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Partnership

Lesson 67 of 113

1. Ye topic hai kya?

Partnership = do-teen log dukaan/firm mein paisa lagate hain. Saal ke profit (ya loss) ko sirf capital se nahi — kitna paisa × kitne mahine. Compound-interest P10 yahi bheja: share = C×T, loan-PV installment nahi.

Paper yahan kya maangta

Same time → capital ratio. Alag time → C×T. Teesra 3 mahine baad ghusna. Beech mein 4000 nikaalna. Working partner ko pehle % commission, baaki ratio. Loss bhi wahi ratio. Inverse: profit equal ho to C₁T₁=C₂T₂.

Yahan kya nahi

A:B=2:3, B:C=4:5 → 8:12:15 — Ratio. x/1.1+x/1.21=2100, CI 210 — Compound interest. CP 200 SP 250 — Profit/loss. 6 men 8 din — Time and work. Milk–water — Mixture.

A ka hissa = (CA × TA) / Σ(C×T) × Profit
Time same → T kat jaata, sirf C. Capital same → sirf T. Loss: minus ki jagah same ratio, sign loss.

2. Time same — capital ka ratio

Dono poora saal. A ₹12000, B ₹16000, profit ₹7000. 12:16 = 3:4. 7000/7=1000. A=3000, B=4000. Ratio-page ka ₹840 ko 3:4 baantna alag story thi (koi time nahi).

Example

12000 aur 16000, 1 saal, profit 7000. A?

Solution

  1. 3:4

    3000. 3500-3500 mat (equal time ≠ equal share jab C alag).

Answer3000

3. Alag mahine — area C×T

A ₹30000 × 8 mahine, B ₹45000 × 6 mahine. Product: 2,40,000 : 2,70,000 = 8:9. Profit 1700 → 17 parts, A=800, B=900. 30:45=2:3 mat — time alag hai.

8 9 30k × 8 mo 45k × 6 mo A = 800 of 1700 B = 900 of 1700

Chaurai×unche = paisa×mahine. 8:9, 8:12:15 nahi.

Capital same ho to sirf months. Teen log ₹1-ek, 10, 8, 6 mahine → 5:4:3. Men×days Time-and-work pe — wahan kaam, yahan profit.
Example

30000×8 mo, 45000×6 mo, profit 1700. A?

Solution

  1. 8/17

    800. 2:3 se 680 trap.

Answer800
Example

A 4000 × 12 mo. B 6000. Profit equal. B kitne mahine?

Solution

  1. C T same

    4000×12=48000=6000×T → T=8.

Answer8 months

4. Late join, nikaalna, working

C 3 mahine baad: saal 12 mo. A 8000×12, B 10000×12, C 12000×9. 96000:120000:108000 = 8:10:9 (12 se kaato). Profit 5400, 27 parts, 200 each. A=1600, B=2000, C=1800. Ratio-chain 8:12:15 yahan nahi.

8 10 9 A B C

8:10:9 = C×T. 8:12:15 chain alag page.

Withdraw: A 12000, 4 mahine baad 4000 nikaala (baaki 8 mo pe 8000). B 10000 poora 12. A: 12000×4+8000×8=1,12,000. B: 1,20,000. 14:15. Profit 5800 → A=2800, B=3000.

Working partner: pehle profit ka commission, baaki capital-ratio. Profit 2100, A ko 10% (210), baaki 1890 ko 1:2. A=630+210=840, B=1260. Yeh CI year-2 110 nahi, shop 25% nahi.

Ulta time: profit A:B=5:3, capital 2:3. (2 t₁):(3 t₂)=5:3 → t₁:t₂=5:2.

Time alag ho to sirf capital ratio mat. Late join pe 12 mo mat de dena. Commission ke baad poora profit dubara mat baanto. 8:12:15 ko is page ka ABC mat. Installment 1210 Compound. PRT/100 Simple.
Example

8000, 10000 poora saal; 12000 last 9 mo. Profit 5400. C?

Solution

  1. 8:10:9

    C=9×200=1800.

Answer1800
Example

A 12000, 4 mo baad 4000 nikaala; B 10000. Profit 5800. A?

Solution

  1. 14:15

    2800. 12k:10k se 2618 trap.

Answer2800
Example

Profit 2100, A 10% working, baaki 1:2. A total?

Solution

  1. 210 + 630

    840. 1050-1050 mat.

Answer840

5. Sawal — basic se pro

Q1 · Basic

12000, 16000, 1 saal, profit 7000. A?

  1. 3000
  2. 4000
  3. 3500
  4. 2100

Solution

  1. 3:4

    3000. C equal-split.

Answer3000
Q2 · Basic

Uska B?

