## Partnership Problem with Explanations

For all competitive exams Partnership is an important chapter. From Partnership chapter at least 2-3 problems are appear in all competitive exams like SSC and bank exams (SBI and IBPS-clerk and PO). This section will teach you to understand Parternership problems with explanation and short cut to solve problems quickly

### Partnership **– Study material for all competitive exams**

Partnership is an important topic for all competitive exams. This Partnership section will teach you how to solve Partnership questions. Some important and repeated questions are covered this chapter.

__Important Formula for Partnership:__

**Partnership:**

** **When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.

**Ratio of Divisions of Gains:**

I) When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.

Suppose A and B invest Rs. x and Rs. y respectively for a year in a business,

then at the end of the year:(A’s share of profit) : (B’s share of profit) = x : y.

II) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now gain or loss is divided in the ratio of these capitals.

Suppose A invests Rs. x for p months and B invests Rs. y for q months then,

(A’s share of profit) : (B’s share of profit)= xp : yq.

**Working and Sleeping Partners:**

A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner.

### Partnership Question & answers with Explanation:

Before go through the problems of Partnership. Please understand and learn basic formulas of Partnership.

Complexity of the question is differ for each exams. While learning solve high difficulty questions to boost your knowledge and success your exams.

**1) A invested Rs 25,300 for 7 months, B invested Rs 25,200 for 11 months and C invested Rs 27,500 fir 7 months. Find the share of A and C together out of a total profit of Rs 33,600.**

** A) Rs 18,600**

** B) Rs 17,500**

** C) Rs 19,500**

** D) Rs 21,500**

** E) Rs 19,200**

**Explanation: **

Ratio of shares of profit of A : B : C is

25300*7 : 25200*11 : 27500*7

23*7 : 252 : 25*7

23 : 36 : 25

Total of profit of A and C is (23+25)/(23+36+25) * 33600 = Rs 19,200

**2) In a business, A invested Rs 25,000 and B invested Rs 24,000. As his salary A got 1/50th of the total profit of Rs 60,000 after which the remaining amount was shared among A and B in the ratio of their shares in profit. Find the difference in the shares of both.**

** A) Rs 2,300**

** B) Rs 2,440**

** C) Rs 2,500**

** D) Rs 2,400**

** E) Rs 2,380**

**Explanation:**

Ratio of shares A : B is

25000 : 24000

25 : 24

A got 1/50 * 60000 = Rs 1200 extra

So remaining profit to be shared between A and B is 60,000 – 1200 = Rs 58,800

So now B got = 24/(25+24) * 58,800 = Rs 28,800

So A got = 1200 + (58800 – 28000) = Rs 31200

So different in shares = 31200 – 28800 = Rs 2400

**3) In a business A and B invested Rs 5,000 and Rs 6,000 respectively. After 9 months from start of business, C invested Rs 12000 and A and B both withdrew Rs 1,000 each from their investments. If at the end of year B and C together got Rs 12,250 from the total profit, then what is the total profit?**

** A) Rs 18,900**

** B) Rs 13,600**

** C) Rs 15,100**

** D) Rs 15,300**

** E) Rs 16,300**

**Explanation: **

Ratio of shares A : B : C is

5000*9 + 4000*3 : 6000*9 + 5000*3 : 12000*3

19 : 23 : 12

Let x is the total profit

So [(23+12)/54]*x = 12,250

Solve, x = Rs 18,900

**4) In a business, A and B invested Rs10,000 and Rs 11,000 respectively. After 4 months they both withdrew Rs 1000 from their respective investments. After a further of 6 months, A invested Rs 1000 more and B invested Rs 2000 more. What is the difference in the shares of both if Rs 54,450 is received as total profit after a year?**

** A) Rs 2480**

** B) Rs 3490**

** C) Rs 2310**

** D) Rs 3150**

** E) Rs 3220**

**Explanation: **

Ratio of shares of profit of A : B is

10000*4 + 9000*6 + 10000*2 : 11000*4 + 10000*6 + 12000*2

10000*6 + 9000*6 : 11000*4 + 10000*6 + 12000*2

10*6 + 9*6 : 11*4 + 10*6 + 12*2

10*3 + 9*3 : 11*2 + 10*3 + 12

57 : 64

Difference = (64-57)/(57+64) * 54450 = Rs 3150

**5) In a business, A and B invested Rs 2600 and Rs 3900 respectively. After half year, A withdrew half and B withdrew 1/3rd from their investments. What is the difference in the shares of both, if a total profit of Rs 16,800 is received after a year?**

