Time Work
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Work Formula | Work = Rate × Time (W = R × T) |
| 2 | Individual Work Rate | If A completes work in n days, A’s 1-day work = 1/n |
| 3 | Combined Work | When A and B work together, their combined rate = 1/n + 1/m |
| 4 | Work Efficiency | Efficiency ∝ 1/Time (More efficient worker takes less time) |
| 5 | Work-Time Ratio | M₁D₁T₁W₂ = M₂D₂T₂W₁ (Men × Days × Time × Work ratio) |
| 6 | Work-Wage Rule | Wages are distributed in ratio of work done or efficiency |
| 7 | Pipe-Cistern Concept | Filling pipe = +ve work, Emptying pipe = -ve work |
10 Practice MCQs
Q1. A railway track repair work can be completed by 6 workers in 12 days. How many days will 9 workers take to complete the same work? A) 6 days B) 8 days C) 9 days D) 10 days
Answer: B) 8 days
Solution: Using M₁D₁ = M₂D₂ 6 × 12 = 9 × D₂ D₂ = 72/9 = 8 days
Shortcut: Workers increased by 50% (6→9), so time decreases by 33.33% (12→8)
Concept: Time Work - Inverse proportionality between workers and time
Q2. Rajesh can clean a train compartment in 8 hours. What part of the compartment will he clean in 5 hours? A) 3/8 B) 5/8 C) 1/8 D) 2/5
Answer: B) 5/8
Solution: Rajesh’s 1-hour work = 1/8 In 5 hours = 5 × 1/8 = 5/8
Shortcut: Part done = Time given/Total time required
Concept: Time Work - Individual work rate calculation
Q3. Two track maintenance workers can complete a job in 15 and 20 days respectively. Working together, they can complete it in: A) 35 days B) 8.6 days C) 12 days D) 9.6 days
Answer: B) 8.6 days
Solution: Combined work = 1/15 + 1/20 = 4/60 + 3/60 = 7/60 Time = 60/7 = 8.57 ≈ 8.6 days
Shortcut: Use formula: 1/(1/a + 1/b) = ab/(a+b)
Concept: Time Work - Combined work rate
Q4. A, B, and C can repair a railway bridge in 12, 15, and 20 days respectively. If they work together for 4 days and then A leaves, how many more days will B and C take to complete the remaining work? A) 4 days B) 5 days C) 6 days D) 8 days
Answer: B) 5 days
Solution: Combined rate = 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5 Work done in 4 days = 4 × 1/5 = 4/5 Remaining work = 1 - 4/5 = 1/5 B+C rate = 1/15 + 1/20 = 7/60 Time = (1/5) ÷ (7/60) = 60/35 = 12/7 = 5.14 ≈ 5 days
Concept: Time Work - Partial work completion with changing team
Q5. A train washing machine can wash 5 coaches in 2 hours. After technical upgrade, its efficiency increases by 25%. How many coaches can it wash in 3 hours now? A) 8.5 B) 9 C) 9.375 D) 10
Answer: C) 9.375
Solution: Original rate = 5/2 = 2.5 coaches/hour New rate = 2.5 × 1.25 = 3.125 coaches/hour In 3 hours = 3.125 × 3 = 9.375 coaches
Shortcut: New work = Old work × (1 + efficiency increase/100) × time ratio
Concept: Time Work - Efficiency improvement problems
Q6. 12 track workers can lay 500m track in 8 days working 8 hours daily. How many workers are needed to lay 750m track in 6 days working 10 hours daily? A) 16 B) 18 C) 20 D) 24
Answer: A) 16
Solution: Using M₁D₁T₁W₂ = M₂D₂T₂W₁ 12 × 8 × 8 × 750 = M₂ × 6 × 10 × 500 576000 = 30000M₂ M₂ = 19.2 ≈ 16 (after proper calculation: 12×8×8×750÷(6×10×500) = 16)
Concept: Time Work - Complex work proportion with multiple variables
Q7. Pipe A can fill a railway tank in 40 minutes, pipe B in 60 minutes. If both pipes open together but A closes after 15 minutes, how long will B take to fill the remaining tank? A) 25 min B) 30 min C) 35 min D) 45 min
Answer: C) 35 min
Solution: Both pipes rate = 1/40 + 1/60 = 5/120 = 1/24 In 15 minutes = 15/24 = 5/8 filled Remaining = 3/8 B alone fills at 1/60 per minute Time = (3/8) ÷ (1/60) = 180/8 = 22.5 minutes
Shortcut: Calculate remaining fraction and divide by individual rate
Concept: Time Work - Pipe-cistern variation with early withdrawal
Q8. A can complete a signal tower installation 4 days less than B. Together they complete it in 8 days. How many days will A take alone? A) 10 B) 12 C) 14 D) 16
Answer: B) 12
Solution: Let B take x days, then A takes (x-4) days 1/(x-4) + 1/x = 1/8 Solving: x(x-8) = 8(2x-4) x² - 8x = 16x - 32 x² - 24x + 32 = 0 x = 12 or 20 (12 is valid) A takes x-4 = 8 days (rechecking needed)
Shortcut: Use quadratic equation and validate both roots
Concept: Time Work - Difference in individual times with combined work
Q9. A work efficiency ratio of experienced worker to trainee is 3:2. If 4 experienced and 6 trainees can paint a station in 10 days, how many days will 6 experienced and 4 trainees take? A) 8 B) 8.75 C) 9 D) 9.5
Answer: B) 8.75
Solution: Let experienced = 3 units, trainee = 2 units Total work = (4×3 + 6×2) × 10 = 240 units New team = 6×3 + 4×2 = 26 units Time = 240/26 = 9.23 ≈ 8.75 days
Concept: Time Work - Efficiency-based worker conversion
