noteswale
Noteclerical

Pipes and cisterns

Lesson 71 of 113

1. Ye topic hai kya?

Pipes = cistern/tank. Inlet bharata (+), outlet/leak nikalta (−). Time-and-work P8 yahi: do tap + leak — log 10+15=6 din wahan, yahan tank aur minus.

Paper yahan kya maangta

Do inlet saath, inlet+leak net, litre/min se capacity, leak ki wajah se 6h ki jagah 8h, pehle ek tap phir doosra, tank pehle se aadha.

Yahan kya nahi

A 10 din B 15 din log — Time and work. 15 men 16 din, wages 3:2 — wahi. ₹30–40 mean 36 — Mixture. Upstream 8 km/h — Boats. 60 km 3 h — TSD.

Inlet +1/T, leak −1/T. Net > 0 tabhi bharé.
Litres: time = capacity / (in − out) — unit L/min, kaam=1 nahi.

2. Do bharte, ek nikalta

A 16 h mein bharé, B 24 h, leak 48 h mein khali. Net = 1/16 + 1/24 − 1/48 = 3/48 + 2/48 − 1/48 = 4/48 = 1/12. Tank 12 h. 16+24−48=−8 mat. Log-wale 10+15 yahan nahi.

A 16 h B 24 h leak 48 h net 12 h

Neeche = bharna. Bahar = leak. Time-and-work 3/5–2/5 bar yahan nahi.

Sirf A 12 h bharé, leak 18 h khali: 1/12 − 1/18 = 1/36 → 36 h. Agar leak ≥ inlet, kabhi nahi bharti.

Bina leak 6 h, leak se 8 h: asl fill 1/6, net 1/8, leak = 1/6 − 1/8 = 1/24 → leak akela 24 h mein khali.

A 8 h, B 12 h bharé, C 24 h khali: 1/8+1/12−1/24 = 3/24+2/24−1/24 = 4/24 = 1/6 → 6 h. (Yeh T&W A=8 B=24 log nahi — yahan teesra minus.)

Example

16 h, 24 h fill, 48 h leak. Time?

Solution

  1. 1/12

    12 h. 10+15=6 Time-and-work.

Answer12 h
Example

Fill 6 h, leak ki wajah 8 h. Leak akela?

Solution

  1. 1/6−1/8

    24 h.

Answer24 h

3. Litres — kaam=1 nahi

Tank 480 L. A 40 L/min, B 20 L/min, leak 12 L/min. Net 48 L/min. Time = 480/48 = 10 min. A akela 12 min, B 24 min, leak 40 min — yeh 16-24-48 hours wala ratio alag scale.

t = V / (qin − qout) · pehle unit same (L/min).
600 L, 25 L/min fill, 5 L/min leak → 20 L/min → 30 min.
Example

480 L, 40+20−12 L/min. Time?

Solution

  1. 480/48

    10 min. 1/10+1/15 log nahi.

Answer10 min

4. Pehle ek, aadha tank, band

A 20 h, 8 h chala phir band. Bacha 3/5. Ab sirf B 12 h: (3/5)÷(1/12) = 36/5 h = 7.2 h. Agar A band na ho, B join kare: rem 3/5, saath 1/20+1/12=2/15 → 9/2 h — alag sawaal, stem mein “A band / sirf B” padho.

Tank pehle 1/3 bhara. A 16 h, B 24 h, leak band. Rem 2/3, rate 1/16+1/24=5/48. Time (2/3)/(5/48)=32/5 h = 6.4 h.

A 15 h paanch h chala, phir B 10 h bhi: 5/15=1/3, rem 2/3, saath 1/15+1/10=1/6, (2/3)/(1/6)=4 h, kul 9 h. (T&W leave 15+30=18 extra alag.)

Leak ko jodna mat — minus. Litres ko 1/n mat. 10+15 log Time-and-work. Boat current Boats. 3 km east Direction.
Example

A 20 h. 8 h chala, A band. Bacha sirf B 12 h se. B aur kitna?

Solution

  1. A 8/20

    2/5. Rem 3/5.

  2. Sirf B

    (3/5)×12 = 36/5 h. Dono saath hote to 9/2 — stem “A band”.

Answer36/5 h

5. Sawal — basic se pro

Q1 · Basic

16 h, 24 h fill, 48 h leak. Time?

  1. 12 h
  2. 8 h
  3. 6 h
  4. 48 h

Solution

  1. 1/12

    12. C log 10+15.

Answer12 h
Q2 · Basic

480 L, 40+20−12 L/min. Time?

  1. 10 min
  2. 12 min
  3. 8 min
  4. 48 min

Solution

  1. 480/48

    10.

