# 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, B, C started a business with their investments in the ratio 1:3 :5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is :

 A) 1 : 2 : 3 B) 3 : 4 : 15 C) 3 : 5 : 10 D) 5 : 6 : 10

Explanation:

Let their initial investments be x, 3x and 5x respectively. Then,

A:B:C = (x*4+2x*8) : (3x*4+(3x/2)*8) : (5x*4+(5x/2)*8)

20x : 24x : 40x = 5 : 6 : 10

73 21014
Q:

A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is :

 A) 500 B) 1000 C) 1500 D) 2000

Explanation:

Let the total profit be Rs. 100.

After paying to charity, A's share  = (95*3/5) = Rs. 57.

If A's share is Rs. 57, total profit = Rs. 100.

If A's share is Rs. 855, total profit  = (100/57*855) = 1500.

59 20486
Q:

A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used ?

 A) 3 months B) 6 months C) 10 months D) 12 months

Explanation:

Let the total profit be Rs. z. Then,

B's share = Rs. 2z/3,  A's share = Rs. ( z - 2z/3 ) = Rs. z/3.

A : B = z/3 : 2z/3 = 1:2

Let the total capital be Rs, X and suppose B's money was used for x months. Then.

(1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3) = 10 .

Thus, B's money was used for 10 months.

48 16530
Q:

A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?

 A) 144 B) 169 C) 225 D) 339

Explanation:

Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.

Let their initial investments be 6x, 2x and 3x respectively.

A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.

B's share =  Rs. (378 * 8/21) = Rs. 144.

15 12415
Q:

A is a working and B is sleeping partners in a business. A puts in Rs. 5000 and B puts in Rs.6000. A receives % of the profit for managing the business and the rest is divided in proportion to their capital. What does each get out of a profit of Rs. 880?

Total profit = Rs. 880

A's share for managing the business i.e

$\inline&space;12\frac{1}{2}$ %  =  $\inline&space;\frac{25\times&space;880}{200}=Rs.110$

Remaining profit of A and B as per their capital = 880 - 110 = Rs. 770

Ratio of amounts = 5000 : 6000 = 5 : 6

Sum of ratios = 5 + 6 = 11

A's share = $\inline&space;770\times&space;\frac{5}{11}=&space;Rs.350$

A's total share = 350 + 110 = Rs. 460

B's share = $\inline&space;770\times&space;\frac{6}{11}=Rs.420$

10727
Q:

A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?

 A) 4 months B) 5 months C) 6 months D) 8 months

Explanation:

Suppose B joined for x months . Then,  ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.

So, B joined for 8 months.

34 9930
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

9620
Q:

If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 4650, C will receive ____

 A) Rs.700 B) Rs.800 C) Rs.900 D) Rs.1000

Explanation:

Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6,  and C =k/10 .

A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.

Hence, C's share (4650 *  6/31) = Rs, 900.