ARITHMETICMATHSPARTNERSHIP

SSC CGL: QUESTIONS ON PARTNERSHIP (PART-I)

QUESTIONS ON PARTNERSHIP (PART-I)

QUERY 1

A and B started a business with Rs. 20,000 and 35,000 respectively. They agreed to share the profit in the ratio of their capital. C joined the partnership with the condition that A , B , C will share profit equally and pays Rs. 2,20,000 as premium for this, to be shared between A and B . This is to be divided between A and B in the ratio of

A) 9 : 10
B) 10 : 9
C) 10 : 1
D) 1 : 10

RONNIE BANSAL
Here the term PREMIUM needs to be understood. Well, when a new partner joins a business he must be sharing some part of profit. Means the old owner or owners will be sacrificing his share/s to the extent new partner will be getting. Therefore they need to be compensated with some amount (Which is determined by the consent of all the partners including the new one). That amount is called PREMIUM, which is to be brought by the new partner in addition to his share of capital (investment in the business). Obviously that amount will be shared by the old partners in their SACRIFICING ratio. Now look how to calculate the sacrificing ratio:

Old ratio of A & B 20,000 : 35,000 = 4 : 7 (They share profit in the ratio of their capitals)
So A’s share is 4/11 & B’s share is 7/11

New Share of A will be 1/3 & B’s 1/3 also (As all the three partners will be sharing profit equally)
Now we have to find their sacrificing shares and then the ratio.
Now A’s sacrifice = Old share — New share =>>> 4/11 — 1/3 = 1/33 & B’s sacrifice = 7/11 — 1/3 = 10/33
Hence the ratio in which the premium is be divided between A and B is 1 : 10 (option ‘D’)


QUERY 2

A and B invested Rs 20000 and Rs 30000 respectively and agreed to share profit in the ratio of their capitals. C entered into the partnership with the condition that profit would be divided between A, B and C in the ratio 3 : 4 : 3 for which he paid Rs 50000 as premium; in what ratio would the premium be divided among A and B?

A) 1 : 2
B) 1 : 3
C) 2 : 3
D) 2 : 1

MAHA GUPTA
Here the term PREMIUM needs to be understood. Well, when a new partner joins a business he must be sharing some part of profit. Means the old owners will be sacrificing their shares to the extent new partner will be getting. Therefore they need to be compensated with some amount (which is determined by the consent of all the partners including the new one). That amount is called PREMIUM, which is to be brought by the new partner in addition to his share of capital (investment in the business). Obviously that amount will be shared by the old partners in their SACRIFICING ratio. Now look how to calculate the sacrificing ratio:

Old ratio of A & B 20,000 : 30,000 = 2 : 3 (They share profit in the ratio of their capitals)
So A’s share is 2/5 and B’s share is 3/5

New Share of A will be in the ratio of 3 : 4 : 3 i.e. A = 3/10; B = 4/10 = 2/5

Now we have to find their sacrificing shares and then the ratio.
Now A’s sacrifice = Old share – New share =>>> 2/5 – 3/10 = 1/10, and B’s sacrifice = 3/5 – 2/5 = 1/5
Hence the ratio in which the premium is be divided between A and B is 1/10 : 1/5 = 1 : 2 (option ‘A’)


QUERY 3

A, B, C started a business by investing Rs.20,000, 25000, 40000 respectively. They decided to receive 10% interest on their capitals and the balance of the profit to be divided equally. If they got Rs 20500 as the annual profit, find the share of C including the interest?

A) 6000
B) 7000
C) 8000
D) 9000

Manoj Poriya
10% of interest on the capitals of A, B & C respectively = 2000, 2500, & 4000

Now the total of interest = 2000 + 2500 + 4000 = 8500
Remaining of the profit after interest on capitals = 20500 – 8500 = 12000

But the remaining of the profit has to be divided equally
So C’s share in it = 12000/3 = 4000

Therefore C’s total share of profit = His interest on capital + his share of profit after interest on capital
= 4000 + 4000 = 8000 (option ‘C’)

QUERY 4

A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs 6500 for 6 months, B Rs 8400 for 5 months and C Rs 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.

A) Rs. 1900
B) Rs. 2660
C) Rs. 2800
D) Rs. 2840

MAHA GUPTA
Money received by A for managing the business = 5% of Rs 7400 = Rs 370

Thus, the remaining profit = 7400 – 370 = Rs 7030

You should remember that when the profit sharing ratio is not given, the profit between the partners is distributed in the ratio of their investments/capitals.

