The aim of this topic is to help you solve problems on partnership. The first section in this topic is an introduction to problems where we have shared some important points and tips and partnership. The exercises contain solved question and answers on partnership. When solving exercises, we recommend you to try solving the problems on your own, then view the solution.
By the end of this post, you will learn to solve the following types of problems:
- A and B start a business by investing certain amount of money. B leaves the business few months after starting the business. In what ratio should the profit generated at the end of the year be shared between A and B.
- A starts a business with Rs. X. B joins after m months investing Rs. Y. C invests Rs. Z for n months. If at the end of the year, an amount of Rs. C, which is P% of the profit goes to charity. Find A’s share.
Introduction to Partnership
Partnership :
When more than one person run a business jointly, then the persons involved in the business are called partners and the agreement between them is called partnership.
Sleeping Partner :
A partner who only is an investor in the business.
Working Partner :
A partner who manages the business is the working partner.
Key Points
- When the partners invest in the business for the same amount of time, then the gain or loss is distributed in the ratio of their investments.
If A and B enter into a partnership, such that they invest their money for equal periods, then
A’s share : B’s share = Capital of A : Capital of B
- When the partners invests in the business for different amount of time, then the gain or loss is distributed based on the capital invested and the time for which it is invested, as shown in the example below
If A and B enter into a partnership, such that they invest their money for different periods of time, then
A’s share : B’s share = Capital of A x Time period of A : Capital of B x Time Period of B
Exercises
Partnership - Exercise - Blog
15 questions
- A and B invest in a business in the ratio 4:5. If profit at the end of the year is Rs. 2700, find A’s share
- Rs. 1200
- Rs. 1500
- 700
- 500
Show the answer
Answer: Rs. 1200
A's share at the end of the year is
$\frac{4}{9}$ x 2700 = Rs. 1200
- A starts a business by investing Rs. 3000. After 4 months A is joined by B, who invests Rs. 4000. What is the ratio of profits that is to be shared between A and B at the end of the year?
- 8 : 9
- 9 : 8
- 3 : 4
- 4 : 3
Show the answer
Answer: 9 : 8
Since A invests Rs. 3000 for 12 months and B invests Rs. 4000 for 8 months, the profit at the end of the year is shared between A and B in the ratio ->
3000 x 12 : 4000 x 8 => 9 : 8
- A starts a business by investing Rs. 10000. B joins A after few months by investing Rs. 12000. If at the end of the year A and B profits are shared in the ratio 5:4, after how many months does B join A.
- 4 months
- 6 months
- 8 months
- 10 months
Show the answer
Answer: 4 months
Let the number of months for which B invests be $x$. Then, since A invests for the entire year, profits at the end of the year is shared in the ratio
10000 x 12 : 12 x $x$
Given than A and B share their profits in the 5:4 at the end of the year. Hence,
10000 x 12 : 12000 x $x$ = 5 : 4
10 : $x$ = 5 : 4
$x$ = 8 months.
Hence invests 8 months, which implies that B joins the business after 12-8 = 4 months.
- A invests Rs. 7000 in a business. B invests Rs. 4000. A leaves after 4 months. Profit at the end of the year is Rs. 2100. find the share B receives, if 5% of the profit gained is given to B as administrative charges.
- Rs. 1260
- Rs. 1000
- Rs. 1365
- Rs. 1995
Show the answer
Answer: Rs. 1365
Ratio of profits shared between A and B is
7000 x 4 : 4000 x 12 = 7 : 12.
Profit to be shared = 2100 - $\frac{5}{100}$ x 2100 = Rs. 1995
B's share = B's share in the profit + Administrative charges
B's share in the profit = $\frac{12}{19}$ x 1995 = Rs. 1260
Amount given to B as administrative charges => $\frac{5}{100}$ x 2100 = Rs. 105
Hence, B's share = Rs. 1260 + Rs. 105 = Rs. 1365
- A and B share profits in ratio 3:4. They invest for 12 and 9 months respectively. Find the ratio of their investments.
- 3 : 4
- 4 : 3
- 16 : 9
- 9 : 16
Show the answer
Answer: 9 : 16
Let A and B's investments be $x$ and $y$ respectively. Then ratio of their investments is given by,
$x$ x 12 : $y$ x 9 = 3 : 4
$x$ : $y$ = 9:16
- A, B and C invest in a business in the ratio 4:3:5 for one year. If C’s profit at the end of the year is Rs. 1250. Find B’s share.
- Rs. 250
- Rs. 500
- Rs. 750
- Rs. 1000
Show the answer
Answer: Rs. 750
Let A, B and C's share be 4$x$, 3$x$ and 5$x$ respectively. Then, given C's share =>
5$x$ = 1250
$x$ = 250.
Hence, B's share => 3 x $x$ = 3 x 250 = Rs. 750
- A, B and C enter into a partnership. A invests Rs. 5000 for 6 months, B invest Rs. 4000 for 5 months and C invests Rs. 3000 for 10 months. If the total profit is Rs. 10000. Find A’s share.
- Rs. 1000
- Rs. 1500
- Rs. 2000
- Rs. 2500
Show the answer
Answer: Rs. 2500
Ratio of profits shared =>
5000 x 6 : 4000 x 5 : 3000 x 10 = 30 : 20 : 30 = 1 : 2 : 1
Hence, A's share => $\frac{1}{4}$ x 10000 = Rs. 2500
- A, B and C start a business by investing Rs. 10000 each. After 6 months A invests Rs. 5000 while B withdraws Rs. 2000 after further 1 month. If the profit at the end of the year is Rs. 19000. Find C’s share.
