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Partnership Questions

41. A, B and C become partners in a business. A contributes (1/3)rd of the capital for (1/4)th of the time. B contributes (1/5)th of the capital for (1/6)th of the time and C the rest of the capital for the whole time. If the profit is Rs. 1,820, then find the share of A out of total profit?




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Correct Ans:Rs. 260
Explanation:
Given, A contributes (1/3)rd of the capital
B contributes (1/5)th of the capital
---> Let the total capital of A, B and C = (L.C.M of 5 and3) = 15 units
So, A's capital = (1/3) * 15 = 5 units
B's capital = (1/5) * 15 = 3 units
C's capital = rest of the capital = 15 - (A's + B's capital)
= 15 - 5 + 3
= 7 units

A contributes in Time period = (1/4)th of total time
A contributes in Time period = (1/6)th of the time
---> Let total time for investment = (L.C.M of 4 and 6) = 12 units
So, A's Time period in business = (1/4) * 12 = 3 units
B's Time = (1/6) * 12 = 2 units
C's Time = whole time = 12 units

According to the given question statements:
Ratio of Profit = {A's capital * time} : {B's capital * time} : {C's capital * time}
= {5 * 3} : {3 * 2} : {7 * 12}
= 5 : 2 : 28

Given that, Total profit = Rs. 1,820
Hence, share of A out of total profit = {5/(5 + 2 + 28)} * 1820
= {5/35} * 1820
= Rs. 260
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42. Sakshi and Divya started a business with investment Rs. 6000 and Rs. 10000 respectively. Divya also worked as working partner for that she charged 20% of total profit and remaining profit was divided between them in the ratio of their investment. After 1year total profit from business was Rs. 1500. Find the profit share of Sakshi.




SHOW ANSWER
Correct Ans:Rs. 450
Explanation:
Given, Sakshi's invested amount = Rs.6000/-
Divya's invested amount = Rs.10000/-
Then, Sakshi's share : Divya's share = 6000 : 10000 = 3 : 5
=> Total parts = 3 + 5 = 8

Given, Total profit = Rs. 1500/-
From which Divya gets 20%
so, 20% of 1500 = (20/100) * 1500 = Rs. 300/-
Divya's Salary for being worked as working partner = Rs.300/-

Remaining profit amount = Rs.1500 - Rs. 300 = Rs 1200
Which was divided between them in the ratio of their investment.
So, Profit share of Sakshi = (3/8) * 1200
= 3 * 150
= Rs. 450
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43. A, B and C enter into a partnership by investing Rs. 1,600, Rs. 3,600 and Rs. 4,800. A is a working partner and gets a fifth of the profit for his services and remaining profit is divided amongst the three in their ratio. What is the sum of the profit of B and C get if A gets Rs. 5330? 




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Correct Ans:Rs. 10,920
Explanation:
Ratio of share of profit between A, B and C = Ratio of investment
= 1600 : 3600 : 4800
= 4 : 9 : 12

Given, Total Profit earned by A = Rs. 5330
--> A's share of Rs.5330 includes a fifth (ie., 1/5) of the total profit for his services and the share of the balance four fifths (i.e, 4/5) of the profit in the ratio of their investments.

A will get (4/25)th, B will get (9/25)th and C will get (12/25)th of four-fifths of the total profit as they share the remaining four-fifths of the profit in the ratio of their investments.

So, Total Profit earned by A = (1/5)x + (4/25)x * (4/5) = 5330
---> (x/5) + (16x/125) = 5330
---> (25x + 16x)/ 125 = 5330
---> 41x / 125 = 5330
---> x = (5330 * 125) / 41
---> x = 16,250

Then, B's profit= (4/5) * (9/25) * x
= (4/5) * (9/25) * 16,250
= Rs. 4,680

C's profit= (4/5) * (12/25) * x
= (4/5) * (12/25) * 16,250
= Rs. 6,240

Sum of the profit of B and C= Rs. 4,680 + Rs. 6,240 = Rs. 10,920
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44. Ankit and Mithul enter into a partnership with their initial investments of Rs. 24,000 and Rs. 40,000 respectively. They decided to distribute 40% of profit equally between them and rest according to their investment ratio. If total profit after a year was Rs. 16,800 then find profit of Ankit. 




