# 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:

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

7323
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 = $\inline&space;770\times&space;\frac{6}{11}=Rs.420$

7291
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.

7 6466
Q:

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 B) Rs. 50 C) Rs. 55 D) Rs. 60

Explanation:

A:B:C = (10×7):(12×5):(15×3)

= 70 :60 :45

= 14 :12 :9

C's rent = Rs.(175×9/35)

=Rs. 45.

7 6166
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.