Tricks To Solve Partnership Problems

In the Quantitative Aptitude section, a very necessary topic is  Partnership for every competitive exam like SBI Clerk Pre, IBPS Clerk Pre, IBPS RRB Pre, Railways, LIC, SSC CGL, SSC CHSL, NICL, OICL and other competitive exams. Every year 1-2 questions can be seen on this topic in Banking Exams, and SSC exams.   

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)

Questions For Practice:-

1. Question
Two friends A and B started a business by investing Rs.1500 and Rs. 7500 respectively. After 1 year find the ratio of their profits.

A) 1:5
B) 2:5
C) 1:4
D) 2:7
E) none of these

Answer :- A
Explanation :-
Investment of A/Investment of B = Profit of A/profit of B

=> Profit of A / profit of B = 1500/7500 = 1:5
Thus, the required ratio = 1:5

Tricks :-

Ratio of profit ,A:B =1500 : 7500 = 1 : 5

2.Question
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

Answer :- B
Explanation :-

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

Tricks:-

Investment ratio of A : B = 1 : 1/3 = 3 : 1

B’s share = 1/4 × 32000 = 8000

3.Question

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

Answer:- D
Explanation:-

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.

4. Question

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

Answer :- A
Explanation :-
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.

5. Question

A man starts a business in 2000 and a woman joins him after 6 months with  Rs. 8000. Find the ratio of their profits after one year.

A) 2 : 3
B) 3 : 4
C) 1 : 3
D) 1 : 2
E) None of these

Answer:- D
Explanation:-

Here, Man invested for 12 months and the Woman invested 6 months later. It means the woman invested for (12 – 6) = 6 months.

The ratio of profit of man and woman = Capital invested x Time period of investment

So, Man’s share: Woman’s share
= (2000 x 12) : (8000 × 6)
= 1 : 2
Here, the correct answer is D.

6. Question
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

Answer :- D
Explanation :-

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

7. Question
A, B and C three partners invest a certain amount in a business for time periods in the ratio of 5:3:8. At the end of the business terms, they got the profits in the ratio of 10:6:24. Find the ratio of Capitals of A, B and C.

A) 2 : 2 : 3
B) 2 : 3 : 2
C) 3 : 1 : 3
D) 4 : 2 : 1
E) none of these

Answer :- A
Explanation :-

Here,  t₁ : t₂ : t3 = 5 : 3 : 8

And P₁ : P₂ : P3 = 10 : 6: 24

Ratio of Capitals (Investment)

= P₁/t₁ : P₂/t₂ : P3/t3

= 10/5 : 6/3 : 24/8

= 2 : 2 : 3

8. Question
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

Answer :- A
Explanation :-

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

9. Question
Rohit and Bikash started a partnership 3 yr. At the start of the business, they invested ₹ 11000 and ₹ 25000, respectively. At the end of 3 yr, their total profit was 7200. What will be a share of Bikash of this profit?

(a) 5000

(b) 2600

(c) 5500

(d) 2100

(e) None of the above

Answer :- A
Explanation :-

Rohit’s investment : Bikash’s investment 
        = 11000 : 25000
        = 11 : 25

Let, Rohit’s investment = 11x
      Bikash’s investment = 25x

Rohit’s share : Bikash’s share 
         = Ratio of their investment
According to the question,
11x + 25x = 7200
x = 7200/36 = 200

Bikash’s share of profit = 25x = 25 × 200 = 5000

10. Question
P starts a business with 40000 and Q joins him after 3 months with 160000. Find the profit ratio at the end of year.

(a) 2:3 
(b) 1:3 
(c) 1:9 
(d) 1:7
(e) None of the above

Answer :- B
Explanation :-

Profits = Investment × time period

P’s share : Q’s share = 40000×12 : 160000×(12 -3)
                                   = 12 : 4 × 9
                                   = 1 : 3

11. Question
P, Q and R  started a business by investing capital in the ratio of 4 : 6 : 9. They received the profit in the ratio of 2 : 3 : 7 after the ending of the business terms. Find the ratio of their time period of capital investment.

(a) 1:1:9

(b) 2:2:9

(c) 10:10:9

(d) 9:9:7

(e) none of these

Answer – D
Tricks :-

Here, 
P₁: P₂ : P3 = 2 : 3 : 7           [Ratio of profit] 
X1: X2 : X3 = 4 : 6 : 9       [ Ratio of investment]

Required ratio
= P₁/X1 : P₂/X2 : P3/X3
= 2/4 : 3/6: 7/9
= 1/2 : 1/2 : 5/9
= 9 : 9 : 7

Here the correct answer is D.

