**Partnership Problems with Solutions :**

In this section, we are going to learn, how to solve problems on partnership step by step.

**Partnership : **

When a business is run by two or more persons, it is known as partnership and the people who are running the business are called partners.We have the following four cases in partnership

**Case 1 : **

If all the partners invest equal amount for same time period then the profit is divided equally among them.

**Case 2 :**

If all the partners invest equal amount for different time period, then the profit is divided among them in the ratio of time period.

**Case 3 :**

If all the partners invest different amount for same time period, then the profit is divided among them in the ratio of amount invested.

**Case 4 :**

If all the partners invest different amount for different time period, then the profit is divided among them in the ratio of the product of investment and time period for each partner.

**Problem 1 :**

A invested 125% as much money as B, C invested 80% as much money as B. The total of all the three is $61,000. How much did C invest ?

**Solution : **

Because both A and C are compared to B, let us assume the investment of B as "x".

**Given :** A invested 125% as much money as B.

Investment of A = 125% of x = 1.25x

**Given : **C invested 80% as much money as B.

Investment of C = 180% of x = 0.8x

**Given : **The total of all the three is $61,000

So, we have

1.25x + x + 0.8x = 61000

3.05x = 61000

Divide both sides by 3.05

x = 61000/3.05

x = 20000

Investment of C is

= 0.8x

= 0.8 ⋅ 20000

= 16000

Hence, C invested $16000.

**Problem 2 :**

Daniel started a business with a capital of $ 8000. After six months, David joined him with investment of some capital. If at the end of the year, each of them gets equal amount as profit, how much did David invest ?

**Solution : **

Let "x" be the investment of David.

David's investment was in the business for six months.

Daniel invested $8000 and his investment was in the business for 12 months.

Then, the profit sharing ratio of David and Daniel is

6x : 12 ⋅ 8000

**Given : ** At the end of the year, each of them gets equal amount as profit.

So, we have

6x = 12 ⋅ 8000

Divide both sides by 6.

x = 2 ⋅ 8000

x = 16000

Hence, David's invested $16,000.

**Problem 3 :**

A, B and C start a partnership.The capitals of A, B and C are in the ratio 10 : 9 : 6 and the time period of A and B is in the ratio 2 : 3. B gets $10,800 as his share out the of a total profit of $26,000. If A's capital was there is in the business for 8 months, for how many months was C's capital in the business ?

**Solution : **

Let C's capital be in the business for "x" months.

Ratio of capitals is

A : B : C = 10 : 9 : 6

Ratio of time period is

A : B : C = 2 : 3 : x

As per case 4, ratio of profit share is

A : B : C = 20 : 27 : 6x

From the above ratio, we have

A's share = 20k

B's share = 27k

C's share = 6x ⋅ k

**Given :** B's share is $10,800.

Then, we have

27k = 10800

k = 400

So, we have

A's share = 20 ⋅ 400 = 8000

C's share = 6x ⋅ 400 = 2400x

**Given :** Total Profit is $26000

So, we have

8000 + 10800 + 2400x = 26000

18800 + 2400x = 26000

2400x = 7200

x = 3

Then, ratio of time period is

A : B : C = 2 : 3 : 3

From the above ratio, we have

A's time period = 2y

B's time period = 3y

C's time period = 3y

**Given : **A's capital was there is in the business for 8 months.

So, we have

2y = 8

y = 4

Then, C's time period is

= 3y

= 3 ⋅ 4

= 12

Hence, C's capital was in the business for 12 months.

**Problem 4 :**

A and B start a partnership by investing $24,000 and $36,000 respectively. Their agreement is to share half of the total profit equally and then share the remaining half in the ratio of their capital. If they share the entire profit in the ratio of their capitals, B would have got $2500 more than what she would have got otherwise. What is the total profit ?

**Solution : **

**Given : **A and B start a partnership by investing $24,000 and $36,000 respectively.

Ratio of capitals A and B is

= 24000 : 360000

= 2 : 3

Let the total profit be "x"

Half of the total profit = x / 2.

**Given :** A and B share half of the total profit equally.

Then,

B's share = (x/2) / 2 = x / 4

**Given :** A and B share remaining half of the total profit in the ratio of their capitals.

Ratio of their capitals is 2 : 3.

So, we have

B's share = 3/5 ⋅ x/2 = 3x / 10

Total profit of B is

= x/4 + 3x/10

= 5x/20 + 6x/20

= 11x / 20 -----(1)

Sharing the entire profit "x" in the ratio of their capitals (That is 2 : 3) :

B's share = 3x / 5 -----(2)

**Given :** In (2), B would get $2500 more than what she gets in (1).

So, we have

3x/5 - 11x/20 = 2500

12x/20 - 11x/20 = 2500

x/20 = 2500

x = 50000

Hence, the total profit is $50,000

After having gone through the stuff given above, we hope that the students would have understood "Partnership problems with solutions"

Apart from the stuff given above, If you want to know more about "Partnership problems with solutions", please click here

Apart from the stuff given on "Partnership problems with solutions", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**