# Partnership Questions

FACTS  AND  FORMULAE  FOR  PARTNERSHIP  PROBLEMS

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 Division of Gains:

(i) When investments of all the partners are for the same time, the gain or loss is distributed a 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 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 business is known as a working partner and the one who simply invests the money is a sleeping partner.

Q:

A and B started a business jointly A's investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B received Rs. 4000 as profit, then their total profit is :

 A) 22000 B) 28000 C) 32000 D) 36000

Explanation:

Suppose B invested Rs. x for y months. Then, A invested Rs. 3x for 2y months.

So, A : B = (3x * 2y) : (x * y) = 6xy : xy = 6 : 1.

B's profit : Total profit  = 1 : 7.

Let the total profit be Rs. x Then,  1/7 = 4000/x  or x = 28000.

22 23561
Q:

A, B and C enter into a partnership with a capital in which A's contribution is Rs. 10,000. If out of a total profit of Rs. 1000, A gets Rs. 500 and B gets Rs. 300, then C's capital is :

 A) 4000 B) 5000 C) 6000 D) 7000

Explanation:

A : B : C = 500 : 300 : 200 = 5 : 3 : 2.

Let their capitals be 5x, 3x and 2x respectively.

Then, 5x = 10000

=>  x = 2000.

C's capital = 2x = Rs. 4000.

25 20814
Q:

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) 10110 B) 10500 C) 12000 D) 13000

Explanation:

Simran : Nanda = (50000 * 36) : (80000 * 30) = 3 : 4.

Simran's share = Rs. ( 24500 * 3/7)  =  Rs. 10500.

19 20306
Q:

A and B start a business jointly. A invests Rs. 16,000 for 8 months and B remains in  the business for 4 months, Out of total profit, B claims - of the profit. How much money was contributed by B ?

 A) 12000 B) 12800 C) 13000 D) 14500

Explanation:

Let the total profit be Rs. x. Then, B = 2x/7 and A = (x - 2x /7) =  5x / 7.

So, A : B = 5x/7 : 2x/7 = 5 : 2.

Let B s capital be Rs. y. Then, (16000 * 8) / ( y * 4) = 5/2  <=> (16000 * 8 * 2) / (5 * 4) = 12800..

23 18304
Q:

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 : 5 B) 3 : 4 : 7 C) 5 : 6 : 4 D) 1 : 3 : 5

Explanation:

A : B : C  = (40000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)

= 144 : 192 : 336

= 3 : 4 : 7.

18 17214
Q:

Two partners investede Rs. 1250 and Rs. 850 respectively in a business. They distributed 60% of the profit equally and decide to distribute the remaining 40% as the ratio of their capitals. If one partner received Rs. 30 more than the other, find the total profit?

Let the total profit be Rs.x

60% of the profit = $\inline&space;\frac{60}{100}\times&space;x=Rs.\frac{3x}{5}$

from  this part of the profit each gets = Rs.$\inline&space;\frac{3x}{10}$

40% of the profit = $\inline&space;\frac{40}{100}\times&space;x=Rs.\frac{2x}{5}$

Now, this amount of Rs.$\inline&space;\frac{2x}{5}$ has been divided in the ratio of capitals 1250 : 850 = 25 :17

$\inline&space;\therefore$ Share on first capital = $\inline&space;(\frac{2x}{5}\times&space;\frac{25}{42})=Rs.\frac{5x}{21}$

Share on second capital = $\inline&space;(\frac{2x}{5}\times&space;\frac{17}{42})=Rs.\frac{17x}{105}$

Total money received by 1st investor = $\inline&space;[\frac{3x}{10}+\frac{5x}{21}]=&space;Rs.\frac{113x}{210}$

Total money received by 2nd investor = $\inline&space;[\frac{113x}{210}+\frac{97x}{210}]=Rs.\frac{97x}{210}$

$\inline&space;\therefore$ x = 393.75

Hence total profit = Rs. 393.75

17011
Q:

Sekar 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, Sekar 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 B) Rs. 50,000 C) Rs. 70,000 D) Rs. 75,000

Explanation:

Sekar: Rajeev: jatin = (25000×12+35000×12+45000×12):(35000×24) : (35000×12)

= 1260000 : 840000 : 420000

= 3 : 2 : 1.

Rajeev's Share =Rs.(150000×2/6)

=Rs.50000.

24 16239
Q:

Aman started a business investing Rs. 70,000. Rakhi  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 among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?

 A) 11 : 13 : 15 B) 11 : 13 : 17 C) 12 : 17 : 18 D) 12 : 15 :16