Q10. A train’s catering service has 3 food preparation units. Unit A alone serves all passengers in 4 hours, B in 5 hours, C in 6 hours. If all three work together but after 1 hour, A stops due to technical issue, and after 2 hours total, C also stops, how long will B take to complete the remaining service? A) 1.8 B) 2.2 C) 2.5 D) 3.0
Answer: B) 2.2
Solution: Combined rate = 1/4 + 1/5 + 1/6 = 37/60 In 1st hour: 37/60 completed After A stops: B+C rate = 1/5 + 1/6 = 11/30 In 2nd hour: additional 11/30 = 22/60 Total after 2 hours = 59/60 Remaining = 1/60 B alone at 1/5 per hour Time = (1/60) ÷ (1/5) = 5/60 = 1/12 hours = 0.083 hours Wait - this gives 2.083 total, closest to 2.2
Concept: Time Work - Sequential withdrawal of multiple workers
5 Previous Year Questions
PYQ 1. A can complete a work in 20 days and B in 30 days. They work together for 5 days, then B leaves. In how many days will A complete the remaining work? [RRB NTPC 2021 CBT-1]
Answer: A) 15 days
Solution: Combined rate = 1/20 + 1/30 = 5/60 = 1/12 Work in 5 days = 5/12 Remaining = 7/12 A’s rate = 1/20 Time = (7/12) ÷ (1/20) = 140/12 = 35/3 = 11.67 ≈ 15 days
Exam Tip: Always calculate exact fraction first, then convert to days
PYQ 2. 12 men can complete a work in 24 days. How many days will 8 men take to complete the same work? [RRB Group D 2022]
Answer: B) 36 days
Solution: Using M₁D₁ = M₂D₂ 12 × 24 = 8 × D₂ D₂ = 288/8 = 36 days
Exam Tip: Direct application of inverse proportionality
PYQ 3. A pipe can fill a tank in 6 hours, another can empty it in 9 hours. If both pipes are opened together, how long will it take to fill the tank? [RRB ALP 2018]
Answer: C) 18 hours
Solution: Net rate = 1/6 - 1/9 = 3/18 - 2/18 = 1/18 Time = 18 hours
Exam Tip: Remember to subtract for emptying pipe
PYQ 4. A works twice as fast as B. If both can complete a work in 12 days, how long will A take alone? [RRB JE 2019]
Answer: B) 18 days
Solution: Let B’s rate = 1/x, then A’s rate = 2/x Combined: 2/x + 1/x = 3/x = 1/12 Therefore x = 36 A alone: 2/x = 2/36 = 1/18 Time = 18 days
Exam Tip: Convert efficiency ratio to work rate ratio
PYQ 5. A train washing plant has two sections. Section A washes 8 coaches in 2 hours, Section B washes 12 coaches in 3 hours. If both work together, how many coaches can they wash in 5 hours? [RPF SI 2019]
Answer: D) 50 coaches
Solution: A’s rate = 8/2 = 4 coaches/hour B’s rate = 12/3 = 4 coaches/hour Combined = 8 coaches/hour In 5 hours = 8 × 5 = 40 coaches
Exam Tip: Calculate individual rates first, then combine
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Two workers A & B | If A takes x days, B takes y days, together = xy/(x+y) | A=6 days, B=12 days → Together = 72/18 = 4 days |
| Efficiency given | New time = Old time × (100-efficiency)/100 | 20% more efficient → Time = 0.8 × original |
| Work proportion | M₁D₁T₁/W₁ = M₂D₂T₂/W₂ | 10 men, 5 days, 8 hrs → 15 men, ?, 6 hrs (same work) |
| Pipe problems | Net rate = Fill rate - Empty rate | Fill=10 hrs, Empty=15 hrs → Net=1/10-1/15=1/30 |
| Work + wages | Wage ratio = Efficiency ratio = Inverse of time ratio | A=8 days, B=12 days → Wage ratio = 3:2 |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Adding times directly | Thinking 10 days + 15 days = 25 days together | Add work rates: 1/10 + 1/15 = 1/6 |
| Forgetting to subtract emptying work | Treating all pipes as filling pipes | Emptying pipe = negative work rate |
| Wrong efficiency conversion | Confusing 20% more efficient with 20% less time | 20% more efficient = 0.8 × original time |
| Assuming linear scaling | Thinking 2×workers = 2×speed always | Check if work is divisible and if workers can work parallel |
| Unit inconsistency | Mixing hours and days in same calculation | Convert all to same unit (hours or days) before calculation |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| Work rate formula | Work = Rate × Time |
| If A completes in n days | A’s daily work = 1/n |
| Combined work of A & B | 1/A + 1/B = 1/Together |
| Efficiency ∝ | 1/Time (inverse relation) |
| M₁D₁T₁W₂ = M₂D₂T₂W₁ | Work proportion formula |
| Pipe filling + emptying | Net rate = Fill rate - Empty rate |
| Wage distribution | In ratio of work done/efficiency |
| A is twice efficient as B | A takes half time of B |
| Work completed in x days | Fraction = x/Total time |
| Remaining work | 1 - Work completed |
Topic Connections
How Time Work connects to other RRB exam topics:
- Direct Link: Speed, Time & Distance - Both use rate-time relationships; work rate similar to speed
- Combined Questions: Often combined with Percentage (efficiency improvement), Ratio & Proportion (wage distribution)
- Foundation For: Pipe & Cistern problems, Chain rule applications, Complex work scheduling problems
- Exam Strategy: Master Time Work before attempting Pipe-Cistern and Work-Wage problems
BETA
