13. PARTNERSHIP
!IMPORTANT FACTS AND FORMULAE I
1. Partnership:
When two or more than two persons run a business jointly, they are
called partners and
the deal is known as partnership.
2. Ratio of Division of Gains:
i) When investments of all the
partners are for the same time, the gain or loss is distributed a
among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for
a year in a business, then at the end of the year:
(A’s share of profit) : (B's share of profit) = x : y.
ii) When investments are for
different time periods, then equivalent
capitals are calculated for a unit of
time by taking (capital x number of units of time). Now, gain or loss is
divided in the ratio of these capitals.
Suppose A invests Rs. x for p months and B invests Rs. y
for q months, then
(A’s share of
profit) : (B's share of profit) = xp : yq.
3. Working and Sleeping Partners: A partner who manages the business is known . as a working partner and the one who simply
invests the money is a sleeping partner.
SOLVED EXAMPLES
Ex.
1. A, B and C started a business by investing Rs.
1,20,000, Rs. 1,35,000 and
,Rs.1,50,000 respectively. Find the share of each, out
of an annual profit of Rs. 56,700.
Sol. Ratio
of shares of A, Band C = Ratio of their investments
= 120000 : 135000 : 150000 = 8 : 9
: 10.
A’s share = Rs. (56700 x (8/27))= Rs. 16800.
B's share = Rs. ( 56700 x (9/27)) = Rs. 18900.
C's share = Rs. ( 56700 x (10/27))=Rs.
21000.
Ex. 2. Alfred started
a business investing Rs. 45,000. After 3 months, Peter joined him with a capital
of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs.
16,500. Find the lire of each.
Sol. Clearly, Alfred
invested his capital for 12 months, Peter for 9 months and Ronald
for 3 months.
So, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3)
=
540000 : 540000 : 270000 = 2 : 2 : 1.
Alfred's
share = Rs. (16500 x (2/5)) = Rs. 6600
Peter's
share = Rs. (16500 x (2/5)) = Rs. 6600
Ronald's
share = Rs. (16500 x (1/5)) = Rs. 3300.
Ex. 3. A, Band C start a
business each investing Rs. 20,000. After 5
months A withdrew Rs.6000 B withdrew Rs. 4000 and C invests Rs. 6000
more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find
the share of each.
Sol. Ratio of the
capitals of A, Band C
= 20000 x
5 + 15000 x 7 : 20000 x 5 + 16000 x 7 : 20000 x 5 + 26000
x 7
= 205000:212000 : 282000 = 205 :
212 : 282.
A’s share =
Rs. 69900 x (205/699) = Rs. 20500 I
B's share = Rs. 69900 x (212/699) = Rs.
21200;
C's share = Rs. 69900 x (282/699) = Rs. 28200.
Ex. 4. A, Band C enter into partnership.
A invests 3 times as much as B
and B invests two-third of what C
invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B ?
Sol. Let C's capital =
Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of
their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 6600 x (2/11))= Rs. 1200.
Ex. 5. Four milkmen rented a
pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21
cows for 3 months. If
A's share of rent is Rs. 720, find the total rent of
the field.
Sol. Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) :
(21 x 3) = 72 : 50 : 140 : 63.
Let total rent be Rs. x. Then, A’s share = Rs.
(72x)/325
(72x)/325=720 ó x=(720 x
325)/72 = 3250
Hence, total rent of the field is
Rs. 3250.
Ex.6. A invested Rs. 76,000 in
a business. After few months, B joined him Rs.
57,000. At the end of the year, the total profit was divided between them in
ratio 2 : 1. After bow many months did B
join?
Sol. Suppose B joined after x months. Then, B's money was invested
for (12 - x)
(76000 x 12)/(57000 x (12-x) =2/1 ó
912000=114000(12-x)
114 (12 - x) = 912ó12-x=8óx=4
Hence, B joined after 4 months.
Ex.7. A, Band C enter into a
partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests
another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At
the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find
initial investment of each.
Sol. Let the initial investments of A,
Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then,
(3x x 36) : [(2x
x 12) + (2x + 270000) x 24] : [(4x x
24) + (4x +270000) x 12]=3:4:5
1O8x
: (72x + 6480000) : (144x + 3240000)
= 3 : 4 : 5
108x /(72x+6480000)=3/4
ó 432x = 216x + 19440000
ó216x = 19440000
x=90000
Hence,
A’s initial investment = 3x = Rs. 2,70,000;
B's initial investment = 2x = Rs. 1,80,000;
C's
initial investment = 4x = Rs. 3,60,000.