But here partners’investments are not comparable as they are given for different periods. In such a case it’s better to find one month equivalent capital so that they become comparable.

Now one month equivalent investment of A = 6500*6 = 39000
One month equivalent investment of B = 8400*5 = 42000
One month equivalent investment of C = 10000*3 = 30000

So, the ratio of investments = 39000 : 42000 : 30000 = 13 : 14 : 10

Therefore, B’s share = 7030 x 14/37 = Rs 2660 (option ‘B’)

QUERY 5

A, B and C enter into a partnership in the ratio 7: 4: 65. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs 21,600, then B’s share in the profit is:

A) Rs 2100
B) Rs 2400
C) Rs 3600
D) Rs 4000

MAHA GUPTA
Ratio of initial investments = 7: 4: 65 = 105 : 40 : 36
Let their initial investments be 1050, 400 and 360

A’s investment after increase of 50% = 1050 + 1050/2 = 1575

Their one month equivalent investments
A = 1050*4 + 1575*8 = 16800
B = 400*12 = 4800
C = 360*12 = 4320

Therefore ratio of their investments = 16800 : 4800 : 4320 = 35 : 10 : 9

Hence, B’s share in the profit = Rs. 21600 x 10/54 = Rs. 4000 (option ‘D’)

QUERY 6

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

A) Rs 8400
B) Rs 11,900
C) Rs 13,600
D) Rs 14,700

MAHA GUPTA
Let C subscribes = Rs x

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

Hence, x + (x + 5000) + (x + 9000) = 50000
=> x = 12000

Therefore ratio of their investments i.e. A : B : C = (12000 + 9000) : (12000 + 5000) : 12000 = 21000 : 17000 : 12000 = 21 : 17 : 12.

Thus A’s share in the profit = 35000 x 21/50 = Rs 14,700 (option ‘D’)

QUERY 7

Jitesh started a business by investing Rs 50,000. After six months, Rahul joined her with a capital of Rs 80,000. After 3 years, they earned a profit of Rs 24,500. What was Jitesh’s share in the profit?

A) Rs 9,423
B) Rs 10,250
C) Rs 12,500
D) Rs 10,500

MAHA GUPTA
Jitesh’s one month equivalent investment = 50000*36
Rahul’s one month equivalent investment = 80000*30

Thus, ratio of their investments =  = 50000*36 : 80000*30 = 3 : 4

Therefore Jitesh’s share in the profit = 24500 x 3/7 = Rs 10,500 (option ‘D’)

QUERY 8

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?

A) Rs 890
B) Rs 1335
C) Rs 1602
D) Rs 1780

MAHA GUPTA
You have to remember here that the profit given is for 8 months, so we’ll find the one month equivalent investments for 8 months, not for 12 months.

So, Arun’s 1 month equivalent investment = 8000*6
Kamal’s 1 month equivalent investment = 4000*8
Vinay’s 1 month equivalent investment = 8000*8

Hence the ratio of investments = 8,000*6 : 4,000*8 : 8,000*8 = 3 : 2 : 4.

Therefore Kamal’s share in the profit = Rs. 4005 x 2/9 = Rs 890 (option ‘A)

QUERY 9

Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

A) 5 : 7 : 8
B) 20 : 49 : 64
C) 38 : 28 : 21
D) 6 : 7 : 9

MAHA GUPTA
Let their investments be Rs x, Rs y and Rs z
Thus their one month equivalent investments = 14x, 8y and 7z

Therefore, 14x : 8y : 7z = 5 : 7 : 8.

Now, 14x/8y = 5/7 => x/y = 40/98 = 20/49
And 8y/7z = 7/8 => y/z = 49/64

Hence, x : y : : y : z = 20 : 49 : : 49 : 64
=> x : y : z = 20 : 49 : 64 (option ‘B’)

QUERY 10

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

MAHA GUPTA
Let B’s capital = Rs x
So, A’s one month equivalent capital = 3500*12 = 42000
And B’s one month equivalent capital = x*7 = 7 x

Therefore,  42000/7x = 2/3
=> x = 9000 (option ‘D’)

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Maha Gupta

Maha Gupta

Founder of www.examscomp.com and guiding aspirants on SSC exam affairs since 2010 when objective pattern of exams was introduced first in SSC. Also the author of the following books:

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