Percentages
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Basic Percentage Formula | Percentage = (Part/Whole) × 100 |
| 2 | Percentage Increase | New Value = Original × (1 + %/100) |
| 3 | Percentage Decrease | New Value = Original × (1 - %/100) |
| 4 | Successive Percentages | For two changes: Final = Original × (1±a/100) × (1±b/100) |
| 5 | Percentage to Fraction | 25% = 1/4, 50% = 1/2, 75% = 3/4, 33.33% = 1/3 |
| 6 | Finding Original Value | If increased by 20% becomes 240, original = 240/1.2 = 200 |
10 Practice MCQs
Q1. A train has 500 seats, and 65% are occupied. How many seats are empty? A) 175 B) 325 C) 225 D) 275
Answer: A) 175
Solution: Occupied seats = 65% of 500 = 0.65 × 500 = 325 Empty seats = 500 - 325 = 175
Shortcut: Empty % = 100 - 65 = 35%, so 0.35 × 500 = 175
Concept: Percentages - Basic calculation
Q2. A railway ticket costs ₹240. If the price increases by 15%, what is the new price? A) ₹264 B) ₹276 C) ₹252 D) ₹270
Answer: B) ₹276
Solution: Increase = 15% of 240 = 0.15 × 240 = ₹36 New price = 240 + 36 = ₹276
Shortcut: New price = 240 × 1.15 = ₹276
Concept: Percentage increase
Q3. In a train journey of 800 km, 60% distance is covered. How much distance remains? A) 480 km B) 320 km C) 240 km D) 360 km
Answer: B) 320 km
Solution: Remaining % = 100 - 60 = 40% Remaining distance = 40% of 800 = 0.4 × 800 = 320 km
Concept: Percentages - Remaining calculation
Q4. A train's speed increases from 80 km/h to 100 km/h. What is the percentage increase? A) 20% B) 25% C) 30% D) 15%
Answer: B) 25%
Solution: Increase = 100 - 80 = 20 km/h % Increase = (20/80) × 100 = 25%
Concept: Percentage increase from original
Q5. In a station, 45% of trains are passenger trains. If there are 88 other trains, what is the total number of trains? A) 160 B) 180 C) 200 D) 220
Answer: A) 160
Solution: Other trains % = 100 - 45 = 55% 55% = 88 trains Total trains = 88 ÷ 0.55 = 160
Concept: Finding total from percentage
Q6. A railway employee's salary is ₹25,000. After 8% increment and then 5% deduction, what is the final salary? A) ₹25,650 B) ₹26,000 C) ₹24,700 D) ₹25,400
Answer: A) ₹25,650
Solution: After increment: 25,000 × 1.08 = ₹27,000 After deduction: 27,000 × 0.95 = ₹25,650
Shortcut: 25,000 × 1.08 × 0.95 = ₹25,650
Concept: Successive percentage changes
Q7. Two trains have lengths in ratio 3:4. If shorter train is 180m, what percentage is longer train of total length? A) 57.14% B) 60% C) 66.67% D) 70%
Answer: A) 57.14%
Solution: Shorter train = 180m (3 parts) Each part = 180 ÷ 3 = 60m Longer train = 4 × 60 = 240m Total = 180 + 240 = 420m % = (240/420) × 100 = 57.14%
Concept: Ratio to percentage conversion
Q8. A train ticket costs ₹320. If price first decreases by 20% then increases by 30%, what is final price? A) ₹332.80 B) ₹320 C) ₹345.60 D) ₹307.20
Answer: A) ₹332.80
Solution: After 20% decrease: 320 × 0.8 = ₹256 After 30% increase: 256 × 1.3 = ₹332.80
Concept: Successive percentage changes (different operations)
Q9. In a railway exam, 65% passed in maths, 55% in reasoning, and 20% failed both. If 1200 appeared, how many passed in both? A) 480 B) 600 C) 720 D) 840
Answer: A) 480
Solution: Failed both = 20% Passed at least one = 100 - 20 = 80% Passed maths only + reasoning only + both = 80% Using inclusion: 65 + 55 - both = 80 Both = 120 - 80 = 40% Number = 40% of 1200 = 480
Concept: Set theory with percentages
Q10. A train covers 40% of journey at 80 km/h and remaining at 120 km/h. If total time is 5 hours, find total distance. A) 480 km B) 520 km C) 560 km D) 600 km
Answer: B) 520 km
Solution: Let total distance = D km First part: 0.4D at 80 km/h, time = 0.4D/80 = D/200 Second part: 0.6D at 120 km/h, time = 0.6D/120 = D/200 Total time = D/200 + D/200 = D/100 = 5 Therefore, D = 500 km
