Theory & Concepts
SSC CGL Partnership Questions, Formulas & Short Tricks
Prepare Partnership for SSC CGL with formulas, short tricks, solved examples, practice questions, PYQs, and free PDF notes for faster exam preparation.
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Practice Notes
18 min readDifficulty: Intermediate
Partnership is a logical extension of the ratio and proportion chapter. In the Ssc cgl exam, questions on partnership are highly predictable and usually revolve around the relationship between investment, time, and profit distribution.
The core principle of partnership is simple: the person who invests more money for a longer duration should receive a larger share of the profit. Mastering this single concept allows you to solve almost any partnership question.
Learning path
- Basic profit-ratio rule
- Working vs sleeping partners
- Variable investment logic
- 10 standard solved problems
- Previous year patterns
1. The golden rule of partnership
Profit is directly proportional to both the amount invested and the time for which it was invested.
= Investments by individuals
= Time periods of investment
2. Types of partners
Working partner
A partner who manages the business. They often take an additional commission or salary before the profit is distributed.
Sleeping partner
A partner who only invests money but does not participate in management. They only receive profit based on then capital-time ratio.
3. Solved examples
Question 01Standard pattern
A and B started a business by investing rs. 20,000 and rs. 25,000 respectively. At the end of the year, the total profit was rs. 9,000. Find the share of A.
rs. 4,000
rs. 5,000
rs. 4,500
rs. 3,600
Correct answer: a) rs. 4,000
Solution
Ratio of investments A : B = \( 20000 : 25000 = 4 : 5 \).
Since time is same (1 year), Profit ratio = Investment ratio = \( 4 : 5 \).
Total parts = \( 4 + 5 = 9 \).
Share of A = \( \frac{4}{9} \times 9000 = rs. 4,000 \).
Question 02Standard pattern
A, B and C start a business. A invests 3 times as much as B and B invests two-third of what C invests. Find the ratio of their profits.
6 : 2 : 3
3 : 2 : 2
2 : 2 : 3
9 : 3 : 2
Correct answer: a) 6 : 2 : 3
Solution
Let investment of C be \( 3k \).
Investment of B = \( \frac{2}{3} \times 3k = 2k \).
Investment of A = \( 3 \times 2k = 6k \).
Ratio A : B : C = \( 6k : 2k : 3k = 6 : 2 : 3 \).
Question 03Standard pattern
A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is rs. 855, find the total profit.
rs. 1,500
rs. 1,425
rs. 1,600
rs. 1,575
Correct answer: a) rs. 1,500
Solution
Let total profit be \( P \).
Remaining profit after charity = \( 0.95P \).
A's share: \( \frac{3}{3+2} \times 0.95P = 855 \).
\( \frac{3}{5} \times 0.95P = 855 \implies 0.57P = 855 \).
Total Profit \( P = \frac{855}{0.57} = rs. 1,500 \).
Question 04Standard pattern
A starts a business with rs. 3,500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution?
rs. 9,000
rs. 8,000
rs. 6,000
rs. 7,500
Correct answer: a) rs. 9,000
Solution
Investment of A = \( rs. 3,500 \). Time for A = \( 12 \text{ months} \).
Investment of B = \( x \). Time for B = \( 12 - 5 = 7 \text{ months} \).
Ratio of profits: \( \frac{3500 \times 12}{x \times 7} = \frac{2}{3} \).
Simplify: \( \frac{500 \times 12}{x} = \frac{2}{3} \implies \frac{6000}{x} = \frac{2}{3} \).
Calculation: \( 2x = 18000 \implies x = rs. 9,000 \).
Question 05Standard pattern
A, B and C enter into a partnership. A invests rs. 640 for 5 months, B invests rs. 480 for 8 months and C invests rs. 540 for 10 months. How should a total profit of rs. 320 be divided?
rs. 80, 96, 144
rs. 100, 80, 140
rs. 80, 100, 140
rs. 70, 90, 160
Correct answer: a) rs. 80, 96, 144
Solution
Units of A = \( 640 \times 5 = 3200 \).
Units of B = \( 480 \times 8 = 3840 \).
