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?

Answer

Let the total profit be Rs.x


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


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


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


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


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


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


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


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


\inline \therefore x = 393.75


Hence total profit = Rs. 393.75

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97 29459
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
 
Answer & Explanation Answer: B) 10500

Explanation:

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

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

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27 29433
Q:

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) 150 B) 160
C) 170 D) 180
 
Answer & Explanation Answer: B) 160

Explanation:

A : B : C = 7 : 8 : 11.

Hire charges paid by B = Rs. (520 *  8/26) = Rs. 160.

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21 28578
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
 
Answer & Explanation Answer: B) 3 : 4 : 7

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.

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28 27412
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
 
Answer & Explanation Answer: B) Rs. 50,000

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.

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30 26201
Q:

A and B enter into partnership. A supplies whole of the capital amounting to Rs. 45000 with the condition that the profits to be equally divided and that B pays A interest on half of the capital at 10% per annum, but receives Rs. 120 per month for carrying on the concern.Find their total yearly profit when B's income is one half of A's income.

Answer

Let the total profit be Rs. x


Amount paid to B as salary = (120 x 12)


                                       = Rs.1440


Share of each = \inline (\frac{x-1440}{2})


Interest paid by B = \inline \frac{22500\times 10}{100}=Rs.2250


Total money received by  A = \inline \frac{x-1440}{2}+2250


                                       = Rs.\inline (\frac{x+3060}{2})


Total money received by B


\inline [(\frac{x-1440}{2})+1440-2250]= (\frac{x-3060}{2})


\inline \Rightarrow \frac{1}{2}-(\frac{x+3060}{2})-(\frac{x-3060}{2})


\inline \Rightarrow x=9180 

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57 24306
Q:

A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more thanC. Out of a total profit  of Rs. 35,000, A receives :

A) 14700 B) 15000
C) 12000 D) 13500
 
Answer & Explanation Answer: A) 14700

Explanation:

Let C = x. Then, B = x + 5000  and A =  x + 5000 + 4000 = x + 9000.

So,  x + x + 5000 + x + 9000 = 50000  <=>  3x = 36000  <=>

x = 12000.

A : B : C =  21000 : 17000 : 12000 = 21 : 17 : 12.

A's share = Rs. (35000 * 21/50 ) = Rs. 14,700.

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25 24144
Q:

A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

A) Rs. 7500 B) Rs. 8000
C) Rs. 8500 D) Rs. 9000
 
Answer & Explanation Answer: D) Rs. 9000

Explanation:

Let B's capital be Rs. x

 

Then,3500×127x=23

=> 14x = 126000 

=> x = 9000.

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23 24101