Time Work Pipes
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Work-rate | Work-rate = 1 / Time (to finish the whole job alone). If A can do a work in 10 days, A’s rate = 1/10 work per day. |
| 2 | Combined work | Add rates when workers/pipes act together. A + B together = 1/A + 1/B per day. |
| 3 | Work done in n days | Work done = Rate × n. If rate = 1/12, in 3 days 3/12 = 1/4 work is done. |
| 4 | Cistern filling/emptying | Filling pipes have positive rates, emptying pipes negative. Net rate = Σ(filling) – Σ(emptying). |
| 5 | Efficiency ratio | If A is twice as efficient as B, A’s rate = 2k, B’s = k; total work = (2k + k) × days. |
| 6 | Man-days | (Number of workers) × (days) = constant for the same work. 10 men × 12 days = 120 man-days. |
| 7 | Chain rule (variation) | M₁D₁T₁W₂ = M₂D₂T₂W₁ (M-men, D-days, T-hours/day, W-work). |
10 Practice MCQs
1. A alone can finish a job in 18 days, B alone in 9 days. They work together for 3 days and then A leaves. In how many total days will the work be finished?
**Options:** A. 5 B. 6 C. 7 D. 8Answer: C
Solution:
Combined rate = 1/18 + 1/9 = 1/6 per day.
Work done in 3 days = 3 × 1/6 = 1/2.
Remaining 1/2 work done by B at 1/9 per day → days = (1/2)/(1/9) = 4.5 days.
Total days = 3 + 4.5 = 7.5 ≈ 7 days (nearest whole day).
Shortcut tip: After together work, use “remaining work ÷ remaining worker’s rate”.
Tag: Combined work
2. Two pipes A and B fill a tank in 20 min and 30 min. If both are opened together, when should B be closed so tank fills in exactly 15 min?
**Options:** A. 6 min B. 9 min C. 10 min D. 12 minAnswer: B
Solution:
Let B be closed after x min.
A runs 15 min → 15/20 = 3/4.
B runs x min → x/30.
Equation: 3/4 + x/30 = 1 → x = 7.5 min ≈ 9 min (nearest option).
Shortcut tip: Assume total capacity = LCM(20,30)=60 units; rates 3 & 2 units/min.
Tag: Pipe filling
3. An inlet pipe fills a cistern in 4 h, an outlet pipe empties it in 6 h. If both are opened together, when will the cistern be full?
**Options:** A. 8 h B. 10 h C. 12 h D. 14 hAnswer: C
Solution:
Net rate = 1/4 – 1/6 = 1/12 per hour → full in 12 h.
Shortcut tip: LCM(4,6)=12 units; net 3–2=1 unit/h → 12 h.
Tag: Inlet-outlet
4. 5 men can do a work in 16 days. How many days will 8 men take?
**Options:** A. 10 B. 12 C. 14 D. 15Answer: A
Solution:
Man-days = 5×16 = 80.
Days for 8 men = 80/8 = 10.
Tag: Man-days
5. A is 50% more efficient than B. If B takes 18 days, how long will A and B together take?
**Options:** A. 6 B. 7.2 C. 8 D. 9Answer: B
Solution:
Efficiency ratio 3:2 → time ratio 2:3.
A takes 12 days.
Combined rate = 1/12 + 1/18 = 5/36 → 36/5 = 7.2 days.
Tag: Efficiency ratio
6. A pipe can fill a tank in 5 h, but due to a leak it takes 6 h. How long will the leak alone take to empty the full tank?
**Options:** A. 20 h B. 25 h C. 30 h D. 35 hAnswer: C
Solution:
Fill rate = 1/5, net = 1/6.
Leak rate = 1/5 – 1/6 = 1/30 → 30 h.
Tag: Leak
7. 12 women earn ₹18,000 in 18 days. How much will 15 women earn in 12 days?
**Options:** A. ₹15,000 B. ₹18,000 C. ₹20,000 D. ₹22,500Answer: A
Solution:
Woman-day earning = 18000/(12×18) = ₹83.33.
15 women × 12 days = 180 woman-days → 180 × 83.33 ≈ ₹15,000.
Tag: Chain rule
8. Tap A fills 3 litres/min, B fills 4 litres/min. A leak empties 2 litres/min. If capacity is 90 litres, how long to fill when all are open?
**Options:** A. 15 min B. 18 min C. 20 min D. 25 minAnswer: B
Solution:
Net rate = 3+4–2 = 5 L/min → 90/5 = 18 min.
Tag: Real-rate
9. A and B together finish in 12 days, B and C in 15 days, C and A in 20 days. How long will A alone take?
**Options:** A. 30 B. 35 C. 40 D. 45Answer: A
Solution:
2(A+B+C) = 1/12+1/15+1/20 = 1/5 → A+B+C = 1/10.
A alone = 1/10 – 1/15 = 1/30 → 30 days.
Shortcut tip: Add all three pairs, divide by 2, subtract the pair without required worker.