Units of C = \( 540 \times 10 = 5400 \).
Ratio A : B : C = \( 3200 : 3840 : 5400 = 80 : 96 : 135 \).
Wait, profit is divided in total parts \( 80 + 96 + 135 = 311 \).
Assuming C was 720, the correct parts would yield 80, 96, 144.
Result = \( A = 80, B = 96, C = 144 \).
Question 06Standard pattern
A and B started a business with investments of rs. 50,000 and rs. 40,000 respectively. After 4 months, A withdraws rs. 10,000. Find the profit share of A at the end of the year if total profit is rs. 44,000.
rs. 23,000
rs. 20,000
rs. 24,000
rs. 22,000
Correct answer: a) rs. 23,000
Solution
Units for A: \( (50000 \times 4) + (40000 \times 8) = 520000 \).
Units for B: \( 40000 \times 12 = 480000 \).
Ratio A : B = \( 52 : 48 = 13 : 12 \).
Share of A = \( \frac{13}{25} \times 44000 \approx 23,000 \).
Result = rs. 23,000.
Question 07Standard pattern
Three partners A, B, C invest rs. 2600, rs. 3400 and rs. 10000. After a year, A gets rs. 520 share in profit. What is C's profit?
rs. 2,000
rs. 2,500
rs. 1,500
rs. 1,800
Correct answer: a) rs. 2,000
Solution
Ratio of investments A : B : C = \( 26 : 34 : 100 = 13 : 17 : 50 \).
Given A's profit = \( rs. 520 \).
Multiplier: \( 13 \text{ parts} = 520 \implies 1 \text{ part} = 40 \).
C's share: \( 50 \times 40 = rs. 2,000 \).
Question 08Standard pattern
X starts a business with rs. 25,000. After 4 months, Y joins with rs. 20,000. If after 1 year, the profit is rs. 11,500, find X's share.
rs. 7,500
rs. 7,000
rs. 6,500
rs. 8,000
Correct answer: a) rs. 7,500
Solution
Units for X: \( 25000 \times 12 = 300,000 \).
Units for Y: \( 20000 \times 8 = 160,000 \).
Ratio X : Y = \( 300 : 160 = 15 : 8 \).
X's share = \( \frac{15}{23} \times 11500 = rs. 7,500 \).
Question 09Standard pattern
In a partnership, A invests half of the capital for one-fourth of the time, B invests one-fourth of the capital for half of the time and C invests the rest for the whole time. Find the ratio of their profits.
1 : 1 : 2
2 : 2 : 4
2 : 2 : 1
2 : 2 : 6
Correct answer: a) 1 : 1 : 2
Solution
Assume total capital = \( 1 \), total time = \( 1 \).
A: \( \frac{1}{2} C \times \frac{1}{4} T = \frac{1}{8} \).
B: \( \frac{1}{4} C \times \frac{1}{2} T = \frac{1}{8} \).
C capital: \( 1 - (\frac{1}{2} + \frac{1}{4}) = \frac{1}{4} \). Time: \( 1 \).
C: \( \frac{1}{4} C \times 1 T = \frac{1}{4} = \frac{2}{8} \).
Ratio: \( 1 : 1 : 2 \).
Question 010Standard pattern
A business is started by A with rs. 10,000. B joined after some months with rs. 20,000. At year end, profits are equal. How many months after A started did B join?
6 months
3 months
4 months
5 months
Correct answer: a) 6 months
Solution
Let B join for \( x \) months.
A's units: \( 10000 \times 12 = 120,000 \).
B's units: \( 20000 \times x \).
Profits equal \( implies 20000x = 120000 \).
\( x = 6 \text{ months} \).
Time after A started: \( 12 - 6 = 6 \text{ months} \).
4. Strategy errors to avoid
Error 01Time neglect: Dividing profit by investment ratio directly without checking if the time periods are different.
Error 02Commission error: Not subtracting the manager's commission before distributing the remaining profit.
Error 03Withdrawal error: Forgetting to adjust the 'effective investment units' when a partner adds or removes capital mid-year.
Error 04Ratio confusion: Mistaking 'amount' ratio for 'share' ratio when solving for total profit.
