Aptitude
Introduction to Partnership
Partnership : When two or more than two persons run a business joinly, they are called partners and the deal is known as partnership.
A simple partnership is the one inwhich the capitals of alll the partners are invested for the same time.
In this partnership, the gain or loss is distributed 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 for a yesar in business, then at the end of the year. (A's share of profit) : (B's share of profit) = x : y.
A compound partnership is the one in which the captital of the partners are invested for different time periods.
In this partnership, the equivalent capitals are calculated for a unit of time by taking (capital x nimber 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.
A partner who manages the business is known as a working partner and the one who simply invests the money is sleeping partner.
1.Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
Options:
A. 5 : 7 : 8
B. 20 : 49 : 64
C. 30 : 28 : 21
D. None of These
Solution:
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now,
$\eqalign{ & \frac{{14x}}{{8y}} = \frac{5}{7} \Rightarrow 98x = 40y \cr & \Rightarrow y = \frac{{49x}}{{20}} \cr & {\text{And, }}\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \Rightarrow 112x = 35z \cr & \Rightarrow z = \frac{{112x}}{{35}} = \frac{{16x}}{5} \cr & {\text{So}}\,x:y:z = x:\frac{{49x}}{{20}}:\frac{{16x}}{5} \cr & ({\text{Multiply by 20}}) \cr & \Rightarrow 20:49:64 \cr} $
Correct option: B
2. Rajesh started a business investing Rs. 10000. After six months, Sumera joined with a capital of Rs 5000. If at the end of the year, they earn a profit of Rs. 10000, then what will be the share of Sumera in the profit ?
Options:
A. Rs. 2380
B. Rs. 2300
C. Rs. 2500
D. Rs. 2460
Solution:
Now as per question, Rajesh invested for 12 months and Sumera invested for 6 months.
So Rajesh : Sumera = (10000 × 12) : (5000 × 6)
= 120000 : 30000
= 4 : 1
Sumera's Ratio in profit will be
$\eqalign{ & = {10000 \times \frac{{1}}{{4}}} \cr & = {\text{Rs}}{\text{. 2500}} \cr} $
Correct option: C
3. A and B invested in a business. The profit earned was divided in the ratio 3 : 4. If A invested Rs 30000, the amount invested by B is
Options:
A. Rs. 40000
B. Rs. 50000
C. Rs. 60000
D. Rs. 70000
Solution:
Let the amount invested by B = q.
$\eqalign{ & 30000:q = 3:4 \cr & \Rightarrow \frac{{30000}}{q} = \frac{3}{4} \cr & \Rightarrow q = 30000 \times \frac{4}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 40000}} \cr} $
Correct Option: A