Ratio Proportion Partnership Questions for BIHAR POLICE CONSTABLE

Ratio Basics & Simplification

A ratio compares two quantities using division. Think of it as a recipe: if flour to sugar is 3:2, it means for every 3 parts flour, use 2 parts sugar. Ratios must be simplified to lowest terms, just like fractions. If you have 15:10, divide both by their GCD (5) to get 3:2. In exams, always check if your final ratio is in simplest form—examiners often mark this wrong.

• Ratio a:b means a/b when converted to fraction form
• Always simplify using GCD of both numbers
• Equivalent ratios: 2:3 = 4:6 = 6:9 (multiply or divide both by same number)
• If ratio is a:b:c, all three parts must be in lowest terms together
• Never leave ratio as decimal unless explicitly asked

Proportion & Cross-Multiplication

Proportion states that two ratios are equal: a:b = c:d, written as a/b = c/d. This is your tool for solving 'if-then' problems. Cross-multiply to solve: a×d = b×c. Bihar Police papers love proportion word problems—'If 5 workers build 10 meters in 2 days, how much in 4 days?' Use proportion to set up and solve. The key is identifying which quantities are directly proportional (both increase together) vs inversely proportional (one increases, other decreases).

• Direct proportion: both quantities increase/decrease together (speed-distance, workers-output)
• Inverse proportion: one increases, other decreases (workers-time, speed-time)
• Cross-multiply: if a/b = c/d, then ad = bc
• Always check: does answer make logical sense? (e.g., more workers = less time)
• Set up proportion carefully—numerator and denominator order matters

Partnership: Profit Sharing

Partnership is when two or more people invest money and share profit. The profit is divided in the ratio of their investments (if time is same) or in ratio of (investment × time). This is the most common partnership question in Bihar Police exams. If A invests Rs 5000 for 12 months and B invests Rs 3000 for 12 months, they share profit in ratio 5000:3000 = 5:3. If time differs, multiply investment by months: A's share = 5000×12, B's share = 3000×8, then ratio those products.

• Profit ratio = Investment ratio (when time period is same)
• Profit ratio = (Investment × Time) ratio (when time differs)
• Always express final ratio in simplest form before dividing profit
• If profit is given, use ratio to find each person's share: (ratio part / total ratio) × total profit
• Watch for: different investment periods, different capital amounts, withdrawals mid-year

Compound Ratio & Mixed Problems

Compound ratio combines multiple ratios. If A:B = 2:3 and B:C = 4:5, find A:B:C by making B the same in both. Multiply first ratio by 4 and second by 3: A:B = 8:12 and B:C = 12:15, so A:B:C = 8:12:15. These appear in harder partnership questions and multi-person scenarios. Bihar Police sometimes asks compound ratio in context of three partners with different investments and time periods.

• To combine ratios, make the common term equal in both ratios
• Multiply entire ratio by needed factor to equalize common term
• Final compound ratio should be in simplest form
• Useful in three-partner problems and complex proportion chains

• Forgetting to simplify ratio to lowest terms—examiners mark this wrong even if calculation is correct
• Confusing direct and inverse proportion—read carefully: 'more workers' means less time (inverse), not more time
• In partnership, multiplying investment by time incorrectly—use months consistently, not years mixed with months
• Setting up proportion backwards—if 5 workers do 10m in 2 days, write (5/10) = (workers/meters), not reversed
• Not checking if answer is logical—if 2 workers take 10 days, 10 workers should take 2 days, not 50 days

• RATIO = Recipe: 3:2 flour-to-sugar means 3 parts flour per 2 parts sugar. Simplify like fractions.
• PROPORTION = Cross-multiply: a/b = c/d becomes a×d = b×c. Think of it as 'butterfly wings'—multiply diagonals.
• DIRECT vs INVERSE = More workers = Less time (inverse). More speed = More distance (direct). Ask: do they move together or opposite?
• PARTNERSHIP = Profit ÷ by ratio of (Investment × Time). If times equal, just use investment ratio. Simplify ratio first, then divide.

• Bihar Police Constable typically asks 2-3 ratio-proportion questions in Numerical section. Expect one direct ratio simplification, one proportion word problem, and one partnership profit question.
• Partnership questions often have twist: different time periods or mid-year withdrawal. Read carefully and note all dates/months.
• Time management: ratio-proportion questions should take 2-3 minutes max. If stuck, skip and return—don't waste time on calculation errors.
• Recent papers show preference for 3-partner problems over 2-partner. Practice compound ratio scenarios.
• Always write ratio in simplest form in final answer. Marks are deducted if ratio is not fully reduced, even if profit division is correct.