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Investments & Partnerships

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Introduction

Partnership problems में दो या ज़्यादा लोग किसी business में पैसा invest करते हैं। Profit (या loss) को investment × time के ratio के अनुसार बांटा जाता है।

ऐसे questions exams में बहुत common होते हैं और यह आपकी ability को test करते हैं कि आप real-life business situations में ratios को कैसे apply करते हैं।

Pattern: Investments & Partnerships

Pattern: Investments & Partnerships

मुख्य rule:

Profit share ∝ (Investment × Time).

अगर A ने P राशि T महीनों के लिए invest की और B ने Q राशि U महीनों के लिए, तो A : B = (P × T) : (Q × U).

Ratio मिलने के बाद profit को उसी proportion में divide किया जाता है।

Step-by-Step Example

Question

A और B ने business शुरू किया। A ने ₹10,000 invest किए 12 months के लिए, और B ने ₹15,000 invest किए 8 months के लिए। अगर total profit ₹9,200 है, तो दोनों का share निकालो।

Solution

  1. Step 1: investment × time निकालो।

    A का base = 10,000 × 12 = 120,000 B का base = 15,000 × 8 = 120,000

  2. Step 2: Ratio लिखो।

    A : B = 120,000 : 120,000 = 1 : 1

  3. Step 3: Profit divide करो।

    Total profit = 9,200 हर एक का हिस्सा = 9,200 ÷ 2 = ₹4,600

  4. Step 4: Final Answer.

    A का share = ₹4,600, B का share = ₹4,600

  5. Step 5: Quick Check.

    Ratio = 1 : 1 → Equal share → 4,600 + 4,600 = 9,200 ✅

Question

A ने ₹8,000 invest किए 12 months के लिए और B ने ₹12,000 invest किए 6 months के लिए। अगर total profit ₹7,200 है, तो दोनों का share निकालो।

Solution

  1. Step 1: investment × time multiply करो।

    A का base = 8,000 × 12 = 96,000 B का base = 12,000 × 6 = 72,000

  2. Step 2: Ratio लिखो।

    A : B = 96,000 : 72,000 Simplify → 4 : 3

  3. Step 3: Profit distribute करो।

    Total profit = 7,200 Total parts = 4 + 3 = 7 1 part = 7,200 ÷ 7 = 1,028.57 A का share = 4 × 1,028.57 = ₹4,114.29 B का share = 3 × 1,028.57 = ₹3,085.71

  4. Step 4: Final Answer.

    A ≈ ₹4,114.29, B ≈ ₹3,085.71

  5. Step 5: Quick Check.

    4,114.29 + 3,085.71 ≈ 7,200 ✅ Ratio check = 4 : 3 ✅

Quick Variations

Sleeping partners: कुछ partners पैसा invest करते हैं लेकिन काम नहीं करते। उनका share फिर भी investment × time पर आधारित होता है।

Profit % न दिया हो: Profit न मिले तब भी investment × time से share ratio पता चल जाता है।

Multiple partners: 3 या उससे ज़्यादा partners हों तो भी इसी rule को extend करके ratio बनाया जाता है।

Trick to Always Use

  • Step 1: हर partner का investment × time निकालो।
  • Step 2: इन products का ratio बनाओ।
  • Step 3: Profit उसी ratio में बाँटो।
  • Step 4: Shares को जोड़कर total profit verify करो।

Summary

Partnership problems में:

  • Profit share ratio = Investment × Time
  • Profit उसी ratio में divide किया जाता है
  • 2 या अधिक partners के लिए भी यही method चलता है
  • हमेशा ratio और total profit verify करें

यह simple method partnership questions को बहुत जल्दी और correctly solve कर देता है।

Practice

(1/5)
1. A and B invest in a business in the ratio 3 : 2. If the total profit is ₹50,000, how much is A’s share?
easy
A. ₹30,000
B. ₹20,000
C. ₹25,000
D. ₹35,000

Solution

  1. Step 1: Find total ratio parts

    Ratio = 3 : 2 → Total parts = 3 + 2 = 5.

  2. Step 2: Compute A's share fraction

    A’s share = (3/5) of total profit = (3/5) × 50,000 = ₹30,000.

