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:

Munna and Chinna are partners in a firm out of which Munna is sleeping partner and Chinna is working partner. Munna invests Rs. 1,40,000 and Chinna invests Rs. 80,000. Chinna receives 14.5% of profit for managing the business and the rest is shared between both in ratio of their investments. Munna's share in the profit of Rs. 19600 is ?

A) Rs. 9580.25 B) Rs. 10600
C) Rs. 10664.15 D) Rs. 11060.48
 
Answer & Explanation Answer: C) Rs. 10664.15

Explanation:

Profit received by Chinna as working partner = 14.5% of Rs. 19600

= 14.5x19600/100 = Rs. 2842

Balance in profit = 19600-2842 = Rs. 16758

Ratio of investment of Chinna & Munna = 80,000 : 1,40,000 = 4 : 7

Hence share of Chinna in investment = 4x16758/100 = Rs. 6093.85

Therefore, Share of Munna = 19600 - 2842 - 6093.85 = Rs. 10664.15

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Q:

If 6 (P's Capital ) = 8 ( Q's Capital ) = 12 ( R's Capital ) , then out of the total profit of Rs 4650 , R will receive ?

A) Rs. 1033.33 B) Rs. 1024
C) Rs. 1148.14 D) Rs. 1245.32
 
Answer & Explanation Answer: A) Rs. 1033.33

Explanation:

Let
P's capital = p,
Q's capital = q and
R's capital = r.
Then

6p = 8q = 12r
=> 3p = 4q = 6r
=>q = 3p/4
r = 3p/6 = p/2
P : Q : R = p : 3p/4 : p/2
= 4 : 3 : 2
R's share = 4650 * (2/9) = 150*6 = Rs. 1033.33.

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3 5587
Q:

Rohith started a business by investing Rs. 3600. After somedays, Puneeth joined him by investing Rs. 2400. At the end of one year, the profit was divided in the ratio 2 : 1. After how many months did Puneeth join the business?

A) 2 months B) 2.5 months
C) 3 months D) 3.5 months
 
Answer & Explanation Answer: C) 3 months

Explanation:

Ratio of profit of Rohith and Puneeth = 3600 x 12 : 2400 x P

= 3600 x 12/2400P = 2/1

=> P = 9

So, Puneeth joined the business after (12 - P) = 12 - 9 = 3 months.

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12 5457
Q:

K and L start a business jointly. K invests Rs.16000 for 8 months and L remains in the business for 4 months. Out of the total profit L claims 2/7th share. How much money is contributed by L?

A) Rs. 13,204 B) Rs. 14,521
C) Rs. 12,800 D) Rs. 15,000
 
Answer & Explanation Answer: C) Rs. 12,800

Explanation:

Given share of L is 2/7 th of profit. Then, their profits are divided in to 5:2 ratio.

Ratio of K and L is


16000×8x×4=52


x = Rs. 12,800.

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8 5199
Q:

A began a business with Rs. 85000. He was joined afterwards by B with Rs. 42,500. For how much perod does B join, if the profits at the end of the year are divided in the ratio of 3:1 ?

A) 8 months B) 6 months
C) 7 months D) 9 months
 
Answer & Explanation Answer: A) 8 months

Explanation:

Suppose B joined for x months.

Given profit is divided in the ratio 3:1. Then,

85000×1242500×x=31

 --> x = 8 months.

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6 5046
Q:

Ravi, Anand and Pranay are running a business firm in partnership. What is Anand's share in the profit earned by them?

a. Ravi, Anand and Pranay invested the amounts in the ratio of 2 : 4 : 7.

b. Pranay's share in the profit is Rs. 8750.

A) Only a is sufficient B) Neither a nor b is sufficient
C) Only b is sufficient D) Both a and b sufficient
 
Answer & Explanation Answer: D) Both a and b sufficient

Explanation:

Given Pranay's profit in the share is Rs. 8750

But given that their investments are in the ratio 2:4:7

713×P = 8750

P = 16250


Now Anand's share = 413×16250 = Rs.5000

Thus both staements a and b are sufficient to answer this question.

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3 4721
Q:

Vishal and Raghu jointly started a business. Vishal invested three times as Raghu did and invested his money for double time as compared to Raghu. Raghu earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was  ?

A) Rs. 28,000 B) Rs. 18,000
C) Rs. 14,000 D) Rs. 8,000
 
Answer & Explanation Answer: A) Rs. 28,000

Explanation:

Investments ratio is = 3:1
Time period ratio is = 2:1

As they are proportional to gain

------
Gain ratio of Vishal and raghu = 6:1

But given Raghu got Rs. 4000, 

=? 1 ----- 4000
     7 -----    ?

=> Rs.28,000

The total gain = Rs.28,000

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4 4491
Q:

Sandeep got Rs. 6000 as his share out of the total profit of Rs. 9000 which he and Saketh earned at the end of one year. If Sandeep invested Rs. 20000 for 6 months, whereas Saketh invested his amount for the whole year, the amount invested by Saketh?

A) Rs. 5000 B) Rs. 6200
C) Rs. 8100 D) R. 7600
 
Answer & Explanation Answer: A) Rs. 5000

Explanation:

Let the amount invested by saketh = RS. p

Now, that of sandeep = 20,000 x 6

saketh = 12 x p

Ratio of their earnings = 120000 : 12p = 6000 : (9000 - 6000)

=> 12000012p = 60003000 => p= Rs. 5000

Hence, the amount investe by saketh  = Rs. p  = Rs. 5000.

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