**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Partnership**

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When two or more people invests in the same business, then this is called partnership and the people who invests in the business are called partners. This chapter is also an application of ratio and proportion like mixture and alligation.

**Types of Partnership**

**1. Simple Partnership** If all the partners invest capital for the same time period, then this is known as simple partnership. In this type of partnership profit or loss is distributed amongst the partners in the ratio of their’ investments.

**2. Compound Partnership** If all the partners invest capital for different period of time, then this is called compound partnership. In this type of partnership, we calculate capital for each partner as (capital x number of units of time).

**Types of Partner**

**1. Active Partner** A partner who manages the business is known as active partner or working partner.

**2. Sleeping Partner** A partner who only invests money and does not take part in managing the company is called sleeping partner.

**Different Cases of Problems of Partnership**

**Case I** When the investments made by all the partners are for the same time period, then gain or loss is distributed amongst them in the ratio of their investments.

**Example A and B invested Rs 24000 and Rs 8000 for a period of 2 yr. After 2 yr, they earned Rs 48000. What will be the shares of A and B out of this earning?**

(a) Rs 12000, Rs 36000

(b) Rs 14000, Rs 34000

(c) Rs 12000, Rs 26000

(d) Rs 18000, Rs 30000

**Case II** If the investments are made for different time periods, then for each partner^ we calculate the capital as (Capital x Number of units of time).

**Example A starts a business with Rs 4000 and B joins the business 4 months later with an investment of Rs 5000. After a year, they earn a profit of Rs 22000. Find the shares of A and B.**

(a) Rs 14000, Rs 8000

(b) Rs 12000, Rs 10000

(c) Rs 15000, Rs 7000

(d) Rs 16000, Rs 6000

**Some Useful Facts/Formula**

- If x1 :x2 :x3 is the ratio of investments and P1: P2 : P3 be the ratio of profits, then ratio of time periods is given by

P1/x1:P2/x2:P3/x3

**Example A, B and C invested capitals in the ratio of 2 : 3 : 5. At the end of the business terms, they received the profit in the ratio of 5 : 3 : 12. Find the ratio of time for which they contributed their capitals?**

(a) 25: 11: 14

(b) 24:13: 15

(c) 25: 10: 24

(d) 27 : 11 : 13

- If ratio of profits and ratio of time periods are given and the ratio of investments is to be known

P1/t1:P2/t2:P3/t3

Where, P1:P2 :P3 and t1:t2:t3 are the ratios of profits and time periods, respectively.

**Example A,B and C, each does certain investments for time periods in the ratio of 5: 6 :8. At the end of the business term, they received the profits in the ratio of 5 : 3 :12. Find the ratio of investments of A, B and C.**

(a) 2 : 4 : 3

(b) 4 : 1 : 3

(c) 2 : 1 : 4

(d) 2 : 1 : 3

**Reference Corner**

**1. At the beginning of a partnership business, the capital of B was 3/2 times that of A. After 8 months B withdrew 1/2 of his capital and after 10 months A withdrew 1/4 of his capital. At the end of the year, if the profit incurred is Rs 53000 find the amount received by A. SSC (10+2) 2013**

(a) Rs 30000

(b) Rs 23000

(c) Rs 30800

(d) Rs 32000

**Answer:**

**2. A, B, C enter into a partnership with shares in the ratio 7/2:4/3:6/5.After 4 months, A increases his share by 50%. If the total profit at the end of the year was Rs 43200, then the B’s share in the profit is SSC (10 + 2) 2013**

(a)Rs 4200

(b)Rs 4800

(c)Rs 7200

(d)Rs 8000

**Answer:**

**Practice Exercise**

**1. Pankaj, Neeraj and Raman subscribes Rs 4700 for a business. Pankaj subscribes Rs 700 more than, Neeraj Rs 300 more than Raman. How much will each receive out of the profit of Rs 846 respectively?**

(a)Rs 270, Rs 396, Rs 180

(b)Rs 396, Rs 180, Rs 270

(c)Rs 396, Rs 270, Rs 180

(d)Rs 296, Rs 370, Rs 180

**2. A starts business with a capital of Rs 1400. Five months later B joins and further two months later C joins them. What amount of capital is put in, by B and C, if at the end of the year their shares of profit are as 4: 3: 2?**

