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Partnership

Aptitude

PARTNERSHIP -> IMPORTANT FACTS AND FORMULAE

I. Partnership : When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership.
II. Ratio of Division 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.
(ii) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital * 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.
III. Working and Sleeping Partners : A partner who manages the business is known as working partner and the one who simply invests the money is a sleeping partner.

PARTNERSHIP -> SOLVED EXAMPLES

1. A, B and C start a business each investing Rs. 20,000. After 5 months A withdrew Rs. 5000, B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.
  Sol. Ratio of the capitals of A, B and C
= 20000 * 5 + 15000 * 7 : 20000 * 5 + 16000 * 7 : 20000 * 5 + 26000 * 7
205000 : 212000 : 282000 = 205 : 212 : 282.
∴ A’s share = Rs. [69900 * 205/699] = Rs. 20500;
B’s share = Rs. [69900 * 212/699] = Rs. 21200;
C’s share = Rs. [69900 * 282/699] = Rs. 28200.
2. Four milkman rented a pasture. A grazed 24 cows for 3 months; B 10 cows for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A’s share of rent is Rs. 720, find the total rent of the field.
  Sol. Ratio of shares of A, B, C, D = (24 * 3) : (10 * 5) : (35 * 4) : (21 * 3)
= 72 : 50 : 140 : 63.
Let total rent be Rs. x Then, A’s share = Rs. 72x / 325
∴ 72x / 325 = 720 ⇔ x = 720 * 325 / 72 = 3250.
3. A, B and C started a business by investing Rs. 1,20,000, Rs. 1,35,000 and Rs 1,50,000 respectively. Find the share of each, out of an annual profit of Rs. 56,700.
  Sol. Ratio of shares of A, B and C = Ratio of their investments
= 120000 : 135000 : 150000 = 8 : 9 : 10.
∴ A’s share = Rs. [56700 * 8/27] = Rs. 16800.
B’s share = Rs. [56700 * 9/27] = Rs. 18900.
C’s share = Rs. [56700 * 10/27] = Rs. 21000.

BOATS AND STREAMS -> EXERCISE

6. 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?
 
  • A. 4
  • B. 5
  • C. 6
  • D. 7
Ans: B.
Sol.
Suppose B joined after x months.
Then, 21000 * 12 = 36000 * (12 - x) ⇔ 36x = 180 ⇔ x = 5.
Hence, B joined after 5 months.
 
7. A, B and C started a shop by investing Rs. 27,000, Rs. 72,000 and Rs. 81,000 respectively. At the end of the year, the profits were distributed among them. If C’s share of profit be Rs. 36,000, then the total profit was :
 
  • A. 30,000
  • B. 60,000
  • C. 80,000
  • D. 120,000
Ans: C.
Sol.
A : B : C = 27000 : 72000 : 81000 = 3: 8 : 9. so, C’s share : Total Profit = 9 : 20.
Let the total profit be Rs. x. Then, 9/20 = 36000/x or x
= 36000 * 20 / 9 = 80000.
 
8. X and Y invested in abusiness. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs. 40,000, the amount invested by Y is :
 
  • A. 35,000
  • B. 40,000
  • C. 50,000
  • D. 60,000
Ans: D.
Sol.
Suppose Y invested Rs. y. Then, 40000/y = 2/3 or y = [40000 * 3 / 2] = 60000.
 
9. 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 among A, B and C?
 
  • A. 5 : 6 : 10
  • B. 6 : 10 : 5
  • C. 6 : 5 : 10
  • D. 10 : 6 : 5
Ans: B.
Sol.
Let the initial investments of A and B be 3x amd 5x.
A : B : C = (3x * 12) : (5x * 12) : (5x * 6) = 36 : 60 : 30 = 6 : 10 : 5.
 
10. A, B and 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. 45
  • B. 50
  • C. 55
  • D. 65
Ans: A.
Sol.
A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.
∴ C’s rent = Rs. [175 * 9/35] = Rs. 45.