Notes
SSC CHSL Exam
Qunatiative Aptitude
Partnership

Partnership: Easy Study Material with Emojis & Practice Questions 👫💰

Key Concepts 📚

  • Partnership: When two or more people invest in a business together, they are called partners, and their relationship is called a partnership. 🤝
  • Capital: The money each partner invests. 💵
  • Simple Partnership: All partners invest for the same time. ⏳
  • Compound Partnership: Partners invest for different times. 🕰️
  • Working Partner: Manages the business (may get extra share). 👩‍💼
  • Sleeping Partner: Only invests money, doesn’t manage. 😴

Important Formulas & Rules 📏

  • Profit Sharing (Same Time): If A invests ₹x and B invests ₹y for the same period:
$$ \text{A's share} : \text{B's share} = x : y $$
  • Profit Sharing (Different Times): If A invests ₹x for p months, B invests ₹y for q months:
$$ \text{A's share} : \text{B's share} = x \times p : y \times q $$
  • Share of Profit:
$$ \text{A's share} = \frac{\text{A's investment} \times \text{A's time}}{\text{Total weighted investment}} \times \text{Total profit} $$

Step-by-Step Example with Emojis 🧑‍🏫

Suppose:

  • A invests ₹10,000 for 12 months
  • B invests ₹12,000 for 10 months
  • C invests ₹7,200 for 8 months

Their profit sharing ratio:

  • A: 10,000 × 12 = 120,000
  • B: 12,000 × 10 = 120,000
  • C: 7,200 × 8 = 57,600

So, A:B:C = 120,000 : 120,000 : 57,600 = 25 : 25 : 12 📊

Practice Questions with Detailed Solutions 📝

Q1.

Raghwendra’s investment is twice Bhanu’s and thrice Chitra’s. Bhanu invested for twice the months as Raghwendra and thrice as Chitra. Who earns the highest profit? (A) Bhanu (B) Chitra (C) Raghwendra (D) Both Raghu and Bhanu

Solution:

  • Investment ratio: Raghwendra:Bhanu:Chitra = 6:3:2
  • Time ratio: Raghwendra:Bhanu:Chitra = 3:6:2
  • Multiply investment × time for each:
    • R = 6×3 = 18
    • B = 3×6 = 18
    • C = 2×2 = 4
  • Final ratio: 18:18:4 → 9:9:2
  • Both Raghwendra and Bhanu earn the highest profit! ✅

Q2.

B, Q, and R start a business in ratio 4:3:6. B and Q start, R joins after 6 months. R gets ₹3,600/month salary for 6 months, which is 10% of annual profit. What is Q’s share? (A) ₹51,000 (B) ₹58,320 (C) ₹57,900 (D) ₹60,600

Solution:

  • R’s salary: 3,600 × 6 = ₹21,600
  • ₹21,600 is 10% of profit → Total profit = ₹216,000
  • Investment × time:
    • B: 4×12 = 48
    • Q: 3×12 = 36
    • R: 6×6 = 36
    • Ratio: 4:3:3
  • Profit left after R’s salary: 216,000 – 21,600 = ₹194,400
  • Q’s share: (3/10) × 194,400 = ₹58,320 🏆

Q3.

Gman and Betu invest ₹36,000 and ₹63,000. Find each share from ₹5,500 profit. (A) ₹2,000, ₹3,500 (B) ₹2,500, ₹3,500 (C) ₹3,500, ₹2,500 (D) None

Solution:

  • Ratio: 36,000:63,000 = 4:7
  • Gman: (4/11) × 5,500 = ₹2,000
  • Betu: (7/11) × 5,500 = ₹3,500
  • Answer: (A)

Q4.

A starts with ₹50,000. S joins after 3 months with ₹70,000. At year-end, in what ratio should they share profit? (A) 1:3 (B) 3:2 (C) 1:5 (D) None

Solution:

  • A: 50,000 × 12 = 600,000
  • S: 70,000 × 9 = 630,000
  • Ratio: 600,000:630,000 = 20:21
  • Answer: (D) 20:21

Q5.

A, B, C’s initial capital ratio: 4:5:6. After 8 months, A’s capital becomes half of C’s initial. If B’s annual profit is ₹15,000, what’s total profit? (A) ₹44,000 (B) ₹36,000 (C) ₹40,000 (D) ₹39,000

Solution:

  • Ratio: [A: (4×8 + 3×4)], [B: 5×12], [C: 6×12] =
  • Simplify: 11:15:18
  • Total ratio sum: 44
  • B’s share: 15
  • So, total profit: (15,000 × 44) / 15 = ₹44,000
  • Answer: (A)

Q6.

