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Boats and streams

Lesson 15 of 113

1. Ye topic hai kya?

Boats = nadi. Still water b, current c. Downstream = stream ke saath, upstream = against. TSD P9 yahi: still 12, current 4 → down 16, up 8.

Paper yahan kya maangta

b+c, b−c, (d+u)/2 still, (d−u)/2 current, same d round trip, up/down se b aur c, time ratio (b+c):(b−c).

Yahan kya nahi

60 km 3 h = 20, train 180 m pole 12 s, 20&30 avg 24 — TSD. 16 h+24 h−48 h tank — Pipes. 3 km east — Direction. Rectangle area — Mensuration.

Down b + c · Up b − c (c < b, warna up nahi)
b = (down + up) / 2 · c = (down − up) / 2

2. 12 aur 4 — kyun 16 aur 8

Still 12 = lake mein. Current 4 nadi dhakelti. Saath: 12+4=16. Against: 12−4=8. Train opposite 54+36=90 TSD pe — wahan do gaadiyan; yahan ek boat + paani.

down 16 up 8 still 12 current 4 →

(16+8)/2=12 still. (16−8)/2=4 current. TSD road 20 km/h nahi.

Example

Still 12, current 4. Down aur up? (TSD P9.)

Solution

  1. + aur −

    16 aur 8. 12×4 mat. Pole 12 s nahi.

Answer16 km/h, 8 km/h

3. Down–up se b, c; round trip

Down 20, up 12: b=(20+12)/2=16, c=(20−12)/2=4.

Down 10 (30 km in 3 h), up 6 (30 km in 5 h): b=8, c=2. (60 km/3 h=20 sadak TSD — yahan 30 km nadi.)

8 km down 1 h (8 km/h), 8 km up 2 h (4 km/h): b=6, c=2.

Same 48 km down then up, still 12 current 4: down 48/16=3 h, up 48/8=6 h, kul 9 h. Avg speed 96/9=10⅔ — yeh 2xy/(x+y) of 16&8=10⅔, TSD equal-d 20&30=24 alag.

Still 5, current 1, 12 km up and back: up 4 km/h → 3 h, down 6 → 2 h, kul 5 h.

Example

Down 20, up 12. Still?

Solution

  1. (20+12)/2

    16. Current 4.

Answer16 km/h
Example

48 km down+up, still 12 current 4. Total time?

Solution

  1. 3+6

    9 h. 48/12=4 mat (current ignore).

Answer9 h

4. Time ratio, stream diya

Same distance: t_up : t_down = down : up = (b+c) : (b−c). 16 aur 8 pe 2:1 (up zyada time).

Current 2 km/h, 20 km down in 2 h → down=10, still=8, up=6. 20 km up = 20/6 = 10/3 h.

Up pe b+c mat. c>b ho to upstream formula kaam nahi (bah jaaye). Train pole metres TSD. Leak minus Pipes. 3 km east Direction. Area l×b Mensuration.
Example

Still 12, current 4, same d. t_up : t_down?

Solution

  1. 16:8

    2:1.

Answer2:1
Example

Current 2, 20 km down in 2 h. 20 km up time?

Solution

  1. down=10, up=6

    10/3 h.

Answer10/3 h

5. Sawal — basic se pro

Q1 · Basic

Still 12, current 4. Downstream?

  1. 16 km/h
  2. 8 km/h
  3. 12 km/h
  4. 48 km/h

Solution

  1. 12+4

    16. B up. D 12×4.

Answer16 km/h
Q2 · Basic

Uska upstream?

  1. 8 km/h
  2. 16
  3. 3
  4. 12

Solution

  1. 12−4

    8.

Answer8 km/h
Q3 · Basic

Down 20, up 12. Still?

  1. 16
  2. 4
  3. 32
  4. 8

Solution

  1. (20+12)/2

    16. B current.

Answer16
Q4 · Medium

Uska current?

