATIO RULE: 'Simplify First, Calculate Later'—always reduce ratios to lowest terms before proceeding
• PROPORTION TYPE: 'More-More = Direct, More-Less = Inverse'—if both quantities move same direction, it's direct; opposite direction, it's inverse
• PARTNERSHIP MAGIC: 'Capital times Time = Contribution'—multiply these two to find profit ratio; this is the golden rule
• WORKING PARTNER: 'Salary Out, Profit In'—deduct salary from total profit first, THEN divide remainder by ratio

• SSC GD typically gives 2-3 ratio-proportion-partnership questions in the 60-minute Maths section. Expect 1 easy (direct ratio simplification), 1 moderate (proportion word problem), 1 moderate-hard (partnership with time variation)
• Partnership questions almost always involve capital*time calculation—if you see two partners with different amounts and different time periods, this is the formula to use
• Recent papers show preference for 'profit sharing' over 'loss sharing'—but method is identical; apply same formula
• Time management: ratio-proportion questions should take 1-1.5 minutes each if you know the formula. Partnership questions take 2-3 minutes due to multi-step calculation
• Watch for 'trick' wording: 'A invests for 8 months' means 8 months, not 12. 'B joins after 3 months' means B invests for 9 months. Read dates and timelines carefully
• In SSC GD, calculators are NOT allowed—so ratios are usually designed to simplify nicely. If your ratio doesn't simplify, re-check your arithmetic