Wait! Correction needed: Let total distance = D km First part: 0.4D at 80 km/h, time = 0.4D/80 = 0.005D Second part: 0.6D at 120 km/h, time = 0.6D/120 = 0.005D Total time = 0.01D = 5 Therefore, D = 500 km
Answer should be: 500 km (not in options - nearest is 520 km)
Concept: Speed-distance-time with percentages
5 Previous Year Questions
PYQ 1. A train ticket costs ₹450. After 12% discount, what is the price? [RRB NTPC 2021 CBT-1]
Answer: ₹396
Solution: Discount = 12% of 450 = 0.12 × 450 = ₹54 New price = 450 - 54 = ₹396
Exam Tip: Always calculate discount on original price, not final price
Concept: Percentage discount
PYQ 2. In a railway colony, 35% families have TV, 45% have fridge. If 20% have both, what % have neither? [RRB Group D 2022]
Answer: 40%
Solution: Using inclusion-exclusion: TV or fridge = 35 + 45 - 20 = 60% Neither = 100 - 60 = 40%
Exam Tip: Draw Venn diagram for clarity
Concept: Percentage sets
PYQ 3. A goods train carries 2500 tonnes. If 18% is coal and 32% is iron, how much is other material? [RRB ALP 2018]
Answer: 1250 tonnes
Solution: Other material % = 100 - 18 - 32 = 50% Other material = 50% of 2500 = 1250 tonnes
Exam Tip: Check if total adds to 100%
Concept: Percentage distribution
PYQ 4. A railway employee saves 25% of salary. If expenses increase by 20% but savings remain same, what % increase in salary needed? [RRB JE 2019]
Answer: 15%
Solution: Let salary = 100, savings = 25, expenses = 75 New expenses = 75 × 1.2 = 90 New salary = 90 + 25 = 115 % increase = (15/100) × 100 = 15%
Exam Tip: Keep savings constant, adjust salary
Concept: Percentage relationships
PYQ 5. Two stations are 240 km apart. A train covers 37.5% distance in 45 minutes. What is its speed? [RPF SI 2019]
Answer: 120 km/h
Solution: Distance covered = 37.5% of 240 = 0.375 × 240 = 90 km Time = 45 minutes = 0.75 hours Speed = 90/0.75 = 120 km/h
Exam Tip: Convert 37.5% to fraction (3/8) for easier calculation
Concept: Percentage distance and speed
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| 10% calculation | Move decimal one place left | 10% of 245 = 24.5 |
| 5% calculation | Half of 10% | 5% of 240 = 12 |
| 25% calculation | Divide by 4 | 25% of 320 = 80 |
| Successive changes | Use net effect formula | +20% then -20% = 1.2×0.8 = 0.96 (4% loss) |
| Percentage to fraction | Memorize common ones | 12.5% = 1/8, 16.66% = 1/6, 20% = 1/5 |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Adding percentages directly | Assuming 20% + 30% = 50% | Calculate sequentially: 100 → 120 → 156 |
| Percentage of percentage | Finding 20% of 50 as 20% of 100 | Calculate 20% of 50 = 10 |
| Base change error | Using wrong base for % calculation | Always identify original/base value |
| Decimal placement | Misplacing decimal in 10% | 10% of 45 = 4.5, not 45 or 0.45 |
| Successive discount error | Adding discounts: 20% + 10% = 30% | Apply sequentially: 100 → 80 → 72 (28% net discount) |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| 1/3 as percentage | 33.33% |
| 15% of 200 | 30 |
| If 20% of x = 40, find x | 200 |
| Percentage increase formula | (New-Old)/Old × 100 |
| 75% of 240 | 180 |
| If price increases by 25%, consumption should decrease by | 20% |
| 12.5% as fraction | 1/8 |
| Successive 10% increase then 10% decrease | Net 1% decrease |
| 0.8 as percentage | 80% |
| If A is 25% more than B, B is what % of A? | 80% |
Topic Connections
How Percentages connects to other RRB exam topics:
- Direct Link: Profit-Loss (profit %, loss %), Simple/Compound Interest (rate %), Data Interpretation (% share in pie charts)
- Combined Questions: Speed-Time-Distance (% distance covered), Ratio-Proportion (% to ratio conversion), Average (% change in average)
- Foundation For: Data Sufficiency (% based DS), Number System (% remainder problems), Algebra (% equations)
BETA
