Math Topic - Partnership

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Helpful Notes for students who are preparing for competitive exams.

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PBI Important Facts and Formulas PBI INSTITUTE PARTNERSHIP 1. 2. 3. 1. Partnership: When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership. Ratio of Divisions of Gains: I. When investments of all the partners are for the same time, 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, then at the end of the year (A's share of profit) : (B's share of profit) = x : y. Il. 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. Working and Sleeping Partners: A partner who manages the the business is known as a working partner and the one who simply invests the money is a sleeping partner. EXERCISE Shekhar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999? A. Rs. 45,000 C. Rs. 70,000 Solution B. Rs. 50,000 D. Rs. 75,000 Shekhar: Rajeev: Jatin= (25000 x : (35000 x 24) Rajeev's share = 1260000 : 840000 : 420000 = Rs.50000. 2. Solution A started a business with Rs.21,000 and is joined afterwards by B with Rs.36,000. After how many months did B join if the profits at the end of the year are divided equally?
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PBI Suppose B joined after x months. Then, PBI INSTITUTE or 3. X and Y invested in a of 2 : 3. If X invested A. Rs. 45,000 C. Rs. 60,000 Solution Suppose Y invested Rs.y Then, 4. business. They earned some profit which they divided in the ratio Rs.40,000. the amount invested by Y is B. Rs.50,OOO D. Rs. 80,000 40000 /y = 2/3 y=60000. A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? A. Rs. 7500 C. Rs. 9500 Solution B's share =Rs. 7500. B. Rs. 9000 D. Rs. 10,000 5. A, B, C hired a car for Rs.520 and used it for 7,8 and 11 hours respectively. Hire charges paid by B were A. Rs.140 C. Rs.180 Solution Hire charges paid by B B. Rs.160 D. Rs.220 = Rs(520x8/26) = Rs.160. 6. A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent? A. Rs. 45 C. Rs. 55 Solution c's rent B. Rs. 50 D. Rs. 60 7. =Rs. 45. Anand and Deepak started a business investing Rs.22,500 and Rs.35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is
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PBI A. c. Solution Rs. 5400 Rs. 8400 B. D. PBI INSTITUTE Rs. 7200 Rs. 9600 Ratio of their shares Deepak's share = 22500 : 35000 : 14. - Rs.(13800x14/23) = Rs. 8400. 8. Kamal started a business investing Rs.9000. After five months, Sameer joined with a capital of Rs.8000. If at the end of the year, they earn a profit of Rs.6970, then what will be the shares of sameer in the profit? A. Rs. 1883.78 C. Rs.3690 Solution Kamal : Sameer Sameer's share B. Rs.2380 D. Rs.3864 = 108 : 56 = 27 : 14. - Rs.(6970 =Rs.2380. 9. Arun , Kamal and Vinay invested Rs.8000, Rs.4000 and Rs.8000 respectively in a business. Arun left after six months . If after eight months , there was a gain of Rs.4005, then what will be the share of Kamal? A. Rs.890 C. Rs.1602 B. Rs. 1335 D. Rs. 1780 Solution Arun : Kamal : Vinay Kamal's share = 48 : 32 : 64 =Rs.890. 10. Solution 11. A, B and C enter into a partnership. They invest Rs. 40,000 , Rs. 80,000 and Rs.1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000 while at the end of the second year, C withdraws Rs.80,000. In what ratio will the profit be shared at the end of 3 years? D. None of these =144 :192 :336 A starts a business with Rs.3500 and after 5 months, B joins with A as his partner. After a year , the profit is divided in the ratio 2 : 3. What is B's contribution in the capitaP A. Rs. 7500 C. Rs. 8500 B. Rs. 8000 D. Rs. 9000
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PBI Solution Let B's capital be Rs.x. Then, PBI INSTITUTE 12. = 2/3 = 126000 x = 9000. Reena and Shaloo are partners in a business. Reena invests Rs. 35,000 for 8 months and shaloo invests Rs.42,000 for 10 months. Out of a profit of Rs.31,570. Reena's share is A. Rs.9471 C. Rs.18,040 Solution Ratio of their shares Reena's share B. Rs. 12,628 D. Rs.18,942 13. = Rs. 12628. Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business? A. 7: 6: 10 c. 42 : 45 : 56 Solution Aman : Rakhi : Sagar B. 12 : 15 : 16 D. cannot be determined x 24) = 12 : 15 : 16. 14. P and Q started a business investing Rs.85,000 and Rs.15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively? c. 15 : 23 Solution D. 17:3 15. = 85000 : 15000 : 15 Simran started a software business by investing Rs.50,000. After six months , Nanda joined her with a capital of Rs.80,000. After 3 years , they earned a profit of Rs. 24,500. What was Simran's share in the profit? A. Rs.9423 C. Rs.10,500 Solution Simran : Nanda Simran's share B. Rs.10,250 D. Rs.14,OOO = Rs.(24500x3/7) = 10500.
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PBI PBI INSTITUTE 16. A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed amount A, B and C? D. None of these Solution: Let the initial investments of A and B be 3x and 5x. = 36 : 60 : 30 or 6: 10 : 5.

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