  1. 4
  2. 16
  3. 8
  4. 32

Solution

  1. (20−12)/2

    4.

Answer4
Q5 · Medium

48 km down+up, 12 still 4 current. Time?

  1. 9 h
  2. 4 h
  3. 8 h
  4. 6 h

Solution

  1. 3+6

    9. B 48/12.

Answer9 h
Q6 · Medium

30 km down 3 h, 30 up 5 h. Still?

  1. 8 km/h
  2. 20 km/h
  3. 10
  4. 6

Solution

  1. (10+6)/2

    8. B TSD 60/3.

Answer8 km/h
Q7 · Medium

Still 5, current 1, 12 km up and back. Time?

  1. 5 h
  2. 4.8 h
  3. 12/5 h
  4. 6 h

Solution

  1. 3+2

    5. B 24/5 ignore current mix.

Answer5 h
Q8 · Pro

12 still 4 current, same d. t_up:t_down?

  1. 2:1
  2. 1:2
  3. 3:1
  4. 8:16

Solution

  1. 16:8

    2:1. B down:up speeds as times.

Answer2:1
Q9 · Pro

Current 2, 20 km down in 2 h. Up 20 km?

  1. 10/3 h
  2. 2 h
  3. 4 h
  4. 10 h

Solution

  1. 20/6

    10/3. C still 8 se 20/8=2.5 nahi (up 6).

Answer10/3 h
Q10 · Pro

60 km, 3 h, 20 km/h sadak. Is chapter?

  1. Nahi — TSD
  2. Haan, still 20
  3. Current 20
  4. Down 20

Solution

  1. Road

    A. Wahan 20 km/h line.

AnswerA

Practice

Pehle khud, phir neeche kholo.

12345 678910

P1

Still 10, current 2. Up?

  1. 8 km/h
  2. 12
  3. 5
  4. 20

Solution

  1. 10−2

    8. B down.

Answer8 km/h
P2

Down 18, up 12. Current?

  1. 3
  2. 15
  3. 6
  4. 30

Solution

  1. (18−12)/2

    3. B still 15.

Answer3
P3

8 km down 1 h, 8 km up 2 h. Still?

  1. 6 km/h
  2. 4
  3. 8
  4. 12

Solution

  1. (8+4)/2

    6.

Answer6 km/h
P4

Uska current?

  1. 2
  2. 6
  3. 4
  4. 1

Solution

  1. (8−4)/2

    2. Featured 4 nahi.

Answer2
P5

Still 8, current 2, 24 km down. Time?

  1. 2.4 h
  2. 3 h
  3. 4 h
  4. 12 h

Solution

  1. 24/10

    2.4. B 24/8.

Answer2.4 h
P6

Same boat, 24 km up?

  1. 4 h
  2. 2.4 h
  3. 3 h
  4. 12 h

Solution

  1. 24/6

    4.

Answer4 h
P7

c ≥ b. Upstream?

  1. Nahi chalega (bah)
  2. b+c
  3. 0
  4. c−b down

Solution

  1. b−c ≤ 0

    A.

AnswerA
P8

180 m train, 54 km/h, pole 12 s. Is chapter?

  1. Nahi — TSD
  2. Haan, boat 180 m
  3. Current 15 m/s
  4. Down 12

Solution

  1. Rail

    A.

AnswerA
P9

16 h, 24 h fill, leak 48 h. Is chapter?

  1. Nahi — Pipes
  2. Haan, 16 down
  3. Current 48
  4. Still 12 h

Solution

  1. Tank

    A.

AnswerA
P10

Rectangle 8 m × 6 m, area 48. Is chapter?

  1. Nahi — Mensuration
  2. Haan, 48 km trip
  3. Still 8 current 6
  4. Boat 48 m²

Solution

  1. l×b

    A. Agle pe 2D/3D.

AnswerA

← Index · TSD · Pipes

Agle topic: Mensuration 2D / 3D.