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Time and work

Lesson 104 of 113

1. Ye topic hai kya?

Time and work = poora kaam = 1. Jo n din mein kare, uski 1 din ki speed 1/n. Mixture P10 yahi bheja: A 10 din, B 15 din, saath?

Paper yahan kya maangta

Do-teen log saath, ek nikal jaaye, alternate din, M₁D₁H₁=M₂D₂H₂, 2 men=3 women, efficiency double, wages kaam-ke-hisse se.

Yahan kya nahi

Tap bharna / leak — Pipes (agle). C×T, 8:10:9 — Partnership. ₹30–₹40 mean 36, milk 4:1 — Mixture. 6 pumps 8 h inverse — Ratio. 40 km/h TSD. 3 km east Direction.

Rate = 1 / din · Saath: rates jod.
LCM units: kaam = LCM(din), roz units = LCM/din. Men: M D H / W same.

2. A 10, B 15 — kyun 6, 25 nahi

1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Saath 6 din. 10+15=25 mat. Average 12.5 mat.

LCM 30 units. A=3/day, B=2/day, saath 5/day. 30/5=6. 6 din mein A=18 units (3/5 kaam), B=12 (2/5). Wages 3:2 — yeh C×T partnership nahi, kitna kaam kiya.

A 3/5 B 2/5 6 din saath · 30 units · 3+2=5 /day Wages 3:2. Partnership 8:10:9 nahi.

Poora bar = 1 kaam. Alligation 4:6 / milk cups yahan nahi.

A+B=12 din, A akela 18. B: 1/B = 1/12 − 1/18 = (3−2)/36 = 1/36 → B=36 din.

A, B, C = 20, 30, 60 din. 1/20+1/30+1/60 = 6/60 = 1/10 → saath 10 din.

A, B se double tez, A=10 din ⇒ B=20. Saath 1/10+1/20=3/20 → 20/3 din.

Example

A=10 din, B=15 din. Saath? (Mixture P10.)

Solution

  1. 1/10+1/15

    1/6 → 6 din. 25 nahi.

Answer6 din
Example

A+B=12, A=18. B?

Solution

  1. 1/12−1/18

    36 din.

Answer36 din

3. Men-days, hours, women

Kaam same ho to M × D × H constant (zyada aadmi, kam din — inverse). 15 men × 16 din = 20 men × D → D=12 din.

Hours bhi: 12 men, 8 din, 10 ghante = 8 men, 6 ghante, D din. 12×8×10 = 8×D×6 → 960=48D → D=20. (Ratio-page 6 pumps 8 h yahan copy nahi.)

2 men = 3 women. 6 men 10 din. 9 women? 2M=3W ⇒ 6M=9W, same strength → 10 din.

M×D partnership ke C×T jaisa dikhta hai — yahan unit kaam hai, wahan profit-share. Numbers alag rakho.
Example

15 men, 16 din. 20 men?

Solution

  1. 240/20

    12 din. 20×16/15 mat (direct).

Answer12 din

4. Beech mein chhodna, alternate, wages

A=15, B=30 (saath 10 din). 4 din saath: 4/10=2/5, bacha 3/5. B akela 3/5 × 30 = 18 din aur.

Alternate, A pehle: A=6, B=12. 2-din cycle = 1/6+1/12=1/4. 4 cycle = 8 din, kaam 1. 8 din exact.

Wages ₹500, 6 din saath (A 10, B 15): hisse 3:2 → A=300, B=200. Working-partner 10% commission Partnership pe.

Din jod ke 25 mat. Alternate pe “average din” mat. Inverse men-days ko direct mat. Tap fill Pipes. Alligation 2:3 Mixture. 8:12:15 Ratio.
Example

A=15, B=30. 4 din saath, phir B. B aur kitne?

Solution

  1. 3/5 × 30

    18. 26 (30−4) nahi.

Answer18 din
Example

A 10, B 15, 6 din, wages 500. A?

Solution

  1. 3:2

    300. Equal 250 mat.

Answer300

5. Sawal — basic se pro

Q1 · Basic

A=10, B=15. Saath?

  1. 6 din
  2. 25 din
  3. 12.5 din
  4. 5 din

Solution

  1. 1/6

    6. B jod.

Answer6 din
Q2 · Basic

LCM 30: A 3/day, B 2/day. Din?

  1. 6
  2. 30
  3. 5
  4. 15

Solution

  1. 30/5

    6.

