4.13 Partnership:

You would have heard the word partners in people are talking about business. In many cases two or more persons join hands together to start business. The business could be a dealership for products, running a Hotel, Setting up a workshop, Trading business, Provision stores….A business can not be started by borrowing money

Loan can be availed from Banks/Hire Purchasing Company to expand business. Before giving loan everyone will check how good the business is is running.  First Business should be running well. For this to happen normally partners invest money in the business. It will be easy to take loan if the business is running well.

The  Partnership’ is a firm  engaged in business and managed by two or more people. The persons involved are called ‘partners’. All the partners need not invest same amount of money. Similarly the period of investment in the partnership need not be same. If all the partners invest amount in a partnership for same period then it is called  ‘Simple Partnership’. In this case it is not necessary that all partners should invest same amount. They share profit in the same proportion (ratio) of their investments:

4.13 Problem 1: Let us take the case of Ram and John entering into a partnership together at the same time with Ram investing Rs. 15,000 and John investing Rs 5,000. Assume that partnership firm makes a profit of Rs.5000.Find out the share of their share of profit

Solution :

Since Ram has invested more he should get more money when compared to John. The question is how much more he should get? The profit should be shared in the same ratio as their investment.

Mathematics has an answer to this question so that partners do not have dispute on profit sharing. The ratio of investment between them is 15000: 5000 what does this indicate? (It indicates that of the total investment of Rs 20,000; Rs.15,000( ¾  or 75%) is  invested by Ram and rest which is 5000(1/4  or25%) is invested by John). In the same ratio the profit also need to be shared between them.

Step 1: The investment ratio of Ram and John is

15000:5000 when simplified becomes 3:1.

It means that  if Ram gets Rs 3 in the profit john should get Rs.1.  When we sum the terms of this ratio we get 4(=3+1). Then if the profit is Rs.4 then Ram should get Rs 3 and John should get Rs.1.

Step 2:

Total Profit =Rs 5000

Let us find their share in the profit:

Share of Ram = 5000*3/4 =  3750

John’s share  = 5000*1/4 =  1250

Verification:

Total profit of Ram and Sham = Rs 5000( 3750+1250) which is as same as given in the problem

The share of profit we distributed between Ram and John is 3750:1250

On simplification   we get the ratio as3:1

This is the same ratio of their investment which we arrived in Step 1. Thus   we are sure that we have distributed the profit to them in the correct proportion.

4.13 Problem 1: Three partners invest 51, 68 and 85 ‘Nishkas’ (Unit of measurement of currency). If they get 300   Nishkas’ back, find their share ( Lilavati Shloka 95)

Solution :

Ratio of their investment = 51:68:85  =3:4:5 = (3/12) : (4/12): (5/12)

In other words, if they had got a return of 12 Nishkas then they would have got 3,4,5 Nishkas

Since they got 300 Nishkas their share is (300*(3/12), (300*(4/12) , (300*(5/12) = 75,100,125

Note that these returns are also in the ratio of  3:4:5

Let us take a case where one of the partner not only invests in the partnership like others but also looks after and manages the business on a daily basis. Other partners just invest money and   do not spend time in managing the business. In this type of set up the person who manages the business by spending time is called ‘Working Partner. Because he spends his time in running the business he is given specified % of profit first before the profit is shared with partners (Working partner not only gets his share of profit in the proportion of investment but also gets extra money for managing the business)

4.13 Problem 3:   A, B and C invest 12,000 Rs 8000, Rs 20000 respectively in a partnership firm. Since B looks after the business he gets 10% of the total profit. If the firm  makes a  profit of Rs 8000 find out the share of each of the partner.

Solution :

Firstly, since B is a working partner he need to be paid 10% profit  =  800(10% of 8000)

The balance profit to be shared among partners is =  Total profit – Working partner’s share is 8000 -800 = 7200

The Proportion of investment by partners A, B , C is 12000:8000:20000

After simplifying we get 12:8:20 on further simplifications we get 3:2:5

Sum of terms of ratio = 10(3+2+5)

Share of A  = (Balance profit)*3/10 = 7200*3/10 = 2160

Share of B = (Balance profit)*3/10 = 7200*2/10 =  1440

Share of C = (Balance profit)*3/10 = 7200*5/10 =  3600

Since B is a working partner in all he got Rs  Rs2240(=800+1440)  and we observe following

- He got more money than A, though A invested more than him (This is because B was paid additional amount for having worked as Working Partner)

Verification:

As per above calculation the Profit shared between A, B and C is 2160: 1440: 3600

On simplification you could see that we get a ratio of 3:2:5 which is the same proportion they have invested in the partnership firm.

