Partnership: Shortcuts & Tricks | Quantitative Techniques for CLAT PDF Download

Concept

When two or more persons join hands for a business to attain profits is called Partnership and the persons are called partners. Every partner invests some amount of money for a certain time to help the partnership firm to get profits. There are two types of partnership:

1. Simple partnership – If all partners invest their different amounts of capital (money) for the same period or the same capital for a different period, then such a partnership is called a simple partnership.
2. Compound partnership – If all the partners invest their different capitals (money) for different periods, then such a partnership is called a compound partnership. In Compound partnership partners’ profit not only depend on their investments but also on the time period.

Profit/Loss = time period
P1 : P2 : P3 : ………  = T1 : T2 : T3 : ……..   ( When capital investment is the same for the different time periods)

Profit/Loss = Capital investment × Time period
P1 : P2 : P3 : ………. = X1T1 : X2T2 : X3T3 : ………..
( When capital investment X1, X2, X3 is different for the different time period)

Examples

Q1: A and B two friends started a business jointly. The investment of B is equal to 1/3 times the investment of A. Find the profit share of B in the annual profit of 32000.
(a) 7000
(b) 8000
(c) 9000
(d) 10000
(e) None of these
Ans: B
Sol: 
Let the share of A = 3x
Then, the share of B = 3x * 1/3 = x
Profit of A/Profit of B = Investment of A/Investment of B
Hence, ratio of their profit = 3x/x = 3:1
According to the question,
3x + x = 32000
⇒4x = 32000
=> x = 32000/4 = 8000
Thus, A’s share= x = Rs. 8000

Q2: Akash and Bikash invested 4000 and 800 for a period of 2 yr. After 2 yr, they earned 6000. What will be the shares of Akash and Bikash out of this total earning?
(a) Rs. 5000,1000
(b) Rs. 4000, 2000
(c) Rs. 3500, 2500
(d) Rs. 1000, 5000
(e) Rs. 2000, 4000
Ans: A
Sol: 
Akash’s share: Bikash’s share= Akash’s investment: Bikash’s investment = 4000: 800 = 5:1
Now, let A’s share= 5x
and B’s share= x
According to the question,
5x + x = 6000
=> 6x = 6000
=> x = 1000
Clearly, share of B =x = 1000
and share of A = 5x = 5 x 1000 = 5000
Here ,the correct answer is A.

Q3: Three friends started a business. A invests 2000 for a year, B invests 4000 for 9 months. C invests an amount of 10000 in the business for 2 months only. At the end of the year, they make a profit of 11200. Find the profits of A, B and C.
(A) 3000 ; 5400 ; 2800
(B) 3200 ; 5100 ; 2900
(C) 3360 ; 2700 ; 5140
(D) 3360 ; 5040 ; 2800
(E) none of these
Ans: D
Sol: 
Profit = Capital investment × time period
A’s profit : B’s profit: C’s profit = 2000 x 12: 4000 x 9: 10000 × 2
= 2 x 12 : 4 x 9 : 10 x 2
= 6:9:5
Let, A’s profit = 6x, B’s profit= 9x; C’s profit = 5x
According to the question,
6x + 9x + 5x =11200
x = 11200/20 = 560
A’s profit= 6x = 6 x 560 = ₹ 3360
B’s profit= 9x = 9 x 560 = 5040
C’s profit= 5x = 5 x 560 = 2800

Q4: P, Q and R three partners start a business with an investment of ₹ 50000 each. P withdraw his capital after 9 months, Q after 6 months and R remains in partnership for 12 months. Find the ratio of their profits.
(a) 1:3:5
(b) 2:1:4
(c) 3:2:5
(d) 3:2:4
(e) none of these
Ans: D
Sol: 
The ratio of profit of P, Q and R will be in the ratio of the time period of their investment. (Investment same)
So. P’s profit: Q’s profit : R’s profit
= 9:6:12
= 3: 2:4
Thus, the correct answer is D.

Q5: A and B  started a business by investing a certain amount in the ratio of 5:3, respectively. After 4 months, C joins the business with an investment equal to that of B. What will be the ratio of the profits of A, B and C at the end of the year?
(a) 5 : 3 : 2
(b) 3 : 5 : 5
(c) 6 : 2 : 3
(d) 6 : 10 : 5
(e) 3 : 5 : 2
Ans: A
Sol: 
Let,
Investment of A = 5x
Investment of B = 3x
Investment of C = 3x
We know,
Ratio of profits = Ratio of Investment × Time period
A’s profit : B’s profit : C’s profit
= 5x * 12 : 3x * 12 : 3x * (12 – 4)
= 60 : 36 : 24
= 5 : 3 : 2