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 |