SHOW ANSWER
Correct Ans:Rs. 7,140
Explanation:
Given, Profit = Rs. 16800
They decided to distribute 40% of Rs. 16800 equally between them
So, Amount received by Ankit and Mithul separately = (1/2) * (40/100) * 16800
= (1/2) * 40 * 168
= (1/2) * 6720
= Rs. 3360

Remaining Profit amount = Rs. 16800 - Rs. 6720
= Rs. 10,080
---> Which is distributed according to their investment ratio

Investment ratio of Ankit and Mithul = 24000 : 40000
= 24 : 40
= 3 : 5

Ankit's share in remaining profit = [3/(3 + 5)] * 10080
= [3/8] * 10080
= 3 * 1260
= Rs. 3780

Total Profit of Ankit = Rs. 3360 + Rs. 3780
= Rs. 7140
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45. A is an active partner and B is an inactive partner in business. A put in Rs. 5,000 and B puts in Rs. 6,000. A received 15% of the total profit for managing the business and the rest is divided in ratio of their invested capitals. Then find the amount received by A out of the total profit of Rs. 880?




SHOW ANSWER
Correct Ans:Rs. 472
Explanation:
Given Total Profit = Rs. 880
A received 15% of the total profit for managing the business
--> A gets 15% of 880 for managing the business
So, Amount received by A for managing the business = (15/100) * 880
= 3 * 44
= Rs. 132

So, Remaining profit amount = 880 - 132
= Rs. 748
--> which is divided in ratio of their invested capitals

Thus, Ratio of profit received by A and B = Ratio of investment of A and B
= Rs. 5,000 : Rs. 6,000
= 5 : 6

Now, A's share of remaining profit = [5 / (5 + 6)] * Remaining profit amount
= [5/11] * 748
= 5 * 68
= Rs. 340

Therefore, Total profit received by A = Rs. 340 + Rs. 132
= Rs. 472
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46. John and Antony are two friends working in an insurance company and get their monthly salaries in the ratio of 4 : 5. After 4 months, John got promotion and his salary increases by 25% after a year, if total salary obtained by them in a year is Rs 1,74,000 then find monthly salary of Antony before increment. 




SHOW ANSWER
Correct Ans:Rs.7,500
Explanation:
Given, ratio of monthly salaries of John and Antony = 4 : 5
Then, John's monthly salary = 4x
Antony's monthly salary = 5x

After 4 months, John's salary increases by 25% (after a year)
So, Annual salary of John = (4x * 4 months) + [(125/100) * 4x * 8 months]
= 16x + [(5/4) * 4x * 8]
= 16x + 40x
= 56x

Annual salary of Antony = (5x * 12 months)
= 60x

At the end of the year, Total salary obtained by them = Rs 1,74,000
---> 56x + 60x = 174000
---> 116x = 174000
---> x = 1500

Then, Monthly salary of Antony before increment = 5x = 5 * 1500 = 7500
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47. M, N, P start a business jointly. Twice the investment of M is equal to thrice the capital of N and the investment of N is four times the investment of P. Find the share of N in annual profit of Rs. 275000.




SHOW ANSWER
Correct Ans:Rs. 1,00,000
Explanation:
From the given data,
2M = 3N
and N = 4P
From these two statements,
---> 2M = 3 (4P)
---> 2M = 12P
---> M = 6P

Ratio of investment of M, N and P = 6P : 4P : P
= 6 : 4 : 1

Total parts of share in Profit = 11
Share of N = 4 parts of 11 * Total profit
= (4/11) * 275000
= 4 * 25000
= 1,00,000
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48. A and B started a business with initial investments in the respective ratio of 18 : 7. After four months from the start of the business, A invested Rs. 2000 more and B invested Rs. 7000 more. At the end of one year, if the profit was distributed among them in the ratio of 2 : 1 respectively, what was the total initial investment with which A and B started the business?