  3. Final Answer:

    ₹30,000 → Option A

  4. Quick Check:

    B’s share = (2/5) × 50,000 = ₹20,000 → 30,000 + 20,000 = 50,000 ✅
Hint: Divide profit in proportion to investment parts.
Common Mistakes: Forgetting to add ratio parts before dividing the total.
2. X invests ₹8,000 for 12 months, Y invests ₹6,000 for 10 months. Find the profit-sharing ratio of X : Y.
easy
A. 3 : 2
B. 8 : 5
C. 4 : 3
D. 5 : 4

Solution

  1. Step 1: Compute investment×time for each

    X’s base = 8,000 × 12 = 96,000; Y’s base = 6,000 × 10 = 60,000.

  2. Step 2: Reduce to simplest ratio

    Ratio = 96,000 : 60,000 = 96 : 60 → divide by 12 → 8 : 5.

  3. Final Answer:

    8 : 5 → Option B

  4. Quick Check:

    96/60 = 1.6 and 8/5 = 1.6 → matches ✅
Hint: Multiply investment × time for each partner, then reduce the ratio.
Common Mistakes: Using investment amounts only and ignoring duration.
3. A invests ₹15,000 for 10 months, B invests ₹12,000 for 12 months, and C invests ₹18,000 for 8 months. If profit = ₹73,000, find C’s share.
medium
A. ₹22,000
B. ₹24,000
C. ₹26,000
D. ₹20,000

Solution

  1. Step 1: Calculate investment×time for each partner

    A = 15,000 × 10 = 150,000; B = 12,000 × 12 = 144,000; C = 18,000 × 8 = 144,000.

  2. Step 2: Simplify the ratio

    Ratio = 150,000 : 144,000 : 144,000 → divide by 6,000 → 25 : 24 : 24.

  3. Step 3: Find C's share from total profit

    Total parts = 25 + 24 + 24 = 73. C’s share = (24/73) × 73,000 = ₹24,000.

  4. Final Answer:

    ₹24,000 → Option B

  5. Quick Check:

    Each part = 73,000 ÷ 73 = 1,000 → C = 24 × 1,000 = 24,000 ✅
Hint: Compute (investment×time) for each, form ratio, then multiply fraction of profit.
Common Mistakes: Not simplifying the investment×time products before computing parts.
4. A invests ₹12,000 and B invests ₹15,000. After 6 months, C joins with ₹18,000. If total profit after 1 year is ₹26,000, find C’s share.
medium
A. ₹6,000
B. ₹7,200
C. ₹6,500
D. ₹9,000

Solution

  1. Step 1: Compute investment×duration for each partner (months participated)

    A = 12,000 × 12 = 144,000; B = 15,000 × 12 = 180,000; C = 18,000 × 6 = 108,000.

  2. Step 2: Reduce the ratio

    Ratio = 144 : 180 : 108 → divide by 12 → 12 : 15 : 9 → divide by 3 → 4 : 5 : 3.

  3. Step 3: Compute C's share from profit

    Total parts = 4 + 5 + 3 = 12. C’s share = (3/12) × 26,000 = (1/4) × 26,000 = ₹6,500.

  4. Final Answer:

    ₹6,500 → Option C

  5. Quick Check:

    One part = 26,000 ÷ 12 = 2,166.67 → C = 3 × 2,166.67 = 6,500 ✅
Hint: Late joiners count only months they participated; use investment×time for each partner.
Common Mistakes: Treating late-join investment as if it lasted whole year.
5. A, B and C invest in a business. A invests ₹10,000, B invests double of A, and C invests half of B. If profit is ₹45,000, how much does B get?
medium
A. ₹15,000
B. ₹18,000
C. ₹20,000
D. ₹22,500

Solution

  1. Step 1: Translate relative investments into numbers

    A = 10,000; B = double A = 20,000; C = half of B = 10,000.

  2. Step 2: Form the ratio

    Ratio = 10,000 : 20,000 : 10,000 = 1 : 2 : 1.

  3. Step 3: Compute B's share from profit

    Total parts = 1 + 2 + 1 = 4. One part = 45,000 ÷ 4 = 11,250. B’s share = 2 × 11,250 = ₹22,500.

  4. Final Answer:

    ₹22,500 → Option D

  5. Quick Check:

    A = 11,250, B = 22,500, C = 11,250 → sum = 45,000 ✅
Hint: Convert 'double'/'half' into numeric multiples, then split profit by total parts.
Common Mistakes: Forgetting to convert relative investment descriptions into exact numbers before forming the ratio.