When two or more than two persons run a business jointly, they are called partners and the deal is known as a partnership.
CONCEPT OF PARTNERSHIP
- 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.
-
=
- Share in total profit
- Profit ratio
- Time
- Capital
Sol: A’s profit: B’s profit: C’s profit = A: B: C
= 380 : 400 : 420
= 19 : 20 : 21
Profit share of A =
= 57 Rs.Profit share of B =
= 60 Rs.Profit share of C =
= 63 Rs.Ex: 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 & B is Rs 2100. Find the total profit.
Sol: Ratio of shares of A, B & C = Ratio of their investment
A : B : C = 120000 : 135000 : 150000
= 8 : 9 : 10
Difference b/w (A & B) = 9 - 8 = 1
1 = 2100
Total profit (8+9+10) = 27
= 27 x 2100
= Rs 56700
Ex: P, Q, and R started a business with investing their money in the ratio of 1 : 2 : 4, after 6 months P invested the half amount more as before and Q invested twice the amount as before while R withdrew 1/4th of their investments. Find the ratio of their profits at the end of the year?
Sol:
Ratio = P : Q : R
= (1 x 6 +
x 6) : (2 x 6 + 4 x 6) : (4 x 6 + 3 x 6)= 5 : 12 : 14
Ex: Two companies A and B entered into a partnership just 5 months ago. The ratio of profit claimed by A and B is 6 : 17. If B had just started his business 12 months ago with Rs.1275, what is the amount contributed by A?
Sol:
A =
= Rs.1080
Ex: 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 invest Rs. 6000 more. At the end of the year, the total profit of Rs. 69,900. Find the share of each.
Sol: Ratio of the capitals of A, B and C.
= (20,000 × 5 + 15000 × 7) : (20000 × 5 + 16000 × 7) : (20000 × 5 + 26000×7)
= 20,5000 : 212000 : 282000
= 205 : 212 : 282
A’s share = 69900 ×
= 20500 RsB’s share = 69900 ×
= 21200 RsC’s share = 69900 ×
= 28200 RsEx: A invested Rs. 76000 in a business. After 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 ?
Sol: Let B joined after x months .
Then B’s money was invested for (12 – x) months
A B
76000 x 12 : 57000 x (12 – x)
76 x 12 : 57 (12 – x )
= 
912 = 114 (12 - x)
8 = 12 - x
x = 4
Hence, B joined after 4 months.
Ex: A and B are partners in a business. They invest in the ratio of 5 : 6, at the end of 8 months A withdraws. If they receive profits in the ratio of 5 : 9, find how long B's investment was used?
Sol:
ratio = A : B
= 5 x 8 : 6 x t
according to the question,
5 x 8 : 6 x t = 5 : 9
t = 12 months
Ex: In a partnership, A invests of
the capital for 
of the time, B invests 
of the capital for 
of the time and C, the rest of the capital for whole time. Find A’s share out of the total profit of Rs. 2300. Sol: Capital of C = 1 -
Let the total time be 1 year.
A’s profit : B’s profit : C’s profit = A : B : C
=
: 
: 
=
: 
: 
= 1 : 4 : 18
Share of A =
= Rs. 100Ex.: A is working and B is a sleeping partner in a business. A puts in Rs.5,000 and B puts in Rs.6,000. A receives
% of the profit for managing the business and the rest is divided in proportion of their capitals. What does each get out of a profit of Rs.880?Sol: The amount which A receives for managing
= 12
% of Rs.880 = 
×880 = Rs.110The amount left = 880 – 110 = Rs.770
The amount left is to be divided in the ratio = 5,000 : 6,000 = 5:6
Out of the amount left, A’s share =
×770 = Rs.350Out of the amount left, B’s share =
×770 = Rs.420Total share receive by A = 110 + 350 = Rs.460
Share received by B = Rs.420
Ex.: 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 ?
Sol: Here, P1: P2: P3= 5 : 3 : 12
and x1: x2: x3= 2 : 3 : 5
The required ratio
=
: 
: 
=
: 
: 
=
: 1 : 
=
: 1×10: 
= 25 : 10 : 24
Ex.: 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.
Sol: A’s share : B’s Share
= 4000 × 12 : 5000 × (12 - 4)
= 4 × 12 : 5 × 8 = 6 : 5
Now, let the share of A = 6x
and the share of B = 5x
According to the question,
6x + 5x = 22000
11x = 22000
x = Rs. 2000
Share of A = 6x = 6 × 2000 = Rs. 12000
and share of B = 5x = 5 × 2000 = Rs. 10000
Ex.: In a business partnership among A,B,C and D, the profit is shared as follows.
=
= 
= 
. If the total profit is Rs.400000, the share of C is-Sol: Given,
A : B = 1 : 3
B : C = 1 : 3
C : D = 1 : 3
A : B : C : D = 1 × 1 × 1 : 3 × 1 × 1 : 3 × 3 × 1 : 3 × 3 × 3 = 1 : 3 : 9 : 27
Let the profits of A,B,C and D are x, 3x, 9x and 27x respectively.
Partnership of C =
× 400000=
× 400000 = 90000Ex.: Alok, Bhism and Chandra hired a meadow jointly for the whole year. Alok put in 80 buffaloes for 10 months, Bhism 100 buffaloes for 5 months and Chandra 150 buffaloes for 4 months. If Alok paid Rs.320 as rent, what is the total rent for the meadow?
Sol: Number of buffaloes put by Alok for 1 month
= 10 × 80 = 800
Number of buffaloes put by Bhisma for 1 month
= 5 × 100 = 500
and number of buffaloes put by Chandra for 1 month
= 4 × 150 = 600
Ratio = 800 : 500 : 600
= 8 : 5 : 6
Sum of ratios = 8 + 5 + 6 = 19
Total rent for the meadow =
= Rs. 760
Ex.: A, B and C started a business by investing Rs.40500, Rs.45,000 and Rs.60,000, respectively. After 6 months C withdrew Rs.15,000 while A invested Rs.4500 more. In annual profit of Rs.56,100 the share of C will exceed that of A by?
Sol: Ratio of equivalent capitals of A, B and C for 1 month
(40500 × 6 + 45000 × 6) : (45000 × 12)
: (60000 × 6 + 45000 × 6)
(405 + 450) : (450 × 2) : (600 + 450)
= 855 : 900 : 1050
= 171 : 180 : 210
= 57 : 60 : 70
Sum of ratios = 57 + 60 + 70 = 187
Required difference =
× 56100= =
× 56100 = Rs. 3900
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MAHENDRA GURU