Percentage Calculation and Change Questions for BIHAR POLICE CONSTABLE

Basic Percentage Concept

A percentage is a fraction with denominator 100. When you say 25%, you mean 25 out of 100, or 25/100 = 0.25. In exams, you will convert percentages to decimals, fractions, and back. The key skill is recognizing what the 'whole' or 'base' is—that's the number you divide by. For example, if a shirt costs Rs 500 and you get a 20% discount, the base is 500, not the discount amount.

• Percentage = (Part / Whole) × 100
• Always identify the BASE (the 100% reference point) before calculating
• Common fractions: 25% = 1/4, 50% = 1/2, 20% = 1/5, 10% = 1/10, 33.33% ≈ 1/3
• To find X% of a number: multiply the number by X/100
• Reverse: if X% of Y = Z, then Y = Z × 100/X

Percentage Increase and Decrease

This is where most mistakes happen. When a quantity changes, the BASE for percentage is always the ORIGINAL value, not the new value. If a price goes from Rs 100 to Rs 120, the increase is Rs 20, and the percentage increase is (20/100) × 100 = 20%, not (20/120) × 100. The formula works the same way for decrease: use the original as the base.

• Percentage Increase = ((New Value - Old Value) / Old Value) × 100
• Percentage Decrease = ((Old Value - New Value) / Old Value) × 100
• Always divide by the ORIGINAL (old) value, never the new value
• If a value increases by X%, the new value = Original × (1 + X/100)
• If a value decreases by X%, the new value = Original × (1 - X/100)
• Watch for 'net change' questions—read carefully whether it's increase or decrease

Successive Percentage Changes

When two or more percentage changes happen one after another, you cannot simply add the percentages. For example, a 10% increase followed by a 10% decrease does NOT equal 0% change—it equals a 1% decrease overall. This is because the second percentage is applied to the new value, not the original. Use the multiplier method: multiply all the factors together.

• Never add successive percentages—always multiply the multipliers
• Multiplier for X% increase = (1 + X/100)
• Multiplier for X% decrease = (1 - X/100)
• Final value = Original × (Multiplier 1) × (Multiplier 2) × ...
• To find net percentage change: (Final - Original) / Original × 100
• Common trap: 10% up then 10% down = 0.99 of original = 1% net decrease

Real-World Applications in Bihar Police Exams

Percentage questions in Bihar Police Constable exams often disguise themselves as word problems about profit-loss, population growth, discount-markup, or efficiency. The underlying math is always the same: identify the base, apply the percentage formula, and watch for successive changes. Read the question twice—once for meaning, once for numbers.

• Profit/Loss: Profit% = (Profit / Cost Price) × 100; Loss% = (Loss / Cost Price) × 100
• Discount: Discount% = (Discount Amount / Marked Price) × 100; Selling Price = MP × (1 - Discount%/100)
• Population: New Population = Old × (1 + Growth Rate/100)^n for n years
• Efficiency: If work increases by X%, time/resources may decrease by a related percentage
• Always check units (Rs, %, people, etc.) and reasonableness of answer

• Using the NEW value as the base instead of the ORIGINAL value when calculating percentage change. Example: If price goes from 100 to 120, the increase is 20%, not 16.67%.
• Adding successive percentages instead of multiplying multipliers. A 10% increase then 10% decrease is NOT 0%; it is 1% decrease.
• Forgetting to multiply by 100 when converting a fraction to percentage, or forgetting to divide by 100 when converting percentage to decimal.
• Misidentifying the base in word problems. In 'A is 25% more than B', B is the base, not A.
• Rounding too early in multi-step problems, leading to final answer errors. Keep decimals until the last step.

• BASE RULE: In any percentage problem, ask 'What is 100%?' That's your base. Divide by it.
• MULTIPLIER METHOD: For successive changes, use (1 + X/100) for increase and (1 - X/100) for decrease. Multiply all multipliers together.
• FRACTION SHORTCUTS: 25% = 1/4, 50% = 1/2, 20% = 1/5, 10% = 1/10. Use these to speed up mental math.
• REVERSE FORMULA: If X% of Y = Z, then Y = Z × 100/X. This solves 'find the original' questions instantly.

• Bihar Police Constable papers typically include 4-6 percentage questions in the Numerical Ability section. Expect 1-2 straightforward 'find X% of Y' questions, 1-2 percentage change questions, and 1-2 word problems (profit-loss or population).
• Time management: Percentage questions should take 1-2 minutes each. If you're spending more than 2 minutes, you're overcomplicating. Use the multiplier method and fraction shortcuts to speed up.
• Recent papers show a trend toward successive percentage changes and real-world scenarios (salary hikes, population growth, discount chains). Practice these heavily.
• Watch for 'net change' language in questions. If a quantity increases by 10% then decreases by 10%, the answer is NOT 0%—calculate using multipliers.
• In word problems, underline the base and the percentage separately before calculating. This prevents the 'wrong base' error, which is the #1 mistake in Bihar Police exams.