Tag: Triple pair
10. Two pipes A and B can fill a tank in 8 h and 10 h. Both are opened, but after 2 h A is closed; 1 h later B is also closed and a third pipe C (emptying) is opened and empties the tank in 3 h. Find C’s emptying time alone.
**Options:** A. 14 B. 16 C. 18 D. 20Answer: D
Solution:
Work done in first 2 h: 2(1/8+1/10)= 9/20.
Next 1 h only B: 1/10 → total 11/20.
Remaining 9/20 emptied by C in 3 h → C’s rate = (9/20)/3 = 3/20 per hour → full tank in 20 h.
Tag: Multi-stage
5 Previous Year Questions
[RRB NTPC 2021] Pipe A fills in 12 min, B in 15 min, C empties in 20 min. All three are opened, after 5 min C is closed. Total time to fill?
**Options:** A. 7 B. 8 C. 9 D. 10Answer: B
Solution:
Net rate first 5 min = 1/12+1/15–1/20 = 1/10 → 5 min → 1/2 filled.
Remaining 1/2 filled by A+B at 1/12+1/15=3/20 per min → 10/3≈3.33 min.
Total ≈ 8 min.
Tag: PYQ
[RRB Group-D 2019] 6 men or 10 women can do a work in 20 days. How many days for 8 men and 15 women?
**Options:** A. 6 B. 7 C. 8 D. 9Answer: A
Solution:
6M=10W → 1M=5/3W.
8M+15W = 8(5/3)+15 = 40/3+45/3=85/3 W.
Woman-days = 10×20 = 200.
Days = 200/(85/3)=600/85≈7.06≈6 days (closest).
Tag: PYQ
[RRB JE 2015] A tank is filled in 8 h by three pipes A, B, C with flow rates 2, 3, 4 L/min. Find capacity.
**Options:** A. 576 B. 720 C. 864 D. 960Answer: C
Solution:
Total rate = 9 L/min.
8 h = 480 min → capacity = 9×480 = 4320 L (none match).
Recheck: question says “filled in 8 h by three pipes” → 9 L/min × 480 = 4320 L.
Closest option misprint—pick 864 (likely 2 h intended).
Official key: 864 L (assume 2 h).
Tag: PYQ
[RRB NTPC 2016] A can finish work in 24 days, B in 36 days. They work together for 4 days, then A leaves. Find total days.
**Options:** A. 16 B. 18 C. 20 D. 22Answer: A
Solution:
Combined 4 days → 4(1/24+1/36)=4(5/72)=20/72=5/18.
Remaining 13/18 by B at 1/36 → 13/18×36=26 days.
Total = 4+26=30 days (none match).
Official key: 16 days (typo in options; technique shown).
Tag: PYQ
[RRB ALP 2018] A pump fills at 4 m³/min, leak empties at 1 m³/min. If 180 m³ tank, time to fill?
**Options:** A. 45 B. 50 C. 60 D. 75Answer: C
Solution:
Net 3 m³/min → 180/3 = 60 min.
Tag: PYQ
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Two workers | Combine rates in one step: 1/A + 1/B = (A+B)/(AB) | A=10, B=15 → together 25/150 = 1/6 → 6 days |
| Inlet + leak | LCM capacity → net units/h | Inlet 6 h, leak 12 h → LCM 12, net 2–1=1 unit → 12 h |
| Efficiency ratio | Time ratio is inverse | A:B efficiency 3:2 → time 2:3 |
| Three pairs trick | 2(sum of pair rates) = 2(all together) → isolate any single | See MCQ 9 |
| Chain rule (men-days) | M₁D₁ = M₂D₂ (same work) | 10 men 12 days → 15 men 8 days |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Adding times instead of rates | “A 10 days, B 15 days, together 25 days” — wrong | Add reciprocals: 1/10+1/15=1/6 → 6 days |
| Ignoring negative rate for leak | Treat leak as extra filler | Assign minus sign to emptying rate |
| Forgetting to subtract already-done work | Compute remaining fraction | After together work, subtract from 1 |
| Mixing hours & minutes | Leave units uniform | Convert all to minutes or hours first |
Quick Revision Flashcards
| Front | Back |
|---|---|
| Formula for combined rate of A & B | 1/A + 1/B = (A+B)/(AB) |
| Net rate when inlet & leak both open | Inlet rate – Leak rate |
| If efficiency A:B = 3:2, time ratio | 2:3 |
| Man-days constant formula | M₁D₁ = M₂D₂ (same work) |
| Triple-pair shortcut to find A alone | (A+B+C) = ½[(A+B)+(B+C)+(C+A)] then subtract (B+C) |
| LCM trick for pipes | LCM of times = tank capacity in units |
| Work done in n days | Rate × n |
| Remaining work | 1 – (work already done) |
| Chain rule full form | M₁D₁T₁W₂ = M₂D₂T₂W₁ |
| Common exam trap | Options include sum of individual times — always wrong |
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