FeedBack Form

Your Name :
Your Email :
Your Location :
Your Message :
   
FeedBack

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

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?
 
  • A. 2 : 3 : 4
  • B. 3 : 2 : 4
  • C. 3: 2 : 1
  • D. 3: 4 : 7
Ans: D.
Sol.
A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =144 : 192 : 336 = 3: 4 : 7
 
12. three partners A, B, C start a business. Twice A’s capital is equal to thrice B’s capital and B’s capital is four times C’s capital. Out of a total profit of Rs. 16,500 at the end of the year, B’ share is:
 
  • A. 2,000
  • B. 4,000
  • C. 5,000
  • D. 6,000
Ans: D.
Sol.
Let C = x. Then, B = 4x and 2A = 3 * 4x = 12x or A = 6x.
∴ A : B : C = 6x : 4x : x = 6 : 4 : 1.
So, B’s capital = Rs. [16500 * 4/11] = Rs. 6000.
 
13. 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. 160
  • B. 180
  • C. 220
  • D. 225
Ans: A.
Sol.
A : B : C = 7 : 8 : 11.
Hire charges paid by B = Rs. [520 * 8/26] = Rs.160
 
14. David started a business investing Rs. 70,000. Robert joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio amoung David, Robert and Sagar respectively, 3 years after David started the business?
 
  • A. 12 : 10 : 16
  • B. 12 : 15 : 16
  • C. 15 : 12 : 16
  • D. 16 : 15 : 12
Ans: B.
Sol.
David : Robert : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12 : 15: 16.
 
15. C and D 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?
 
  • A. 10 : 3
  • B. 12 : 3
  • C. 17 : 3
  • D. 20 : 15
Ans: C.
Sol.
C : D = 85000 : 15000 = 85 : 15 = 17 : 3.