Answer6
Q3 · Basic

A+B=12, A=18. B?

  1. 36
  2. 6
  3. 30
  4. 9

Solution

  1. 1/36

    36. B 18−12.

Answer36
Q4 · Medium

15 men 16 din. 20 men?

  1. 12 din
  2. 21⅓ din
  3. 16 din
  4. 20 din

Solution

  1. inverse

    12. B direct.

Answer12 din
Q5 · Medium

A, B se double; A=10. Saath?

  1. 20/3 din
  2. 15 din
  3. 30 din
  4. 5 din

Solution

  1. B=20

    3/20 → 20/3. D 1/10+1/10.

Answer20/3 din
Q6 · Medium

A=6, B=12, alternate A pehle. Kitne din?

  1. 8
  2. 9
  3. 4
  4. 18

Solution

  1. cycle 1/4

    4×2=8.

Answer8
Q7 · Medium

A=15, B=30, 4 din saath phir B. B extra?

  1. 18 din
  2. 26 din
  3. 11 din
  4. 6 din

Solution

  1. 3/5 × 30

    18. B 30−4.

Answer18 din
Q8 · Pro

12 men, 8 din, 10 h. 8 men, 6 h. Din?

  1. 20
  2. 10
  3. 16
  4. 12

Solution

  1. 960/48

    20. Pumps 6-8 Ratio pe.

Answer20
Q9 · Pro

A 10, B 15, 6 din, ₹500. A ki wage?

  1. 300
  2. 250
  3. 200
  4. 350

Solution

  1. 3:2

    300. Partnership commission nahi.

Answer300
Q10 · Pro

₹30 aur ₹40, mean ₹36, 2:3. Is chapter?

  1. Nahi — Mixture
  2. Haan, wages 2:3
  3. A 30 B 40 din
  4. Alligation days

Solution

  1. Price mix

    A. Wahan 4:6.

AnswerA

Practice

Pehle khud, phir neeche kholo.

12345 678910

P1

A=8, B=24. Saath?

  1. 6 din
  2. 32 din
  3. 16 din
  4. 4 din

Solution

  1. 1/8+1/24

    1/6 → 6.

Answer6 din
P2

A+B=8, A=12. B?

  1. 24 din
  2. 4 din
  3. 20 din
  4. 10 din

Solution

  1. 1/8−1/12

    24.

Answer24 din
P3

8 men 15 din. 10 men?

  1. 12 din
  2. 18.75 din
  3. 15 din
  4. 10 din

Solution

  1. 120/10

    12.

Answer12 din
P4

20, 30, 60 din. Teenon saath?

  1. 10 din
  2. 110 din
  3. 20 din
  4. 15 din

Solution

  1. 6/60

    10.

Answer10 din
P5

2 men=3 women. 6 men, 10 din. 9 women?

  1. 10 din
  2. 15 din
  3. 6⅔ din
  4. 20 din

Solution

  1. 6M=9W

    10. C inverse galat.

Answer10 din
P6

A 20% zyada tez, A=20 din. B?

  1. 24 din
  2. 16 din
  3. 22 din
  4. 25 din

Solution

  1. B=1.2×20

    24. B 20×0.8 (time kam socha ulta).

Answer24 din
P7

A=16, 4 din kaam, bacha B 12 din mein. B akela?

  1. 16 din
  2. 12 din
  3. 20 din
  4. 8 din

Solution

  1. 3/4 in 12

    B rate 1/16, B=16.

Answer16 din
P8

Do tap bharte, ek leak. Is chapter?

  1. Nahi — Pipes
  2. Haan, 1/10+1/15
  3. A 10 B 15 tank
  4. Men-days

Solution

  1. Tank

    A. Agle pe. 1/10+1/15 yahan log.

AnswerA
P9

Share C×T = 8:10:9. Is chapter?

  1. Nahi — Partnership
  2. Haan, wages 8:10:9
  3. Men 8,10,9
  4. 8:12:15

Solution

  1. Paisa×mahine

    A.

AnswerA
P10

40 L milk, 10 L water, 4:1. Is chapter?

  1. Nahi — Mixture
  2. Haan, 4 din : 1 din
  3. Men 4 women 1
  4. Alligation work

Solution

  1. Milk

    A. Wahan 4:1 cups.

AnswerA

← Index · Mixture · Partnership

Agle topic: Pipes and cisterns.