**Partnership**

This section gives you a statement like these, 3 Friends that have inverted in a Business, each of them have putted an different amount of money for a different amount of time, at the end of the year you will get a profit, now the problem statement that you have to find out profit of each individual as per their investment. Lets get started..

A Partnership is basically a Business venture that has two or more people that has invested money in that these people are called as partners. The profit need to be divide accordingly.

Lets see two cases how this is done

Case 1 : Same time periods.

Lets us say we have two partners A and B, A has inverted rs X, and B has invested rs Y for the same time period. When they given a profit, they divide it accordingly, in the same ratio.

Ratio of Profit = A/B = X/Y , A get X amount of profit and b gets Y amount of profit.

Now you can also have both different amount of money for different of time, that is case 2.

Case 2 : Different Time periods.

A has invested money for P amount of months and B has invested rs Y for Q months. And when profit will come, then A gets X × P amount of profit, and Y get Q × Y amount of profit. That is how much money they have invested multiply by months for investment.

Ratio of Profit = A/B = XP/YQ

Now lets go through simple problem and work out step by step.

**Problem 1**: Three friends A, B and C started a business by investing Rs. 1,20,000, Rs. 1,35,00 and Rs. 1,50,000 resp. Find out the share of each, out of an annual profit of Rs. 56,700.

**Solution :**

Given A invest 1,20,000,

B invest 1,35,000

C invest 1,50,000

Profit = 56,700

First step of our problem is to make a ratio.

Ratio = 1,20,000 : 1,35,000 : 1,50,000,

In solving a ratio one simple trick is to find a common, so we can remove the Last three 000, So the ratio will be.

120 : 135 : 150 , now we can see that the difference id 15,

so we can Divide this ratio by 15. 120/15 : 135/15 : 150/15

So the ratio will be = 8 : 9 : 10 and sum = 27

So the A’s Share will be 8/27*56700 = 16,800

B’s Share will be 9/27* 56700 = 18,899

C’s Share will be 10/27*56700= 20,999

Lets Solve some typical problem.

**Problem 2.**A, B and C start a business each investing Rs. 20,000. After 5 months a withdrew 5000, B withdrew Rs. 4000 and C invest Rs. 6000 more . At the end of year, a total profit of Rs. 69900 was recorded. Find the share of each.

**Solution**: now here is 3 investors A, B and C, they invested same amount of money for the different amount of time. Given that,

A invest B invest C invest

20,000 for 5 month 20,200 for 5 Month 20,000 for 5 month

After 5 months A 5000 Removes B 4000 Remove C 6000 Add

So the calculation will be.

20,000 × for 5 month 20,000 × for 5 month 20,000× for 5 month

+ 15000 × for 7 month + 16000× for 7 months +26000× for 7 month

Total will be = 205000 : 212000 : 282000

This is eventually our ratios. We can simplify this to eliminate last three 000, so the ratio will be

.

205 : 212 : 282 and the ratios total is 205+212+282=699

So the A’s Share will be 205/699*69900 = 20,500

B’s Share will be 212/699*69900 = 21,200

C’s Share will be 282/699*69900= 28,200

If we add this three value we will get 69,900 total.

**Problem 3**: A, B and C enter in to Partnership. A invest 3 times as much as B invest two-third of what C invests. At the end of year, the profit earned is Rs. 6600. What is the share of B.

**Solution**: Read the problem Carefully, they have not given any investment amount, but we don’t need it, we can assign variables and solve this problem.

The only thing is given you is the profit of 6600.

Lets assign

Investment by

C B A

Is X B is 2/3 (C’s investment) A is 3 (B’s) = 3(is 2/3(x) )

=

**X : 2/3(X) : 2X**

We don’t wont 3 in Denominator, so we can simply Multiply & Divide by 3, So it will be..

3×X : 3×(2/3): 3×2X = 3X : 2X : 6X

We can also see that X is common, so remove it, so eq will be 3 : 2 : 6 and 6+2+3=11

So the B’s Share will be = 1200 Rs.

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