** A) Rs 4200**

** B) Rs 5700**

** C) Rs 4500**

** D) Rs 5830**

** E) Rs 4770**

**Explanation:**

B withdrew =1/3 * 3900 = 1300, so for last 6 months invested 3900-1300 = 2600

Ratio of shares of profit of A : B is

2600*6 + 1300*6 : 3900*6 + 2600*6

26 + 13 : 39 + 26

2 + 1 : 3 + 2 = 3 : 5

So difference = (5-3)/(3+5) * 16800 = Rs 4200

**6) Vijay and Ajay started a business by investing Rs 2000 and Rs 1500 respectively. 4 months after start, Vijay withdrew all his money and Amit joined Ajay by investing Rs 3000. After the end of year, the difference between the shares of Amit and Vijay together and Ajay is Rs 3423. What is the total profit after a year?**

** A) Rs 12375**

** B) Rs 13455**

** C) Rs 14265**

** D) Rs 14350**

** E) Rs 12225**

**Explanation:**

Ratio of shares of Vijay : Ajay : Amit is

2000*4 : 1500*12 : 3000*8

4 : 9 : 12

[(12+4)-9]/(4+9+12) * x = 3423

Solve, x = Rs 12225

**7) Karuna and Varuna invested Rs 2400 and Rs x in a business. After 3 months, Karuna added Rs 600 while Varuna withdrew Rs 300. After a year out of a total profit of Rs 36,920, Varuna received Rs 17,160. Find the amount invested by Varuna at the starting of business.**

** A) Rs 2700**

** B) Rs 1900**

** C) Rs 2100**

** D) Rs 2400**

** E) Rs 1600**

**Explanation:**

Ratio of shares of Karuna and Varuna is

2400*3 + 3000*9 : x*3 + (x-300)*9

gives 11400 : (4x-900)

So (4x-900)/(11400+4x-900) * 36920 = 17160

Solve, x = Rs 2700

**8) Kashish and Sheena started a business by investing Rs 2600 and Rs 2400 respectively. After 7 months, they added Rs 600 and Rs 800 respectively. 33% of the total profit earned after a year is given in donation. If after giving donation, the difference between the shares of Kashish and Sheena is Rs 350, find the total profit earned after a year.**

** A) Rs 17,000**

** B) Rs 25,000**

** C) Rs 18,000**

** D) Rs 12,000**

** E) Rs 27,000**

**Explanation:**

Ratio of shares of profit of Kashish : Sheena is

2600*7 + 3200*5 : 2400*7 + 3200*5

171 : 164

So (171-164)/(171+164) * x = 350

Solve, x = Rs 16750

So (100-33)% of y (total profit) = 16750

Solve, y = Rs 25000

**9) Shikha and Shreya invested in the ratio 7 : 8 in a business. They got an annual profit of Rs 34,450. If Shikha withdrew her entire money at the end of 9 years, then what is the difference between their shares of profit?**

** A) Rs 7570**

** B) Rs 6400**

** C) Rs 7560**

** D) Rs 7150**

** E) Rs 8180**

**Explanation:**

Ratio of shares of profit of Shikha : Shreya is

7*9 : 8*12

21 : 32

So difference in shares = (32-21)/(21+32) * 34450 = Rs 7150

**10) Antra and Manvi invested Rs 3780 and Rs 3960 in a business. After 3 months, Antra withdew Rs 420 and Manvi withdrew Rs 180. At the same time Chetna joined them by investing Rs 4620. After a year, they made a profit of Rs 35,850. Find Manvi’s share in the annual profit.**

** A) Rs 13,450**

** B) Rs 12,750**

** C) Rs 12,350**

** D) Rs 13,650**

** E) Rs 13,950**

**Explanation: **

Ratio of shares of Antra : Manvi : Chetna is

3780*3 + 3360*9 : 3960*3 + 3780*9 + 4620*9

77 : 85 : 77

So Manvi’s share = 85/(77+85+77) * 35850 = Rs 12,750