12. Question

A and B started a business by investing 1200 and 1500, respectively. After 3 months A takes out 700, while B puts in 500 more. After 3 months more, C joins the business with a capital of 2100. After a year, they earned a profit of 1920. By what value does the share of C exceed the share of A?

A) 200

B) 800

C) 2100

D) 600

E) None of these

Answer:- B         

Tricks:-

A’s share : B’s share : C’s share
= [(1200×3) + (1200-700) × 9] : [(1500×3) + (1500+500)×9] : [ 2100× 6]
= (12×3 + 5×9) : ( 15×3 + 20×9) : ( 21 × 6)
= 81 : 225 : 126
= 9 : 25 : 14
Here ,the share of C exceeds A’s share by
= [(14-9) × 1920]/(9+25+14) 
= 800
 Thus,the correct answer is B.

13. Question

P, Q and R  invest certain capitals for time periods in the ratio of 4 : 2 : 1. At the end of the business, they received the profits in the ratio of 3: 4: 2. Find the ratio of investments of P, Q and R.

(a) 2: 5: 1

(b) 6 :19 :3

(c) 3 : 8 : 8

(d) 6: 6:1

(e) 6:17: 1

Answer :- C
Tricks :-

Here, t1 : t2 : t3 = 4 : 2 : 1
 And P1 : P2 : P3 = 3 : 4 : 2
We know , 
Investment ratio of P, Q and R
= P1/t1 : P2/t2 :P3/t3
= 3/4 : 4/2 : 2/1
= 3/4 : 2 : 2
= 3 : 8 : 8

Here,the correct answer is C.

14. Question  

Samar invested 10% more than the investment of Mina and Mina invested 10% less than the investment of Raju. If the total investment of all the three persons is 5780, find the investment of Raju.

A) 3000
B) 2000
C) 4000
D) 5000
E) none of these

Answer :- B
Tricks :-
Let, the investment of Raju = 100
Mina’s investment = 90             ( 10% less of 100)
Samar’s investment = 99          (10% more of 99)

Samar : Mina : Raju = 99 : 90 : 100
Investment of Raju = 5780× 100/ 289 
                                  = 2000
Here, the correct answer is B.

15. Question

A B and C started a business in partnership. A’s profit was 1/5 of the total profit and B and C distributed the remaining profit equally. If B got 500 more than A, then find the total profit.

(a) ₹ 1200

(b) ₹ 800

(c) ₹ 1000

(d) ₹ 1600

(e) ₹ 2500

Answer :- E
Explanation :-
Let, total profit = x
A’s profit = x * 1/5 = x/5
Remaining profit = x – x/5 = 4x/5
So, B’s profit = C’s profit = 2x/5
According to the question,
    (2x/5 – x/5 )= 500
=> x/5 = 500
=> x = 2500
Thus, the total profit = 2500 Rs.

16. Question
M and N  start a business in partnership. M invests 9000 for 8 months and N invests a certain amount for 6 months. Out of the total profit, N got 3/7 of the profit. How much capital was invested by N?

(a) ₹ 5400

(b) ₹ 6400

(c) ₹ 9000

(d) ₹ 7400

(e) ₹ 5000

Answer :- C
Tricks:-

Profit of N = 3/7
Profit of M = (1 – 3/7) = 4/7
Profit Ratio of M and N = 4/7 : 3/7   = 4 : 3
Let,Capital investment by N = P
According to question,
   (9000 × 8) : ( N’s capital × 6) = 4 : 3
=> 72000/ 6P = 4/3
=> P = 9000
Thus, the capital invested by N = Rs. 9000

17. Question
P and Q started a business by investing capital in the ratio 5 : 6 and their annual profits were in the ratio 2 : 3. If A invested the money for 8 months. B invest his money for how many months?

A) 7 months
B) 8 months
C) 9 months
D) 10 months
E) None of these

Answer:- D
Explanation:-
Let, A invested Rs. 5x for 8 months and B invested 6x for y months.
then,
(5x × 8) /(6x × y) = 2/3
=>  40/6y = 2/3
⇒ y = 10
Thus, B invests his money for 10 months.
Hence, option D is correct.

18. Question
P and Q start a business in partnership. P invests a certain amount at the beginning, Q invests double the amount of P after 4 months and R invests thrice the amount of P after 8 months. If the annual profit is Rs.3000, then find the R’s share in profit.

A) Rs 1200
B) Rs 1000
C) Rs 3000
D) Rs 500
E) Rs 900

Answer :- E
Explanation :-

Let ,
P’s investment = x
Q’s investment = 2x
R’s investment = 3x
then, ratio of their capitals 
= (x * 12) : (2x * 8) : (3x * 4)
= 12x : 16x : 12x  
= 3 : 4 : 3

∴   R’s profit  = 3000 × 3/10  = 900
Hence, option E is correct.

