Partnership : Partnership is an association of two or more parties, they put money for business.
Simple Partnership: Simple partnership is one in which the capitals of the partners are invested for the same time. The profit or losses are divided among the partners in the ratio of their investments.
Compound Partnership: Compound Partnership is one which the capitals of the partners are invested for different periods. In such cases equivalent capitals are calculated for a unit time by multiplying the capital with the number of units of time. The profits or losses are then divided in the ratio of these equivalent capitals. Tus the ratio of profits is directly proportional to both capital invested as time.
Working partner: A partner who participates in the working and manages the business is called a Working Partner.
Sleeping Partner: A partner who only invests capital but does not participate in the working of the business is called a Sleeping Partner.
Division of Profit and Loss:
1. Rule :When investment of all partners are for the same time, the loss or profit is distributed among partners in the ratio of investment. P’s share of profit : Q’s share profit = a : b 2.Rule : When investments are for different time period, then profit ratio is calculated as capital multiplied by length of investment Ex. P’s share of profit : Q’s share profit = a* t1 : b* t2
Questions with solutions LevelI

 A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdrawns Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
Solution: A : B : C = (40,000 X 36) : (80,000 X 12 + 40,000 X 24) : (120,000 X 24 + 40,000 X 12) = 3: 4: 16
 A, B, C enter into a partnership investing Rs. 35,000, Rs.45,000 and Rs.55,000 respectively. The respective shares of A, B, C in an annual profit of Rs.40,500 are ?
Solution : A : B : C = 35000 : 45000 : 55000 = 7 : 9 : 11.
A’s share = Rs (40500 x 7/27) = Rs. 10500
B’s share = Rs.(40500× 9/27) = Rs. 13500
C’s share = Rs.(40500×11/27)= Rs. 16500
 In a business, Lucky invests Rs. 35,000 for 8 months and manju invests Rs 42,000 for 10 months. Out of a profit of Rs. 31,570. Manju’s share is 😕
Solution : lucky: Manju = (35000 X 8) : (42,000 X 10) = 2:3
Manju’s share = Rs.3/5×31570 = Rs. 18,942
 Amar started a business investing Rs. 70,000. Ramki joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
Solution: Amar : Ramki : Sagar =
(70000 X 36) : (105000 X 30) : (140000 X24) = 12 : 15 : 16.
5 . A begins a business with Rs 450 and is joined afterwards by B with Rs 300. After how many months does B join if the profits at the end of the year is divided in the ratio 2 : 1?
Solution..(B) Suppose B joins for x months.
Then, 450 ´12 = 2
300 ´ x 1
x =450× 6
300
x= 9 months
\B joins after (12 – 9) = 3 months.
 Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and Jatin joined them with an amount of Rs. 35,000. What will be Rajeev’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?.
Solution : Shekhar : Rajeev : Jatin =
(25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
Rajeev’s share = Rs.(150000×26) = Rs. 50000
 A,B and C started a business with Rs.15000, Rs.25000 and Rs.35000 respectively. A was paid 10% of the total profit as a salary and the balance was divided in the ration of investment. If A’s share is Rs.4,200, then C’s share is: ?
Solution : A, B and C must divide their salaries in the ratio :
15,000 : 25,000:35,000 = 3:5:7
Assume total Profit = 100X.
then A share is 10% of 100X for managing business and 3/15 part of 90X for his investment (as the remaining profit is (100X – 10X = 90X)
So total A’s share = 10X + 315 × 90X = 4,200
⇒X = 150
Substituting X = 150 in 90X we get remaining profit for sharing. That is Rs.13,500
Now C’s share = 715×13,500 = Rs.6,300
LevelII
1.  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, the total profit is:  
Answer:1 Option B Explanation: Let the total profit be Rs. 100.
If A’s share is Rs. 57, total profit = Rs. 100.
 
2. 
A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.  
Answer: 2 Option B
Explanation: For managing, A received = 5% of Rs. 7400 = Rs. 370. Balance = Rs. (7400 – 370) = Rs. 7030. Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3) = 39000 : 42000 : 30000 = 13 : 14 : 10

3 .A, B and C enter into a partnership in the ratio : : . After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B’s share in the profit is:  
Answer:3 Option D
Explanation:
Let the initial investments be 105x, 40x and 36x.
= 1680x : 480x : 432x = 35 : 10 : 9.
 
4.  A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:  
Answer:4 Option D
Explanation: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000. So, x + x + 5000 + x + 9000 = 50000 3x = 36000 x = 12000 A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.

5.  Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?  
Answer:5 Option B
Explanation: Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively. Then, 14x : 8y : 7z = 5 : 7 : 8.
 
6.  A starts business with Rs. 3500 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 in the capital?  
Answer:6 Option D
Explanation: Let B’s capital be Rs. x.
14x = 126000 x = 9000. 
7.  A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew of his capital and B withdrew of his capital. The gain at the end of 10 months was Rs. 760. A’s share in this profit is:  
Answer:7 Option A
Explanation:
= (12x + 21x) : (15x + 28x) = 33x :43x = 33 : 43.

8.  A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?  
Answer:8 Option C
Explanation: Let the initial investments of A and B be 3x and 5x. A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5. 
9.  A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?  
Answer:9 Option A
Explanation: A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.

10.  A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B’s share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?  
Answer: 10 Option A
Explanation: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