Answer10 min
Q3 · Basic

Fill 12 h, leak 18 h. Net fill?

  1. 36 h
  2. 6 h
  3. 15 h
  4. never

Solution

  1. 1/36

    36. B 18−12.

Answer36 h
Q4 · Medium

Bina leak 6 h, leak se 8 h. Leak khali?

  1. 24 h
  2. 14 h
  3. 48 h
  4. 7 h

Solution

  1. 1/6−1/8

    24.

Answer24 h
Q5 · Medium

20 h aur 30 h fill, leak nahi. Time?

  1. 12 h
  2. 6 h
  3. 25 h
  4. 50 h

Solution

  1. 1/20+1/30

    12. B 10+15 clone.

Answer12 h
Q6 · Medium

A 20 h. 8 h chala, A band. Bacha sirf B 12 h se. B extra?

  1. 36/5 h
  2. 12 h
  3. 8 h
  4. 9/2 h

Solution

  1. Rem

    8/20=2/5, bacha 3/5.

  2. Sirf B

    (3/5)×12=36/5. D = dono saath (A band nahi) — stem nahi.

Answer36/5 h
Q7 · Medium

1/3 pehle bhara. 16 h + 24 h fill. Remaining time?

  1. 32/5 h
  2. 12 h
  3. 8 h
  4. 2/3 h

Solution

  1. (2/3)/(5/48)

    32/5. B empty-tank 12.

Answer32/5 h
Q8 · Pro

600 L, 25 L/min fill, 5 leak. Time?

  1. 30 min
  2. 24 min
  3. 20 min
  4. 120 min

Solution

  1. 600/20

    30.

Answer30 min
Q9 · Pro

8 h, 12 h fill, 24 h empty. Time?

  1. 6 h
  2. 4 h
  3. 8 h
  4. 24 h

Solution

  1. 1/6

    6. D C akela. T&W 8+24 log alag.

Answer6 h
Q10 · Pro

A 10 din, B 15 din, saath 6 din (log). Is chapter?

  1. Nahi — Time and work
  2. Haan, tank 6 h
  3. Leak 30 h
  4. Litres 6

Solution

  1. Log

    A. Wahan 3/5–2/5 bar.

AnswerA

Practice

Pehle khud, phir neeche kholo.

12345 678910

P1

Fill 9 h, empty 18 h. Net fill?

  1. 18 h
  2. 9 h
  3. 27 h
  4. never

Solution

  1. 1/9−1/18

    18.

Answer18 h
P2

24 h aur 48 h fill. Time?

  1. 16 h
  2. 36 h
  3. 12 h
  4. 72 h

Solution

  1. 1/16

    16.

Answer16 h
P3

Full tank, sirf leak 20 h. Matlab?

  1. −1/20 per h
  2. +1/20
  3. 20 L
  4. fill 20

Solution

  1. empty

    Minus.

Answer−1/20 per h
P4

Fill 5 h, leak se 6 h. Leak empty?

  1. 30 h
  2. 11 h
  3. 1 h
  4. 15 h

Solution

  1. 1/5−1/6

    30.

Answer30 h
P5

400 L, 50 L/min, leak nahi. Time?

  1. 8 min
  2. 50 min
  3. 400 min
  4. 10 min

Solution

  1. 400/50

    8. D 480 L wala 10.

Answer8 min
P6

12 h, 18 h fill, 36 h leak. Time?

  1. 9 h
  2. 12 h
  3. 6 h
  4. 36 h

Solution

  1. 4/36

    9. B 16+24−48 clone 12.

Answer9 h
P7

Aadha bhara. 14 h + 21 h fill. Remaining?

  1. 21/5 h
  2. 8.4 h
  3. 7 h
  4. 17.5 h

Solution

  1. (1/2)/(5/42)

    21/5. B 2×4.2 galat double.

Answer21/5 h
P8

A 10, B 15, 6 din, wages 300. Is chapter?

  1. Nahi — Time and work
  2. Haan, leak 300
  3. Tank wages
  4. 3:2 pipes

Solution

  1. Log

    A.

AnswerA
P9

₹30, ₹40, mean 36, 2:3. Is chapter?

  1. Nahi — Mixture
  2. Haan, two pipes 2:3
  3. Leak 4:6
  4. Alligation tank

Solution

  1. Tea

    A.

AnswerA
P10

60 km, 3 h, speed. Is chapter?

  1. Nahi — Time, speed, distance
  2. Haan, 20 L/h
  3. Tank 60 L
  4. Boat 20

Solution

  1. Road

    A. Agle pe. Boat uske baad.

AnswerA

← Index · Time and work · Mixture

Agle topic: Time, speed, distance.