What is Involved in Partnership
1. Simple Partnership: If all the partners invest their capital (money) for the same period, then such partnership is known as the simple partnership.
2. Compound Partnership: if all the partners invest their capital (money) for different periods, then such a partnership is called the compound partnership.
There are also two types of partners:
1. Active Partner: A partner who manages the business, is known as the active partner. He is also known as the working partner.
2. Sleeping Partner: A partner who simply invests money and does not manage the business actively, is called the sleeping partner.
Different cases of Problems of Partnership.
Case-I
When the investments made by all the partners are for the same time-period, then gain or loss is distributed amongst them in the ratio of their investments. (This is the case of simple partnership)
Case-2
If the investments are made for different time periods, then for each partner, we calculate the capital as (Capital x Number of units of time)
Techniqe 1:
If x1 : x2 : X3 is the ratio of investments and P1 : P2 : P3 be the ratio of profits, then ratio of time periods is given by
P1/x1:P2/x2:P3/x3
To find ‘A’ and ‘B’, the 1st and foremost task is to keep following basic points in mind:
1. While solving problems, theowrk done is always
supposed to be equal to 1.
2. If a person can do a piece of work in ‘n’ days, then
that person’s 1 day’s work = 1/n
3. If a person’s 1 day’s work = 1/n, then the person will
complete the work in ‘n’ days.
4. A person works equally every day.
SOLVED EXAMPLES
- Ex.1: Ajit has Rs. 26 more than Anuj. Anuj has Rs. 60 more than Ravi. If all of the three together have a
total of Rs. 200, then how much amount does Ajit have?
(1) Rs. 78 (2) Rs. 68
(3) Rs. 104 (4) Rs. 106
(5) None of these
Sol.: Let the amount with Ajit be Rs. x.
Amount with Anuj = Rs. (x – 26)
Amount with Ravi = Rs. (x – 86)
X + x – 26 + x – 86 = 200
3x = 200 + 112 = 312
x = 312/3
= Rs. 104 - Ex.2: Yuvraj and Sehwag invested Rs 90,000 & Rs 60,000 respectively in a business. Yuvraj was the sleeping
partner while Sehwag managed the business. Sehwag got 25% of the profits for being the working partner. The profit for the year was Rs 60,000. How much does Yuvraj receive as profit? What is his return on investment?
Sol.: Profit to be shared = 60,000 x ¾ = Rs 45,000 (as Rs 15,000 is given to Sehwag for managing the show). Ratio of profit s to be shared = 90,000:60,000 = 9 : 6
Yuvraj’s = 9/(9+6) x (45,000) = Rs 27,000
Return on investment = (27,000/90,000) x 100 = 30% - Ex.3: A started a business with Rs. 80,000 and is joined afterwards by B with Rs. 120,000. After how many
months did B join if profits are shared equally?
Sol.: If profits are shared equally, effective investments for the month are same.
80,000 x 12 = 120,000 x x (x is the number of months
B invested)
x = 8
B joined after (12 – 8) = 4 months. - Ex.4: Three partners A, B and C invest Rs 1600, Rs 1800 and Rs 2300 respectively in business. How should
they divide a profit of Rs 1938 ?
Sol.: The profit should be divided in the ratios of the capitals, i.e. in the ratio 16:18:23.
Now, 16+18+23 = 57
A’s share = 16/57 of Rs 1938 = Rs 544
B’s share = 18/57 of Rs 1938 = Rs 612
C’s share = 23/57 of Rs 1938 = Rs 782 - Ex.5: A, B and C enter into partnership. A advances Rs 1200 for 4 months, B Rs 1400 for 8 months, and C
Rs 1000 for 10 months. They gain Rs 585 altogether. Find the share of each.
Sol.: Rs 1200 in 4 months earns as much profit as Rs1200 x 4 or Rs 4800 in 1 months.
Rs 1400 in 8 months earns as much profit as Rs 1400 x 8 or Rs 11200 in 1 month.
Rs 1000 in 10 months earns as much profit as Rs 1000 x 10 or Rs 10,000 in 1 month.
Therefore, the profit should be divided in the ratio of 4800, 11,200 and 10,000 i.e. in the ratios of 12,28 and 25.
Now, 12 + 28 + 25 = 65
A’s share = 12/65×585= Rs 108
B’s share = 28/65 x 585 = Rs 252
C’s share = 25/65 x 585 = Rs 225