A invests ₹10,000, B joins after 2 months with 20% more, C joins after 2 more months with 40% less than B. If profit = twice the difference between A’s and 10×C’s investment, what is B’s profit? (A) ₹35,500 (B) ₹42,000 (C) ₹38,000 (D) ₹41,100

Solution:

  • A: 10,000 × 12 = 120,000
  • B: 12,000 × 10 = 120,000
  • C: 7,200 × 8 = 57,600
  • Ratio: 25:25:12
  • Profit = 2 × (72,000 – 10,000) = ₹124,000
  • B’s share: (25/62) × 124,000 = ₹50,000
  • Profit of B: 50,000 – 12,000 = ₹38,000

Q7.

Manisha (sleeping partner) invests ₹1,80,000, Nida (working) invests ₹90,000. Nida gets 14.5% of profit for managing. If total profit is ₹24,000, what is Manisha’s share? (A) ₹10,100 (B) ₹11,500 (C) ₹12,520 (D) ₹13,680

Solution:

  • Nida’s commission: 14.5% × 24,000 = ₹3,480
  • Remaining profit: 24,000 – 3,480 = ₹20,520
  • Ratio: 1,80,000:90,000 = 2:1
  • Manisha’s share: (2/3) × 20,520 = ₹13,680

Q8.

Stuti’s working partner gets 20% commission after her commission. If commission is ₹8,000, what is total profit? (A) ₹47,000 (B) ₹45,000 (C) ₹48,000 (D) None

Solution:

  • Let total profit = K
  • (K – 8,000) × 20% = 8,000
  • K – 8,000 = 40,000
  • K = ₹48,000

Q9.

Vijay starts with ₹45,000, Unnati joins later with ₹30,000. Profit is shared 2:1. After how many months did Unnati join? (A) 1 (B) 2 (C) 3 (D) 4

Solution:

  • (45,000 × 12)/(30,000 × t) = 2/1
  • 540,000/(30,000 × t) = 2
  • t = 9 months
  • Joined after 3 months. (C)

Q10.

Naveed invests 4× Komal’s amount for double the time. Komal earns ₹5,400. What is total gain? (A) ₹45,000 (B) ₹48,600 (C) ₹52,000 (D) ₹55,500

Solution:

  • Ratio: 4×1 (capital), 2×1 (time) → 8:1
  • Komal’s share: 1 part = ₹5,400
  • Total = 9 parts = ₹48,600
  • Answer: (B)

Q11.

C & B are partners. C contributes 1/4 capital for 15 months, B gets 2/3 profit. For how long was B’s money used? (A) 8 (B) 6 (C) 10 (D) 7

Solution:

  • C:B = 1:2
  • C: (x/4 × 15), B: (3x/4 × a) = 1:2
  • 15:3a = 1:2 → a = 10
  • Answer: (C)

Q12.

P and Q invest in 5:6. P withdraws after 8 months. Profits shared 5:9. How long was Q’s money used? (A) 12 (B) 10 (C) 15 (D) 14

Solution:

  • 5×8 : 6×t = 5:9
  • 40/(6t) = 5/9 → t = 12
  • Answer: (A)

Q13.

C & B invest ₹3,500 and ₹5,600. C’s profit is ₹4,500. What is total profit? (A) ₹8,100 (B) ₹12,700 (C) ₹7,200 (D) ₹11,700

Solution:

  • Ratio: 3,500:5,600 = 5:8
  • Total = x, 5/13 × x = 4,500 → x = 11,700
  • Answer: (D)

Q14.

X, Y, Z share in ratio 1/2 : 1/3 : 1/4. X withdraws half after 2 months. After 10 months, profit is ₹4,200. What is Y’s share? (A) ₹1,800 (B) ₹1,650 (C) ₹1,600 (D) ₹1,950

Solution:

  • Initial: 6:4:3
  • Weighted: (6×2 + 3×10):(4×12):(3×12) = 42:48:36 = 7:8:6
  • Y’s share: 8/21 × 4,200 = ₹1,600

Q15.

If 8X = 10Y = 12Z, total profit is ₹2,590. What does Z get? (A) ₹740 (B) ₹630 (C) ₹840 (D) ₹730

Solution:

  • 8X = 10Y = 12Z → 4X = 5Y = 6Z
  • P:Q:R = X:4X/5:2X/3 = 15:12:10
  • Z’s share: (10/37) × 2,590 = ₹700

Emoji Legend 🗺️

  • 👫 Partners
  • 💰 Profit/Money
  • 💵 Investment
  • ⏳ Time
  • 📏 Ratio
  • 🧑‍🏫 Explanation
  • 📝 Practice
  • 🏆 Answer

Tip:

  • Always multiply investment by time for each partner.
  • Use ratios to divide profits.
  • For working/sleeping partners, subtract working allowance before dividing the rest.

All content is simplified from your PDF with emojis, clear explanations, and detailed solutions for each question, as you requested!

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Trigonometry