19. Question
A, B and C three friends hired an ola car for Rs. 810 and used it for 3, 2 and 4 hours respectively. Find the hire charges paid by B .

A)  Rs.180 
B)  Rs.210
C)  Rs.320
D)  Rs.160
E)  Rs.200

Answer:-A

Tricks :-

A : B : C = 3 : 2 : 4
B = 810 × 2/9 = 180
Thus , the hire charges paid by B is Rs. 180.

20. Question
A, B and C three partners started a business jointly. A and B invested capitals in the ratio of 5 : 3 whereas B and C invested capitals in the ratio of 2 : 1. If their total annual profit is Rs. 15200, then find the B’s share in the total profit.

A) 6200
B) 5800
C) 7500
D) 4800
E) None of these

Answer:- D

Tricks :-
A : B = 5 : 3   …..(×2)    = 10 : 6
B : C = 2 : 1   …..(×3)    =  6 : 3
A : B : C = 10 : 6 : 3
B’s share in profit = 15200 × 6/19  = 4800
Here, the correct answer is D.

21. Question

P, Q and R are three partners of a company. During a particular year P received half of the profit, Q received one-third of the profit and R received the remaining Rs. 3,000. How much did Q receive?

A) Rs. 5,000
B) Rs. 6,000
C) Rs. 3,000
D) Rs. 1,000
E) None of these

Answer:- B

Tricks :-

Profit earned by R 
= 1 – (1/2 + 1/3)  
= 1 – 5/6  
= 1/6

So,

1/6 = 3,000

∴ 1  =  18,000

∴    Profit received by Q = 1/3×18,000 
                                         = Rs. 6,000

Hence, option B is correct.

22. Question
Aman and Anushka started a business by investing Rs. 5000 and 6200 respectively. After one year the difference between their profits is Rs 600. Find the total profit.

A) Rs. 8500
B) Rs. 8450
C) Rs. 8960
D) Rs. 8740
E) None of these

Answer:- E
Explanation:-

The ratio of their capital = 5000 : 6200
= 25 : 31

Difference between their profit = 600 Rs. 
So, 
(31-25) –>600
=> 6 —> 600
=> (31+25) —-> 56 × 600/6     = Rs.5600
Thus,the total profit = Rs. 5600
Hence, option E is correct.

23. Question

Virat, Sanjay and Vikram started a business by investing certain money for equal time. Virat invested a certain amount, Sanjay invested 75% of Virat’s investment and Vikram’s investment is 50% more than Virat. Vikram earned Rs. 12600 of the total profit, Find the total profit.

A) Rs. 30400
B) Rs. 36200
C) Rs. 27300
D) Rs. 30100
E) None of these

Answer :- C
Explanation :-

Let,
Virat’s investment = x
Sanjay’ investment = x * 75/100
Vikram’s investment = x * 150/100
Investment of ratio of Virat : Sanjay : Vikram 
= x  : x * 75/100 : x * 150/100
= 1 : 3/4 : 3/2
= 4 : 3 : 6
Vikram’s profit = Rs.12600
Total profit  = 12600 × 13/6
                    = 27300

Hence option C is correct.

24. Question
A and B invested the amount for a year in the ratio of 6:5. Next year A increased 25% more of his investment and B took back 25% of his investment. At the end of the term, A gets Rs. 5500 of the total profit. Find the total profit.

A) Rs. 8000
B) Rs. 8250
C) Rs. 8350
D) Rs. 8250
E) None of these

Answer:- D

Tricks:-

A : B = 6 : 5

Ratio of Next year = 6 × 125% : 5 × 75% = 2 : 1

A’s Profit = Rs. 5500

Thus,Total Profit = 5500 × 3/2 = Rs. 8250

Hence, option D is correct.

25. Question
Sachin starts a business with  Rs. 3600. After a certain period of time, Diksha joins by investing Rs. 2700. At the end of the year, they got a profit in the ratio of 8 : 3. Find the time period of Diksha’s investment?

A) 8 months
B) 9 months
C) 7 months
D) 11 months
E) 6 months

Answer:- E
Explanation:-

The ratio of profit = (Capital of Suresh × Time)/(Capital of Deepak × Time)
Let Diksha’s investment be for x months.

Then, 
   8/3 = (3600 * 12)/(2700 * x)
=> x = (3600 × 12 × 3)/(2700×8)
=> x = 6 months
Hence, option E is correct.