SHOW ANSWER
Correct Ans:Rs. 50,000
Explanation:
Given:
Ratio of initial investments = 18 : 7
Ratio of profit = 2 : 1
Let the initial investments be 18x and 7x.
WKT,
Ratio of captial investment of A/Ratio of captial investment of B = Ratio of profit of A/Ratio of profit of B
[(18x * 12) + (2000 * 8)]/[(7x * 12) + (7000 * 8)] = 2/1
[216x + 16000]/[84x + 56000] = 2/1
216x + 16000 = 2[84x + 56000]
216x + 16000 = 168x + 112000
216x - 168x = 112000 - 16000
48x = 96000
x = 2000
Total initial investment of A and B = (18x + 7x)
= (18 + 7)2000
= Rs. 50,000
Therefore, initial invesment of A and B = Rs. 50,000.
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49. Ajit invested two—third of the investment for three-fourth of total period and Ram invested one—fifth of the investment for one fourth of the total period and Silambu invested the remaining amount for 4 months. Total profit at the end of the year is Rs.96300. Find the share of Ajit? 




SHOW ANSWER
Correct Ans:Rs. 8100
Explanation:
Let the total investment be x,
The ratio of profit of Ajit, Ram and Silambu
= ((2/3)x * (3/4) * 12) : ((1/5)x * (1/4) * 12) : ((2/15)x * 4)
= 6x : (3/5)x : (13/15)x
= 90 : 9 : 8
Total profit = Rs. 96300
90x + 9x + 8x = 96300
107x = 96300
x = 96300/107
x = 900
The share of Ajit = 900*9 = Rs. 8100
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50. Sathi and Rathin invested some money in a business in the ratio 6 : 5, but Sathi withdrew her money after a few months. If the end of twelve months profit was shared between Sathi and Rathin in the ratio 7 : 10, for how many months did Rathin alone invest?




SHOW ANSWER
Correct Ans:5
Explanation:
Let's take Sathi invest for x months.
WKT, Ratio of equivalent capital of A : Ratio of equivalent captial of B = Share of profit A : Share of profit B
Here, Sathi's capital ratio in x months/Rathin capital ratio in 12 months = Profit share of Sathi/Profit shar of Rathin
(6*x)/(5*12) = 7/10
6x = (7 * 60)/10
x = 42/6
x = 7 months
Sathi invested for 7 months.
Therefore, Rathin alone invested for = 12 - 7 = 5 months.
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51. Rs. 1082 was divided among A, B and C. Such that if Rs. 10, Rs. 13 and Rs. 14 be diminished from their shares respectively, the remainders will be in the ratio of 3 : 5 : 7. What is the share of A?




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Correct Ans:Rs. 220
Explanation:
Total money divided among three = Rs. 1087
Total amount of money diminished = (10 + 13 + 14) = Rs. 37
Remaining money = 1087 - 37 = Rs. 1050.
Given that, remaining amount is in the ratio of 3 : 5 : 7.
So, share of A = (3/15)*1050 + 10
= 210 + 10 = Rs. 220
Therefore, share of A = Rs. 220.
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52. P, Q and R started a business by investing in the ratio of 3 : 4 : 5. After 6 months, Q invested 50 % more than the initial investment and after 2 months, P withdraw 1/3 of the initial investment. Find the total profit, if the share of P after one year is Rs. 40000?




