Time Work Shortcuts
Time Work Shortcuts | Railway Exams
🔑 Core Formulas
- Work = 1 unit (assume total work = 1)
- Work Rate = 1 / Time
- Combined Rate = 1/A + 1/B
- Time Together = (A × B) / (A + B)
- Efficiency ∝ 1 / Time
🧠 Memory Tricks
| Mnemonic | Meaning |
|---|---|
| “LCM = Total Work” | Take LCM of times → treat as total units |
| “Flip for Rate” | Time → flip to get work per day |
| “Minus for Leave” | If someone leaves, subtract their rate |
📊 Quick Comparison Table
| Scenario | Formula | Example |
|---|---|---|
| A & B together | T = AB/(A+B) | A=10d, B=15d → T=6d |
| A leaves after x days | Work left = 1 – x/A | A=12d, works 3d → ¾ left |
| A is k× efficient | Time taken = Time/k | A is 2× → 10d becomes 5d |
⚡ 5 Second Shortcuts
- Chain Rule: M₁D₁T₁W₂ = M₂D₂T₂W₁ (Men-Days-Time-Work)
- Wages ∝ Work ∝ Efficiency
- Alternate days: Treat 2-day cycle → add rates
- Pipe Cisterns: Inlet (+), Outlet (–) rates
Rapid-Fire MCQs
-
A alone 20 d, B alone 30 d. Together?
a) 12 d b) 15 d c) 10 d d) 50 d -
A+B finish in 12 d, A alone 20 d. B alone?
a) 25 d b) 30 d c) 32 d d) 35 d -
A is 50% more efficient → time ratio A:B?
a) 2:3 b) 3:2 c) 5:4 d) 4:5 -
Pipe A fills in 4 h, B empties in 6 h. Together?
a) 12 h fill b) 12 h empty c) 10 h fill d) 10 h empty -
4 men do in 21 d. 7 men in?
a) 9 d b) 10 d c) 12 d d) 14 d -
Work 3 d, completes ⅖. Total days?
a) 6.5 b) 7.5 c) 8 d) 9 -
A+B+C=6 d, A=12 d, B=18 d. C alone?
a) 24 d b) 27 d c) 30 d d) 36 d -
Efficiency A:B=3:2. Time to finish together if A takes 20 d?
a) 10 d b) 12 d c) 15 d d) 8 d -
Pipe fills ½ tank in 3 h. Full in?
a) 5 h b) 6 h c) 7 h d) 8 h -
A works 4 d, leaves; B finishes 10 d. If A=15 d alone, total?
a) 12 d b) 14 d c) 16 d d) 18 d
BETA