- Rs. 7500
- Rs. 5500
- Rs. 6000
- Rs. 4500
Show the answer
Answer: Rs. 6000
Ratio of profits shared =>
(10000 x 6) + (15000 x 6) : (10000 x 7) + (8000 x 5) : 10000 x 12 = 15 : 11 : 12
C's share => $\frac{12}{38}$ x 19000 = Rs. 6000
- A and B start a business by investing Rs. 4000 and Rs. 5000 respectively. C joins after 4 months investing Rs. 3000. If A leaves after 8 months and the profit at the end of the year is Rs.4350. Find B’s share.
- Rs. 900
- Rs. 1200
- Rs. 1800
- Rs. 2250
Show the answer
Answer: Rs. 2250
Ratio of profits shared =>
4000 x 8 : 5000 x 12 : 3000 x 8 = 32 : 60 : 24 = 8 : 15 : 6
B's share =>
$\frac{15}{29}$ x 4350 = Rs. 2250
- A starts a business with Rs. 3000. B joins after 4 months investing Rs. 5000. C invests Rs. 6000 for 2 months. If at the end of the year, an amount of Rs. 1500, which is 12% of the profit goes to charity. Find A’s share.
- Rs. 4500
- Rs. 1000
- Rs. 2500
- Rs. 4500
Show the answer
Answer: Rs. 4500
Ratio of profits =>
3000 x 12 : 5000 x 8 : 6000 x 2 = 36 : 40 : 12 = 9 : 10 : 3
Let profit at the end of the year be $x$, then
$\frac{12}{100}$ x $x$ = 1500 => $x$ = Rs. 12500
Profit to be shared => Rs. 12500 - Rs. 1500 = Rs. 11000
A's share => $\frac{9}{22}$ x 11000 = Rs. 4500
- By investing in a business, A and B make some profit which they divide in the ratio 3:5. If A invests Rs. 15000. Find the amount invested by B.
- Rs. 18000
- Rs. 20000
- Rs. 21000
- Rs. 25000
Show the answer
Answer: Rs. 25000
Let the profit earned by A and B be 3$x$ and 5$x$ respectively and let the amount invested by B be $y$.
Then, ratio of profits shared by A and B is given by
3$x$ : 5$x$ = 15000 : $y$
=> $y$ = 25000
Hence, the amount invested by B is Rs. 25000
- A starts a business by investing Rs. 10000. B joins after few months with Rs. 15,000. After how months does B join if the profits are divided equally.
- 8 months
- 4 months
- 6 months
- 3 months
Show the answer
Answer: 4 months
Let B invest for $x$ months. Then, the ratio of profits divided is given by,
10000 x 12 : 15000 x $x$ = 1 : 1
15$x$ = 120
$x$ = 8
Hence, B joined after 12 - $x$ => 12 - 8 = 4 months
- A, B and C share profit from a business in the ratio 3 : 5 : 7. They partner for 9 months, 7 months and 5 months respectively. Find the ratio of their investments.
- 3 : 5 : 7
- 9 : 7 : 5
- 27 : 35 : 35
- 35 : 75 : 147
Show the answer
Answer: 35 : 75 : 147
Let A invest Rs. $x$ for 9 months, B invest Rs. $y$ for 7 months and C invest Rs. $z$ for 5 months. Then the ratio of their profits shared is given by
9$x$ : 7$y$ : 5$z$ = 3 : 5 : 7
First get the relation between $x$ and $y$ using the above ratio:
9$x$ : 7$y$ = 3 : 5
$x$ : $y$ = 7 : 15 _____ A
Now, get the relation between $y$ and $z$
7$y$ : 5$z$ = 5 : 7
$y$ : $z$ = 25 : 49 ______ B
From A and B taking the LCM of the value of $y$ in A and $y$ in B, we the value of $y$ as 75. The corresponding values for $x$ and $y$ will be 35 and 147. Hence,
$x$ : $y$ : $z$ = 35 : 75 : 147
- A and B start a business by investing together Rs. 20000. If C joins after 3 months and invests Rs. 10000, find the amount invested by B alone, if the profit at the end of the year is divided b/n A and C in the ratio 2:3.
- Rs. 5000
- Rs. 10000
- Rs. 15000
- Rs. 20000
Show the answer
Answer: Rs. 15000
Let A invest Rs. $x$, then B invests Rs. 20000 - $x$. The ratio of the profits shared by A and C is given by
12 x $x$ : 9 x 10000 = 2 : 3
$x$ = 5000.
Since A invests Rs. 5000, B invests 20000 - 5000 = Rs. 15000
- A and B invest in a business in the ratio 4:5. C joins after 4 months by investing an amount that is equal to the sum of investments of A and B. Find the ratio of profits shared by A, B and C.
- 4 : 5 : 6
- 4 : 5 : 3
- 3 : 2 : 5
- 5 : 6 : 7
Show the answer
Answer: 4 : 5 : 6
Let A and B invest 4$x$ and 5$x$ respectively, then C invests 9$x$.
Ratio of profits shared by A, B and C is given by,
4$x$ x 12 : 5$x$ x 12 : 9$x$ x 8
=> 48 : 60 : 72
=> 4 : 5 : 6
