A partnership is an association of two or more persons who put their money together to carry on a certain business. It is of two kinds – **(i) Simple (ii) Compound**

**Simple partnership**: If the wealth of the associates is capitalized for the Same period, the partnership is called simple.

Compound Partnership: If the capitals of the partners are invested for different lengths of time, the partnership is called a compound. In a set of n persons devoted different amounts for diverse periods then their profit ratio is:

At : Bt: Ct : Dt. ……….: Xt [Now first person capitalized sum A for t, period, second person invested amount B for t, period, and so on.]

**Ex. 1: Three partners A, B, and C invest 1600, 1800, and 2300 respectively in a business. How should they divide the profit of 1938?**

Ans**:** The profit should be divided in the ratios of the capitals, i.e. in the ratio 16:18:23. Now, 16 + 18+ 23 = 57

A’s share = of 1938 = 3544

B’s share = of 1938 = 3612

23 C’s share = of 1938 = 3782

**Ex. 2: A, B and Center into partnership. A advances 1200 for 4 months, B 1400 for 8 months, and C*1000 for 10 months. They gain 585 altogether. Find the share of each.**

Ans**:** 1200 in 4 months earns as much profit as 1200 x 4 or 4800 in 1 month.

1400 in 8 months earns as much profit as 1400 ~ 8 or 11200 in 1 month.

1000 in 10 months earns as much profit as 1000 × 10 or 10,000 in 1 month. Consequently, the income should be alienated in the ratios of 4800, 11,200 and 10,000 i.e. in the ratios of 12, 28 and 25.

Now, 12 +28 + 25 = 65

A’s share = 12/65 X585 = 108

B’s share = 28/65 x 585= 252

C’s share =25/65 x 585 =225

Note: In compound partnership, the ratio of profits is directly proportional to both money and time, so they are multiplied together to get the corresponding shares in the ratio of profits.

**Ex. 3: A starts a business with 2,000. B seams that after 3 months with 4,000.C sets a sum of 10,000 in the business for 2 months only. At the end of the year, the business ended an income of 5600. How should the profit be divided among them?**

Ans: Ratio of their profits (A’s:B’s:C’s)=2 12:

4 9 :10 * 2=6:9:5 Now, 6 +9+ 5 = 20

Then A’s share – 5600/20 x6 = 1680

B’s share =5600/20 x9=25200

C’s share =5600 /20 x 5= 1400

**Ex. 4: A and B come in into a partnership for a year. A contributes 1500and B 32000. Subsequently 4 months they add C, who contributes 2250. If B draws his involvement after 9 months, how would they share a profit of $900 at the end of the year?**

Ans : A’s share : B’s share : C’s share

= 1500 x 12:2000 9 : 2250 x 8 = 15 x 12:20 x 9:22.5 x 8 = 180: 180 : 180 = 1:1:1

Therefore, each of them gets 900/3 = 300.

**Ex. 5: A and B enter into a speculation. A puts in 50 and B puts in 45.At the end of 4 months, A withdraws half his capital and at the end of 6 months B withdraws half of his capital. C then enters with a capital of 70. At the conclusion of 12 months, in what ratio will the income be separated?**

**Soln:** A’s portion: B’s portion : C’s portion

= 50×4+50/2× 8:45×6+45/2×6:70×6

= 400:405 : 420 = 80:81: 84

So, the income will be separated in the ratio of 80:81:84.

Now, you must have assumed both simple partnership and compound partnership. The method for compound partnership can also be inscribed as

A’s Wealth ×A’s Time in partnership A’s Income

B’s wealth ×B’s Time in partnership B’s Income

The overhead connection should be reminisced because it is used actual often in some kinds of question.

**Ex. 6: A began a business with 3450 and was joined afterwards by B with$300. When did B join if the incomes at the end of the year were separated in the ratio 2:1?**

Soln: Presume B merged the business for x months.

Then using the above formula, we have 450×12/300×x =1/2 or 300×2x = 450×12 x =450×12/2×300 = 9 months.

Therefore, B joined after (12-9=) 3 months.

**Ex.7 : A and B rent a pasture for 10 months. A puts in 100 cows for 8 months. How many cows can B set in for the residual 2 months, if he pays half as much as A?**

Soln. Suppose B puts in x cows. The ratio of A’s and B’s rents

= 1:1+1/2 = 1:3/2 = 2:3 then 100×8/x×2 = 2/3 or x = 100×8×3/2×2 = 600 cows.

Ex 8: A and B enter into a partnership with their capitals in the ratio 7:9.

At the end of 8 months, A extracts his wealth. If they receive the Incomes in the ratio 8:9, bargain how long B’s capital was used.

Ans: Suppose B’s capital was used for x months. Following the same rule ,we have 7×8/9×x = 8/9 So, B’s wealth was used for 7 months.

**Ex 9: A, B and C invested capitals in the ratio 2:3:5; the timing of their investments being in the ratio 4:5: 6. In what ratio would their profit be distributed?**

Ans: We should know that if the three investments be in the ratio a: b:c and the duration for their investments be in the ratio x:y:z, then the income would be dispersed in the ratio ax : by: cz. Therefore, subsequent the similar rule, the required ratio = 2 * 4:3 x 5:5 x 6 = 8:15:30

**Ex 10: A, B and C invested capitals in the ratio 5:6:8. At the end of the Professional term, they established the incomes in the ratio 5:3:12. Find the ratio of period for which they paid their capitals?**

**Soln: Succeeding the similar rule:**

If asset is in the ratio a: b:c and income in the ratio p:q:r then the ratio of time = p/a : q/b : r/c

Therefore, the required ratio = 5/5:3/6:12/= 1:1/2:3/2 = 2:1:3