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:

Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R ?

A) Rs. 1100 B) Rs. 500
C) Rs. 1200 D) Rs. 700
 
Answer & Explanation Answer: B) Rs. 500

Explanation:

Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r

Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400

q = 1/3 (p + r) => 3q = p + r

Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300

r = 1200 - (p + q) => r = Rs.500.

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8 6591
Q:

A and B entered into a partnership investing Rs. 13,000 and Rs. 12,000 respectively.After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more, After 3 more months, C  joins the business with a capital of Rs. 21,000, The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by

A) 3500 B) 3600
C) 3700 D) 3800
 
Answer & Explanation Answer: B) 3600

Explanation:

A : B : C = (16000 * 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)

= 147 : 189 : 126

= 7 : 9 ; 6.

Difference of B and C's shares = Rs.  ( 26400 * 9/22 - 26400 * 6/22 ) = Rs. 3600.

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9 6347
Q:

Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is

A) Rs 200 B) Rs 300
C) Rs 400 D) Rs 500
 
Answer & Explanation Answer: C) Rs 400

Explanation:

Let C = x.
Then B = x/2
and A = x/4

A:B:C = 1:2:4.
C's share Rs.[(4/7)*700) = 400

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8 6257
Q:

Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ?

A) 11/3 B) 2/13
C) 3/11 D) 13/4
 
Answer & Explanation Answer: C) 3/11

Explanation:

Let Veena paid x,
so Akshitha paid 2x/3 , and Lasya paid 2x,
So total bill paid is given by
x+(2x/3) +2x = 1, we get
i.e. x = 3/11

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9 5866
Q:

A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A ?

A) Rs. 240 B) Rs. 75
C) Rs. 125 D) Rs. 354
 
Answer & Explanation Answer: A) Rs. 240

Explanation:

The ratio of A & B investments = (3x8 + 2x4):(4x8 + 5x4)

=> 8:13

=> 8/21 x 630 = 240.

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4 5434
Q:

Three milkmen rented a pasture. A grazed 24 cows for 4 months; B 10 cows for 6 months; C 56 cows for 5 months. If A's share of rent is Rs. 960, find the total rent of the field?

A) 4530 B) 4440
C) 4360 D) 4280
 
Answer & Explanation Answer: C) 4360

Explanation:

Ratio of shares of A,B,C = (24 x 4) : (10 x 6) : (56 x 5)

                                    = 96 : 60 : 280.

 

Let total rent be Rs. x. Then, A's share = Rs.96x436

 96x436=960 x=960×43696=4360

 

Hence total rent of the field is Rs. 4360.

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7 5371
Q:

Vishal invested 10% more than Trishul. Trishul invested 10% less than Raghu. If the total sum of their investments is Rs. 5780, how much amount did Raghu invest ?

A) Rs.2010 B) Rs.2200
C) Rs.2000 D) Rs.2100
 
Answer & Explanation Answer: C) Rs.2000

Explanation:

Let money invested by Raghu = Rs. x
Money invested by Trishul = 9/10 x = 0.9x
Money invested by Vishal = 9/10x * 110/100 = 0.99x
Also, x+0.9x+0.99x = 5780
= x= 5780/2.89 = 2000

Therefore, amount invested by Raghu is Rs. 2000.

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8 5242
Q:

Arun, Kamal and Vinay invested Rs.8000, Rs.4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?

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