  1. 4000
  2. 3000
  3. 3500
  4. 1600

Solution

  1. 4/7

    4000.

Answer4000
Q3 · Basic

30000×8, 45000×6, profit 1700. A?

  1. 800
  2. 900
  3. 680
  4. 850

Solution

  1. 8:9

    800. C capital 2:3.

Answer800
Q4 · Medium

4000×12 mo, 6000, equal profit. B ke months?

  1. 8
  2. 12
  3. 6
  4. 18

Solution

  1. 48000/6000

    8. B same-year trap.

Answer8
Q5 · Medium

8:10:9, profit 5400. A?

  1. 1600
  2. 1800
  3. 2000
  4. 2160

Solution

  1. 8×200

    1600. D 8:12:15 mix (5400×8/35).

Answer1600
Q6 · Medium

Usi mein C?

  1. 1800
  2. 1600
  3. 2000
  4. 900

Solution

  1. 9×200

    1800.

Answer1800
Q7 · Medium

Withdraw wala: 14:15, profit 5800. A?

  1. 2800
  2. 3000
  3. 2900
  4. 2618

Solution

  1. 14×200

    2800. D capital-only 12:10.

Answer2800
Q8 · Pro

Profit 2100, A 10% working, baaki 1:2. A?

  1. 840
  2. 700
  3. 1050
  4. 1260

Solution

  1. 210+630

    840. D B ka.

Answer840
Q9 · Pro

Profit 5:3, capital 2:3. Time A:B?

  1. 5:2
  2. 2:3
  3. 5:3
  4. 4:9

Solution

  1. (2t₁):(3t₂)=5:3

    t₁:t₂=5:2.

Answer5:2
Q10 · Pro

Loan 2100, 10% CI, installment 1210. Is chapter?

  1. Nahi — Compound interest
  2. Haan, 2 partners
  3. C×T=1210
  4. Working 10%

Solution

  1. PV

    A. Bank loan, firm-share nahi.

AnswerA

Practice

Pehle khud, phir neeche kholo.

12345 678910

P1

20000, 30000, 1 saal, profit 5000. A?

  1. 2000
  2. 3000
  3. 2500
  4. 1500

Solution

  1. 2:3

    2000.

Answer2000
P2

8000×6 mo, 12000×4 mo, profit 9000. Har ek?

  1. 4500
  2. 3600 aur 5400
  3. 3000 aur 6000
  4. 4000 aur 5000

Solution

  1. 48k:48k

    1:1 → 4500. B capital 2:3.

Answer4500
P3

Equal capital, months 10, 8, 6. Profit 4800. A?

  1. 2000
  2. 1600
  3. 1200
  4. 2400

Solution

  1. 5:4:3

    2000. Men-days nahi.

Answer2000
P4

Capital 2:3. A 12 mo, B 8 mo. Profit 6400. A?

  1. 3200
  2. 2560
  3. 3840
  4. 3600

Solution

  1. 24:24

    3200. B 2:3 of 6400.

Answer3200
P5

Loss 2700, ratio 5:4. A ka loss?

  1. 1500
  2. 1200
  3. 1350
  4. 270

Solution

  1. 5/9

    1500. Loss bhi C×T.

Answer1500
P6

Profit 2700, A 10% working, baaki 4:5. A total?

  1. 1350
  2. 1080
  3. 1620
  4. 270

Solution

  1. 270+1080

    1350. B sirf 4/9 of 2700.

Answer1350
P7

A 12000×8 mo, B ×6 mo, share 4:3. B ka capital?

  1. 12000
  2. 16000
  3. 9000
  4. 8000

Solution

  1. 96000 : 6B = 4:3

    B=12000.

Answer12000
P8

10% phir 20% shop discount. Is chapter?

  1. Nahi — Profit / loss
  2. Haan, two partners
  3. 28% share
  4. Working 10%

Solution

  1. Off

    A. Net 28% wahan.

AnswerA
P9

1000, 10%, 2 saal, CI=210. Is chapter?

  1. Nahi — Compound interest
  2. Haan, 210 share
  3. C×T=200
  4. Simple 200

Solution

  1. Bank

    A. SI 200 Simple pe.

AnswerA
P10

Milk–water mix, alligation. Is chapter?

  1. Nahi — Mixture
  2. Haan, 3:2 partners
  3. C×T milk
  4. Ratio 8:12:15

Solution

  1. Milana

    A. Alligation agle pe.

AnswerA

← Index · Compound interest · Ratio

Agle topic: Mixture / alligation.