SHOW ANSWER
Correct Ans:Rs.190000
Explanation:
The share of P, Q and R
= [3x*3 + 3x*(2/3)*4] : [4x*6 + 4x*(150/100)*6] : [5x*12]
= 32x : 60x : 60x
= 8 : 15 : 15
8’s = 40000
1’s = 5000
Total profit = 38’s = Rs.190000
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53. Rishi and Dinesh enter into a partnership with Rs. 60,000 and Rs. 50000 respectively. Vinay joins ‘b’ months before end of the year, contributing Rs. 70000 and Rishi leaves them after ‘a’ months from the start of the year. If they share the profit in the ratio of 18 : 20 : 21, then find the value of a and b.




SHOW ANSWER
Correct Ans:9 months, 3 months
Explanation:
Let's take number of months Rishi invested be a and number of months Vinay invested be (12 - b).
Ratio of their investments,
Rishi : Dinesh : Vinay = (60,000*a) : (50,000*12) : (70,000*(12 - b))
=> 6a : 60 : 7(12 - b)
Given that share of profit in the ratio = 18 : 20 : 21
So, 6a/60 = 18/20
a = (18*60)/(20*6)
a = 9 months
Also, 60/7(12 - b) = 20/21
(12 - b) = (21*60)/(20*7)
(12 - b) = 9
b = 12 - 9 = 3 months
Therefore, Rishi left after 9 months and Vinay joined at the end of the 3 months.
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54. Ankit and Adarsh invest Rs. 4000 and Rs. 3000 in a business Ankit receives Rs. 20 per month out of the profit as a remuneration for running the business and the rest of profit is divided in proportion to the investments. If in a year Ankit totally receives Rs. 360, what does Adarsh receive?




SHOW ANSWER
Correct Ans:Rs. 90
Explanation:
Total profit - Remuneration = Balance profit
So, balance profit of Ankit = 360 - (20*12) = Rs.120
This balanced profit is divided in proportion to their investments,
=> Balance profit of Ankit/Balance profit of Adarsh = Ankit investment/Adarsh investment
=> 120/Balance profit of Adarsh = 4000/3000
Balance profit of Adarsh = 120*(3/4) = Rs. 90
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55. P, Q and R started a business by investing Rs.27,000, Rs.35,000 and Rs.42,000 respectively. After 6 months, P withdraws half of his investment but Q invested 20% of initial investment more. Find the share of R, if the total profit at the end of the year is Rs.84,630? 




SHOW ANSWER
Correct Ans:Rs. 35,280
Explanation:
The share of P = [(27000*6) + (13500*6)]
The share of Q = [(35000*6) + (35000)*(120/100)*6]
The share of R = [42000*12]
The ratio of share of P, Q and R
=> [(27000*6) + (13500*6)] : [(35000*6) + (35000)*(120/100)*6] : [42000*12]
=> 243000 : 462000 : 504000
=> 81 : 154 : 168
Given, total profit = Rs.84,630
Total Shares, 403 = 84630
One’s Share = 84630/403 = 210
Therefore, Share of R = 168(210) = Rs. 35,280.
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56. Shubham invested Rs. 2250 in a business and after some time Shivam also join him and invested Rs. 2500. At the end of year Shivam received Rs. 2750 profit out of Rs. 6050. After how much time did he join the business?




SHOW ANSWER
Correct Ans:None of these
Explanation:
Total profit = Rs. Rs. 6050
Shivam’s profit = Rs.2750
Shubham’s profit = 6050 - 2750 = Rs. 3300
Ratio of the profit = 3300 : 2750 = 6 : 5

Let the shivam investment time period be x.
WKT, the ratio of the capital is equal to the ratio of the profit,
2250*12 : 2500*x = 6 : 5
5(2250*12) = 6(2500*x)
x= 9 months
So Shivam invested after 3 months.
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57.
Mr.X starts a business with Rs.7000 and after 10 months, Mr.Y joins with Mr.X by investing certain amount. At the end of 2 years, if 2:3 is the proportion of the profit then Mr.Y's contribution in the capital is:




SHOW ANSWER
Correct Ans:18,000
Explanation:
Let Mr.Y's capital be Rs.P
Mr.X's investment = Rs.7000 for 24 months
Mr.Y's investment = Rs.P for 14 months
we know that, Profit ratio = investing ratio
i.e., (7000 x 24):(P x 14) = 2:3
168000 : 14P = 2:3
12000 : P = 2:3
12000/P = 2/3
P = 3 x 12000 / 2 = 18000
Required answer is Rs.18,000.

