Shortcut – Partnership
Finding ratio of the profit share:
Income (or) Profit share from a business is determined using two parameters – Investment and Duration.
Profit share is directly proportional to the duration of investment and the amount invested.
P1 : P2 : P3 = Ratio between profits
T1, T2, T3 = Respective time of investment
I1, I2, I3 = Respective investment
Question:
A started a business investing Rs. 5000. After 1 year B joined him investing Rs. 6000. After another year C joined them investing Rs. 9000. What is the ratio between their profit shares at the end of 3 years?
Answer:P1 : P2 : P3 = 5000 x 3 : 6000 x 2 : 9000 x 1
P1 : P2 : P3 = 15000 : 12000 x 9000
P1 : P2 : P3 = 5 : 4 : 3
Shortcuts-Partnership
Types of Partnership:
1) Simple partnership:
Partners invest for same time.
Suppose P and Q invest
Rs. x and Rs. y respectively for a year in a business, at the end of the year:
P’s share of profit/Q's share of profit=$\dfrac{x}{y}$
x : y = P’s share of profit : Q’s share of profit
2) Compound partnership:
When partners invest for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time).
Suppose P and Q invest
Rs. x for a months and Rs. y for b months respectively then,
P’s share of profit/Q's share of profit=$\dfrac{xa}{yb}$
Capital (amount) of P x Time period of P: Capital (amount) of Q x Time period of Q = P’s share of profit : Q’s share of profit
When n number of partners invests for different time periods T, then
$A_{1}T_{1}: A_{2}T_{2}: A_{3}T_{3} ……: A_{n}T_{n} = P_{1}: P_{2}: P_
{3}....: P_{n}$
A is the amount, T is the time period and P is the profit earned.
Type 1: Simple
Partnership:
a) 2 partners join at same time to start a business
b) 3 partners join at same time to start a business
Question:
Smith and Kate started a business investing Rs. 84,000 and Rs. 28,000 respectively. In what ratio the profit earned after 2 years be divided between Smith and Kate respectively?
Answer:P’s share of profit/Q's share of profit=$\dfrac{x}{y}$
(Where X and Y are investments)
X:Y =P's share of profit :Q's share of profit
Therefore,
smith's share of profit/Kate's share of profit =$\dfrac{84000}{28000}$=$\dfrac{3}
{1}$
The profit earned after 2 years will be divided between smith and kate in the ratio of 3:1
b) Three partners join at same time to start a business
Question:
John, Tyson and Mike started a business by investing Rs.1,00,000, Rs. 1,50,000 and Rs. 1,75,000 respectively. Find the share of Mike, out of an annual profit of Rs. 46,000.
Answer:Here, three partners invest together and earn a profit of Rs. 46,000 at the end.
Hint: Ratio of shares of John, Tyson and Mike = Ratio of their investments
Therefore,
100000 : 150000 : 175000 = 4 : 6 : 7
Now, we have to calculate share belonging to each person from all the shares considering the
annual profit.
Total shares = 4 + 6 + 7 = 17 shares
John’s Share =$\dfrac{4}{17} \times 46000 $= Rs. 10823.53
Tyson’s Share =$\dfrac{6}{17}\times 46000$ = Rs. 16235.294
Mike’s Share =$\dfrac{7}{17} \times 46000$ = Rs. 18941.176
Type 2: Compound
Partnership:
A) 2 Partners Join at Different Time in a Business:
i) 2 partners join at different time in a business
ii) 2 partners join at same time and 3rd partners joins the same business later
iii) 3 Partners join at different time
Question:
George started a hardware business by investing Rs. 50,000. After six months, Kate joined him with a capital of Rs. 70,000. After 3 years, they earned a profit of Rs. 25,000. Find George’s share in profit.
Answer:This type of partnership is called as compound partnership. George invested for 3 years
(36 months) and Kate for 2 years 6 months (30 months). After George’s investment for 36
months and Kate’s investment for 30 months, both get a profit of Rs. 25,000.
b) 2 Partners Join at Same Time and 3rd Partners Joins the Same Business Later
Question:
Two partners X and Y started a business by investing in the ratio of 5 : 8. Z joined them after 8 months investing an amount equal to that of Y. At the end of the year, 20 % profit was earned which is equal to Rs. 98,000. Find the amount invested by Z.
Answer:Let the total profit be p.
Given: 20 % profit is equal to Rs. 98,000
20 % of p = 98000
p = 490000
Capital of X = 5 x
Capital of Y = 8 x
Capital of Z = 8 x
Therefore,
(5x × 12) + (8x × 12) + (8x + 8) = 490000 × 12
220x = 5880000
x = Rs. 26727.27
We have find the amount invested by z.
8x = 8 x 26727.27 = Rs. 213818.16
C) 3 Partners Join at Different Time
Question:
Three partners partnered for 14 months, 8 months and 7 months respectively. Find the ratio of their investments, if they shared a profit in the ratio 5 : 7 : 8.
Answer:Hint: Capital (amount) of P x Time period of P: Capital (amount) of Q x Time period of
Q = P’s share of profit : Q’s share of profit
Let us assume the investments of 3 partners as x, y and z.
Therefore,
14x : 8y : 7z = 5 : 7 : 8
$\dfrac{14x}{8y}=\dfrac{5}{7}$
70x=40y---->(1)
$\dfrac{14x}{7z}=\dfrac{5}{8}$
112x=35z---->(2)
From (1) and (2), we get
y=$\dfrac{7}{4}x and z=\dfrac{16}{5}x$
We have to find the ratio of investments of 3 partners.
x:y:z=x:$\dfrac{7}{4}x:\dfrac{16}{5}x$
Solving we get, the solution as:
x : y : z = 20 : 35 : 64