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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 |