Quantitative Aptitude Partnership
When two or more persons agree to invest their sum of money to run a business, then this kind of agreement is called partnership. The persons involved in the partnership are called partners.
There are two types of partnership:
- Simple Partnership: In simple partnership, partners invest their capital for the same period of time.
- Compound Partnership: In compound partnership, partners invest their capital for the different period of time.
- If two partners X and Y are investing their money to run a business for the same period of time i.e., in case of Simple partnership
Capital of X: Capital of Y = Profit of X: Profit of Y
- If two partners A and B are investing their money to run a business for the different period of time i.e., in case of Compound Partnership.
Capital of X × Time period of X: Capital of Y × Time period of Y
= Profit of X: Profit of Y
Let us understand the concept of Partnership with the help of some examples:
Eg: A, B, and C started a business by investing Rs.20,000 each. After 4 months, A withdraws Rs.6000, B withdraws Rs.8000, C invests Rs.6000 more. At the end of the 1 year, a total profit of Rs.65600 was registered. Find the profit share of C.
A. Rs. 24000 B. Rs. 28800 C. Rs. 16500 D. Rs. 19200 E. None of these
Sol: Ratio of capital invested by A, B, and C
= (20,000 x 4 + 14000 x 8):(20,000 x 4 + 12000 x 8):(20,000 x 4 + 26000 x 8)
= 192000:176000: 288000
A’s share = (65600 x 192 / 656) = 19200
B’s share = (65600 x 176 / 656) = 17600
C’s share = (65600 x 288 / 656) = 28800
Eg: Rahul started a business by investing Rs.76000 in it. After some month, Amit came to join a business with him and invested Rs.57000. At the end of the year, the total profit was divided among them in the ratio of2: 1.Find after how many months Amit joined the business.
A. 4 B. 2 C. 8 D. 5 E. None of these
Sol: Let us assume that Amit joined the business after x months. So, Amit money was invested in the business for (12 – x) months.
So, 76000 x 12 / 57000 x (12 – x) = 2 / 1
912000 = 114000 (12 – x)
= 114 (12 – x) = 912
= x = 4
So, we can say after 4 months Amit joined the business.
Eg: Mohit started a hardware business by investing Rs 40,000. After six months, Prakash joined him by investing Rs. 60,000. After 3 years, they earned a total profit of Rs. 27,900. What is Mohit’s share of the overall profit earned?
A. Rs. 12400 B. Rs. 13600 C. Rs. 14200 D. Rs. 15500 E. None of these
Sol: Mohit: Prakash (ratio of capital invested)
= (40,000 x 36):(60,000 x 30) = 1440000: 1800000 = 4:5.
Therefore, Mohit’s share in the overall profit is = Rs. 27900 x 4 / 9 = Rs. 12400.
Eg: Manik received Rs. 6000 as his share out of the overall profit of Rs. 9000 which he and Rahul together could earn at the end of one year. If Manik invested Rs.120000 for 6 months, whereas Rahul invested his amount for the whole year, what was the amount invested by Rahul?
A. Rs. 25000 B. Rs. 30000 C. Rs. 46000 D. Rs. 52000 E. None of these
Sol:Let us assume that Rahul invested Rs. x for the whole year. Then,
Manik: Rahul = 120000 * 6: x *12.
x = 30000
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