Let us take another case of partnership where   partners invest money for different periods

4.13 Problem 4 : X , Y and Z enter into a partnership, X invests Rs 5000 for 4 months, Y invests Rs 6000 for 5 months and Z invests Rs 4000 for 6 months. At the end of one year they make a profit of Rs 3700. Calculate the share of profit.

Solution :

In this Problem partners have invested money for different period. This type of Partnership is called

‘Compound   Partnership’

Let us calculate their share of profit. Since They have invested for different period we need to calculate their period of investment for uniform period so that profit is shared without disputes.

Step 1 :  X invests Rs. 5000 for  4 months

Y invests Rs. 6000 for 5 Months

Z invests Rs. 4000 for 6 months

Step 2 : Since their investments are for a different period and is of different  amount we  need to calculate their total investments for uniform period. Let us calculate their investment   as if they have invested their amount for one month. For example, investing   Rs 500 for 12 Months is equivalent to saying that the amount of 6000=(500*12)  is invested for one month. By this logic we have

X invests  Rs.20,000(=5000*4) for 1 month

Y invests  Rs.30,000(=6000*5) for 1 month

Z Invests  Rs. 24,000(=4000*6) for 1 month

Step 3 :

Since we have arrived at their investments as if their investment is for a uniform period of 1 month,we can find the ratio of their investments which is

20,000:30,000:24,000  and on simplification we get 10:15:12

Total profit is Rs 3700

Step 4:

X’s share of profit is = 10/37*3700 = Rs 1000

Y’s share of profit is = 15/37*3700 = Rs 1500

Z’s share of profit is = 12/37*3700 =  Rs.1200

Verification:

Sum of their profit = Rs3700(100+1500+1200)  which is as given in the problem

Share of their profit  is 1000:1500:1200 and on simplification we get 10:15:12  which is the proportion of their investment which we arrived at Step 3.

4.13 Problem 5:A  B and C  start a partnership firm. A starts with an investment of Rs 2000. After 2 month B invests 2000 and after 6 months C invests 6000.  After one year they make a profit of Rs 5000.  A is a Working partner and he gets 20% of profit. Find out the share of each partner in the total profit.

Solution :

Since Partners are investing for different periods this is a ‘Compound Partnership’

Step 1

A invests for full year and thus investment is for 12 months

Since B joins after 2 months his investment is for 10 months

Since C joins after 6 months his investment is for 6 months

A invests Rs 2000 for 12 months

B invests Rs.2000 for 10 months

C invests Rs 6000 for 6 months

Step 2

A’s investment for 1 month =  24,000(=2000*12)

B’s investment for 1 month  = 20,000(=2000*10)

C’s investment for 1 month =   36,000(=6000*6)

Their investment ratio is 24000:20000:36000 which on simplification we get 6:5:9

Step  3

Total profit =  Rs 5000

A’s share  as A is a Working partner = Rs 1000(20% of Rs 5000)

Profit remaining to be shared among partners = Total Profit – Working partners share = Rs 5000-1000 = Rs.4000

Share of profit of partners A, B and C in the same proportion  of their investment as per Step 2 = 6:5:9

(sum of terms of ratio = 6+5+9=20)

A’s share in profit =   6/20*4000 = 1200

B’s share in profit = 5/20*4000=    1000

C’s share in profit = 9/20*4000 =   1800

Verification:

Total of share of their profits = Rs 1200+1000+1800 = Rs 4000(for this if you add Rs 1000 which is Working Partner’s share we get the total profit of Rs 5000 which is same as given in the problem)

Ratio of A, B and C in profit = 1200:1000:1800 which on simplification gives 6:5:9 which is same as their investment ratio (as per Step 2)

These workings confirm that the profit has been shared in the same proportion of their investment

4.13 Summary of learning

 No Points learnt 1 Partnership, Simple partnership, Compound partnership  Working Partner