## Partnership Part 1

Important formula:

When time is the same; Investment = Profit

When time is different; Profit = Investment*Time

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

$\frac{A'S&space;Investment}{B'S&space;Investment}=\frac{ProfitShareOfA}{Profit&space;ShareOf&space;B}$

Problem 1: A, B, and c started a business by investing Rs.120000, Rs.135000 and Rs.150000 respectively. If the difference between the profit of A and B is RS. 2100. Find the total profit?

Solution:

120000  :  135000  :  150000

8               :         9       :      10

8-9=1

8+9+10=27

1——>2100

27——>?$\frac{2100\times&space;27}{1}=56700$

Problem 2: A invested RS. 76000 in a business. After a few months, B joined him with RS. 57000. At the end of the year, the total profit was divided between them in the ratio 2:1. After how many months did B join?

Solution:

76000         57000

4              :          3 ————>  Investment

$\frac{4\times&space;12}{3\times&space;(12-x)}=\frac{2}{1}$

12-x=8

x=4

B=12-4=8 months

After 8 months B had joined

Problem 3: A, B, and C start a business each investing RS. 20,000. After 5 months A withdraws RS. 5000, B withdraws RS.4000 and C invests RS. 6000 more. At the end of the year, the total profit is 69,900. Find the share of B?

Solution:

20000        20000           20000

20000*5=100000+15000*7=205000

20000*5=100000+16000*7=212000

20000*5=100000+26000*7=282000

205  :  212  :  282

Share of B = $\frac{212}{699}\times&space;69900=21200$

## Partnership Part 2

Problem 1: A, B, and C started a business with an investment in the ratio 5:7:8 respectively. After one year C withdraw 50% of his capital and A increased his capital by 60% of the total investment. After 3 years in what ratio should profit be distributed among A, B and C respectively?

Solution:

5:7:8

C withdraws 50%=$8\times&space;\frac{150}{100}=4$

A is increased 60%=$5\times&space;\frac{160}{100}=8$

(5  :  7  :  8)*1

(8  :  7  :  4)*2

16  :  14  :  8

21  :  21  :  16

Problem 2: A sum of RS. 8280 was distributed among 3 friends A, B and C in such a way that ratio of the amount of A to the amount of B and C was 2:7 whereas the ratio of the amount of C to the amount of A and B was 5:7. Find the amount that B will get?

Solution:

4*A  :  B+C  =  2 : 7——->9

3*C  :  A+B  =  5  :  7——->12

A  :  B+C  =  8  :  28

C  :  A+B  =  15  :  21

A=8     B=13    C=21

$\frac{13}{36}\times&space;8280=2990$

Problem 3: A and B started a business by investing RS. 20400 and RS. 25500 respectively. After 9 months A withdraw half of his investment and C joined with 2/3rd as invest of B If at the end of two years C got RS. 425. as his share in profit. find the total profit?

Solution :

20400        25500

4              :           5

C = $\frac{5\times&space;2}{3}=\frac{10}{3}$

4*9 + 2*15  :  5*24  :  $\frac{10}{3}$*15

66  :  120  :  50

33  :  60  :  25

25———>425

1———->?17

118——–>?2006

## Partnership Part 3

Problem 1: A and B started a business by investing Rs.37200, Rs.46500 respectively. After some time B left and C joined with Rs.55800 if at the end of 15 months a profit of Rs.36800 was generated in which C claimed Rs.13800. Find after how many months B left and C joined?

Solution:

37200  :  46500  :  55800

124  :  155  :  186

A  :  B  :  C

4  :  5  :  6

4*15  :  5*X  :6(12-X)

Total profit = 368

C profit = 138

A+B=368 –  138=230

$\frac{6(15-x)}{60+5x}=\frac{138}{230}$

12+x=30-2x

x=6

After 6 months B left and C joined

Problem 2: X, Y, and Z enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After two months, X withdraw half of his capital and after 10 months, a profit of RS. 4200 is divided among them. What is the Y’S share?