(a)Rs 1800, Rs 1688

(b)Rs 1680, Rs 1800

(c)Rs 1700, Rs1780

(d)Rs 1780, Rs 1700

**3. Anand and Manish enter into partnership with capitals as 5 : 6. At the end of 8 months Anand withdraws. If they receive profit in the ratio of 5 : 9, find how long B’s capital was used?**

(a) 4 months

(b) 8 months

(c) 12 months

(d) 6 months

**4. Two partners invests Rs 12500 and Rs 8500 respectively in their business arid arrange that 60% of the profit should be divided equally between them and the remaining profit treated as interest on the capital. If one partner’s share is Rs 300 more than that of the other, find the whole amount of the profit.**

(a) Rs 4000

(b) Rs 500

(c) Rs 3837.5

(d) Rs 3937.50

**5. Nitin opened a workshop investing Rs 40000. He invested additional amount of Rs 100 every year. After 2 yr, his friend Sameer joined him with an amount of Rs 85000. Thereafter, Sameer did not invest any additional amount. On completion of 4 yr from the opening of workshop, they earned an amount of Rs 97500. What will be Nitin’s share in the earning? **

(a) Rs 55000

(b) Rs 66000

(c) Rs 75000

(d) Rs 45000

**6. A began a business with Rs 4500 and was joined afterward by B with Rs 5400. When did B join if the profit at the end of the year were divided in the ratio 2:1?**

(a) 4 months

(b) 5 months

(c) 6 months

(d) 7 months

**7. A, B and C enter into a partnership. A initially invests Rs 25 lakh and adds another Rs 10 lakh after one year, B initially invests Rs 35 lakh and withdraws Rs 10 lakh . After 2 yr and C invests Rs 30 lakh. In what ratio should the profits be divided at the end of three years?**

(a) 20: 19: 18

(b) 10 : 10 : 9

(c) 20 : 20′: 19

(d) None of these

**8. Atul arid Babita enter into a business partnership in which Atul contributes Rs 2000 for 9 months and Babita contributes Rs 5000 for 7 months. A profit of Rs 1100 will be divided between Atul and Babita in the ratio of **

(a) 6: 11

(b) 2 : 5

(c) 7 : 9

(d) 18 : 35

**9. Raju and Aman invested in a trade. They earned some profit which they divided in the ratio 2:3 of their investment. If Raju invested Rs 40, then the amount invested by Aman is**

(a) Rs 30

(b) Rs 60

(c) Rs 90

(d) Rs 100

**10. Krishna started a business with a capital of Rs 18000. Four months later, Suneeta joined him with a capital of Rs 24000. At the end of the year, total profit earned was Rs 5100. Suneeta’s share in the profit is**

(a)Rs 2100

(b)Rs 2200

(c)Rs 2300

(d)Rs 2400

**11. Dilip, Ram and Amar started a shop by investing Rs 2700, Rs 8100 and Rs 7200, respectively. At the end of one year, the profit was distributed. If Ram’s share was Rs 3600, their total profit was **

(a) Rs 10800

(b) Rs 11600

(c) Rs 8000

(d) None of these

**12. A person invests money in 3 different schemes for 6 yr, 10 yr and 12 yr at 10%, 12% and 15% respectively. At the completion of the duration of each scheme, he gets the same amount. What is the ratio of his investments?**

(a) 6 : 3 : 2

(b) 2 : 3 : 4

(c) 3 : 4 : 6

(d) 4 : 6 : 2

**13.Jayant started a business investing Rs 40000. After four months, Arjun joined him with a capital of Rs 60000. At the end of one year, what ratio should Jayant and Aijurj shares the profit?**

(a) 1 : 2

(b) 2:1

(c) 1 : 1

(d) 1 : 3

**14. Ali, Bahadur and Chetan enter into partnership and their capitals are in the proportion 1/3:1/4:1/5. Ali withdraws half his capital at the end of 4 months. Out of a total annual profit of Rs 8470, A’s share is**

(a) Rs 2520

(b) Rs 2800

(c) Rs 3150

(d) Rs 4120

**15. A is a working and B is a sleeping partner in a business, A puts in Rs 12000 and B, Rs 20000. A receives 10% of the profits for managing, the rest being divided in proportion to their capitals. Out of a total profit of Rs 18000, the money received by A is **

(a)Rs 6480

(b)Rs 8400

(c)Rs 7875

(d)Rs 8328

**Answers**

**Hints & Solutions**

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