Quantitative Aptitude Partnership Study Material
Partnership is a form of association of two or more persons who contribute their resources like money in order to carry on a certain business together. It may be of simple or compound type.
Simple Partnership is one in which the capitals of the partners are invested for the same time. The profits or losses are divided among the partners in the ratio of their investments.
Compound Partnership is one in which the capitals of the partners are invested for different periods. In such cases equivalent capitals are calculated for a unit time by multiplying the capital with the number of units of time. The profits or losses are then divided in the ratio of these equivalent capitals. Thus the ratio of profits is directly proportional to both capital invested as well as time.
A partner who participates in the working and manages the business is called a Working Partner while the one who only-invests capital but does not participate in the working of the business is called a Sleeping Partner. A working partner gets either monthly payment or a part of the profit for his contribution in the management of the business. This payment is deducted from the total profit before its distribution.
It is advisable to do thoroughly the chapter on “Ratio and Proportion” as its concept will be used extensively in this chapter.
Ex. 1. Ram, Shyam and Mohan invest Rs. 1500, Rs. 2000 and Rs. 2500 respectively in a business. The profit earned is Rs. 1200. Find the share of each in the profit.
Sol. This is a case of simple partnership
Ratio of investments, Ram : Shyam: Mohan =1500:2000 :2500 = 3 :4 :5
Sum of the ratios = 3 + 4 + 5=12
Share in the profit
For Ram = (3/12) x 1200 = Rs. 300
For Shyam = (4/12) x 1200 = Rs. 400
For Mohan = (5/12) x 1200 = Rs. 500
Ex. 2. Rs. 5200 is to be divided among the partners A, B and C. The ratio of their investments is 1/2 :1/3 : 1/4 Find the share each partner receives
Sol. This is a case of simple partnership 1/2 :1/3 : 1/4 = 6/12 :4/12 : 3/12 ((Here 12 is the LCM of 2, 3 and 4) = 6:4:3
Sum of ratios 6+4+3 =13 and 5200 /13 = 400
A’s share = 6 x 400 = Rs. 2400
B’s share = 4 x 400 = Rs. 1600
Cs share = 3 x 400 = Rs. 1200
Ex. 3.A,B and C invest Rs. 1000, Rs. 4000 and Rs. 5000 respectively in a business. At the end of the year the balance sheet shows a loss of 20% of the total initial investment. Find the share of loss of each partner.
Sol. Total initial investment = Rs. 1000 + Rs. 4000 + Rs. 5000 = Rs. 10,000
Total loss= 20% of total initial investment
= 20/100 x10,000 = Rs.2000
This is an example of simple partnership So, the loss has to be divided among the partners in proportion to their investments.
Ratio of their investments, A.B: C=Rs. 1000: Rs. 4000: Rs. 5000= 1:4:5
Sum of the ratios =1+4 + 5=10
and Rs 2000/10 = Rs 200
Share of loss for A= 1 x Rs. 200 = Rs. 200
for B= 4 x Rs. 200 = Rs. 800
for C= 5 x Rs. 200 = Rs. 1000
Ex. 4. A, B and C enter into a partnership. A invests Rs. 2400 for 4 years, B Rs. 2800 for 8 years and C Rs. 2000 for 10 years. They earn Rs. 1170. Find the share of each.
Sol. This is a case of compound partnership.
Rs. 2400 investment for 4 years earns as much as Rs. 2400 x 4 = Rs. 9600 in 1 year .
Similarly, Rs. 2800 for 8 years is equivalent to Rs. 2800 x 8 = Rs. 22400 in 1 year
Rs. 2000 for 10 years is equivalent to Rs. 2000 x 10 = Rs. 20,000 in 1 year
The profit is, therefore, divided in the ratio Rs. 9600: Rs. 22400: Rs. 20000 or, 12:28:25
Sum of the ratios = 12 + 28 + 25 = 65 .
and, Rs. 1170/65 =Rs. 18
So, A’s share= 12 xRs. 18 = Rs. 216
B’s share=28xRs. 18 = Rs.504
C’s share= 25 x Rs. 18 = Rs. 450
Ex, 5. Ram and Shyam are partners in a firm. Ram invests Rs. 1500 and Shyam Rs. 2500. Ram is the working partner and gets 20% of the profit for his contribution in the management of the firm. Shyam is a sleeping partner. If the profit is Rs. 475, find the share of each.
Sol. First we have to deduct the payment to be made to Ram for his contribution in the management of the firm.
20% of Rs. 475 = 20/100 x 475 = Rs. 95
Balance profit = Rs. (475 – 95) = Rs. 380.
This has to be divided between Ram and Shyam in the ratio of their investment i.e., Rs. 1500: Rs. 2500 = 3:5
Ram’s share= Rs. 380 x 3/8 = Rs. 142.5
Shyam’s share= Rs. 380 x 5/8 = Rs. 237.5 8
Finally, Ram gets a total of (95 + 142.5) = Rs. 237.5
and Shyam gets Rs. 237.5
Ex.6. A starts an industry with Rs. 20 lakhs. After 4 months he enters into a partnership with B who contributes Rs. 40 lakhs. C joins them after another 3 months with a capital of Rs. 60 lakhs. At the year end, the balance sheet shows a profit of Rs. 74000. Find the share of each in the profit.
Sol. A’s contribution of Rs. 20 lakhs is for the whole year i.e., 12 months which is equivalent to 20 x 12 = Rs. 240 lakhs for 1 month
B’s contribution of Rs. 40 lakhs for (12 – 4) = 8 months is equivalent to 40 x 8 = Rs. 320 lakhs for 1 month.
C’s contribution of Rs. 60 lakhs for 3 months is equiva¬lent to 60 x 3 = Rs. 180 lakhs for 1 month.
The share in the profit should be in the following ratio,
A: B : 0=240:320:180= 12: 16:9
and 74000/1216+9 = Rs 2000
A’s share =Rs. (12 x 2000) =Rs,24000
B’s share = Rs.(16×2000) =Rs.32000
C’s share =Rs.(9 x 2000) =Rs. 18000
Ex. 7. Ram and Shyam enter into a partnership and to¬gether start a business with contributions of Rs. 15000 and Rs. 20000 respectively. After 4 months Mohan also joins them with contribution of Rs. 22500. After 9 months Shyam withdraws his contribution. At the end of the year there is a profit of Rs.9000.Find the share of each in the profit.
Sol. The ratio of equivalent capital is Ram : Shyam : Mohan = (15000×12): (20000 x 9): (22500 x 8)
= 180000:180000:180000= 1:1:1
Therefore, the share of each in the profit is Rs 9000 = Rs. 3000
Ex. 8. Ram starts a business with Rs. 45000. After a cer¬tain period of time he is joined by Shyam who invests Rs. 30000. At the end of the year they divide the profit in the ratio 9:4. When did Shyam join Ram?
Sol. Suppose Shyam is with Ram for A’ months Ratio of equivalent capitals of the partners is equal to the ratio of their share in the total profit
45000×12/30000x x =9/4 or x = 45x12x4 /30 x 9 or x = 8 months
So, Shyam joined after (12 – 8 =) 4 months