Solution:

$\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$

6  :  4  :  3———-> Investment

6*2 + 3*10 :  4*12  :  3*12

42  :  48  :  36

7  :  8  :  6

7+8+6=21

21——->4200

1——–>?200

8——–>?200*8=1600

Problem 3: A, B, and C started a business with the investment in the ratio of 7/2:4/3:6/5. After how 4 months, A increases her share by 50%. If at the end of one year, they earn a total profit of RS.43200. Then find the share of C?

Solution:

$\frac{7}{2}:\frac{4}{3}:\frac{6}{5}$

$\frac{7}{2}\times&space;4+\frac{7}{2}\times&space;1.5\times&space;8:\frac{4}{3}\times&space;12:\frac{6}{5}\times&space;12$

$56:16:\frac{72}{5}$

$56\times&space;5:16\times&space;5:72$

35  :  10  :  9

54——–>43200

1———->?800

9———->?800*9=7200

## Partnership Part 4

Problem 1: A started a business by investing Rs.34500. B joined him after 8 months with an investment of Rs.41400 and business continuity after that. At the end of the partnership, B claimed 4/9th of total profit. Find for how long their partnership lasts since B joined?

Solution:

B=$\frac{4}{9}$

A+B=9

A = 9-4 = 5

A                        B

34500   :     41400

115        :    130

5             :         6

$\frac{5(X+8)}{6\times&space;X}=\frac{5}{4}$

2X+16=3X

X=16

Problem 2: A and B started a business with the investments in the ratio of 9:5 respectively. After 9 months from the start of the business, C joined them and the respective ratio between the investments of B and C was 3:5. If the annual profit earned by them was RS. 6760 at the end of 15 months, then find the difference between A’s share and C’s share in total profit?

Solution:

A  :  B  =  9  :  5

B  :  C  =  3  :  5

A :  B  :  C  =  27  :  15  :  25

25*15  :  15*15  :  25*6

27  :  15  :  10

27-10=17

$\frac{17}{52}\times&space;6760=2210$

Problem 3: A and B start a business by investing in the ratio 3:4. After 6 months C and D joined them by investing 25% more than B and 25% less than B respectively. If at the end of 2 years total profit of 20800 was generated. Find the share of B?

Solution:

A     :      B

3      :      4

25%=$\frac{1}{4}$

25% more thane B= 1+4 = 5

25% less then B= 4-1 =3

A   :   B   :   C   :   D

3   :   4   :   5   :   3

A = 3*2 = 6

B = 4*2 = 8

C = 5*1.5 = 7.5

D = 3*1.5 = 4.5

6    :    8    :    7.5    :4.5

60   :   80   :   75   :   45

12   :   16   :   15   :   9

12+16+15+9=52

52———–>20800

16————->?  $\frac{20800*16}{52}=6400$

## Partnership Part 5

Problem 1: A started a business with Rs.50,000 and after 4 months B joined with Rs.120,000. A received Rs.58000 as a share of profit including 10% commission for managing the business. What amount did B receive?

Solution:

A                                   B

50,000                    120,000

5                     :                8

$A=1+9\times&space;\frac{5}{13}=\frac{58}{13}$

$\frac{58}{13}$———->58000

1————>?13000

$10-\frac{58}{13}=\frac{72}{13}$

$\frac{72}{13}$————>?72000

Problem 2: A and B start a partnership by investing in the ratio 7:5. After 3 months C also joined with 20% less investment as B. After few months A left and D joined with 200/7% less investment as A. If after one and half years B claimed of$\frac{5}{14}$ the total profit. Find the investment time of D?

Solution:

C = $\frac{5\times&space;20}{100}=1$  =  5-1  =4

D = $\frac{7\times&space;200}{7\times&space;100}=2$  =  7-2  =5

A   :   B   :   C   :   D

7   :   5   :    4   :    5

(18-X)  :  18  :  15  :  X

126-7X   :   90  :  60  :  5X

$\frac{5}{14}$   ,A+B+C+D=14  , B—>5

$\frac{5}{9}$   ,A+B+C=9  ,  B=5

$\frac{90}{186-2X}=\frac{5}{9}$

$152=186-2X$

$2X=24$

$X=12$