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58. A, B and C start a business and their investments are in the ratio 4 : 3 : 6. Both A and B starts the business and C joins them after 6 months. It was decided that C will get a monthly salary of Rs 500 from the annual profits. C’s total salary came out to be 10% of the annual profit after a year. What is the share of A in the total profits? 




SHOW ANSWER
Correct Ans:Rs 10,800
Explanation:
After a year C gets salary = 500*6 = Rs 3,000 [Since C was for 6 months in the business with each month earning 500]
So 10% of total profit after a year = 3,000
Total profit = Rs 30,000
A invested for 12 months, B for 12, and C for 6 months
Ratio of profit shares =
4*12 : 3*12 : 6*6 = 4 : 3 : 3
Profit left after deducting salary of C = 30,000 – 3,000 = 27,000
So share of A
= [4/(4+3+3)] * 27,000
= [4 / (10)] *27,000
= 2700 * 4
= 10,800.
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59. A and B enter into a partnership and A invests Rs.10,000 in the partnership. At the end of 4 months he withdraws Rs.2000. At the end of another 5 months, he withdraws another Rs.3000. If B invests a certain sum in the partnership at the beginning of the year and leaves it intact and receives Rs.9600 as his share of the total profit of Rs.19,100 for the year, how much did B invest in the company? 




SHOW ANSWER
Correct Ans:Rs.8,000
Explanation:
Given
The total profit for the year is 19100. Of this B gets Rs.9600. Therefore, A would get (19100 – 9600) = Rs.9500.

The partners split their profits in the ratio of their investments.

Therefore, the ratio of the investments of A : B = 9500 : 9600 = 95 : 96.

A invested Rs.10000 initially for a period of 4 months. Then, he withdrew Rs.2000.
Hence, his investment has reduced to Rs.8000 (for the next 5 months).
Then he withdraws another Rs.3000. Hence, his investment will stand reduced to Rs.5000 during the last three months.

So, the amount of money that he had invested in the company on a money-month basis will be
= 4 * 10000 + 5 * 8000 + 3 * 5000
= 40000 + 40000 + 15000
= 95000

If A had 95000 money months invested in the company, B would have had 96,000 money months invested in the company (as the ratio of their investments is 95: 96).

If B had 96,000 money-months invested in the company, he has essentially invested 96000/12 = Rs.8000.
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60. Sony, Mony and Tony started a business each investing Rs.20,000. After 5 months Sony withdrew Rs.5000, Mony withdrew Rs.4000 and Tony added Rs.6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of Tony? 




SHOW ANSWER
Correct Ans:28,200
Explanation:
Ratio of the investments of Sony, Mony, Tony are calculated as
[Sony invested Rs.20,000 for first 5 months and after 5 months, Sony withdrew Rs.5000, so Sony invested Rs.15,000 for remaining 7 months (because in the given question, total profit is given for one year i.e, 12 months)]
Sony's investment = Amount invested * No. of months = 20,000 * 5 + 15,000 * 7 = 2,05,000

[Mony invested Rs.20,000 for first 5 months and after 5 months, Mony withdrew Rs.4000, so Mony invested Rs.16,000 for remaining 7 months]
Mony'sinvestment=20000 * 5 + 16000 * 7 = 2,12,000

[Tony invested Rs.20,000 for first 5 months and after 5 months, Tony added Rs.6000 more, so Tony invested Rs.26,000 for remaining 7 months]
Tony'sinvestment = 20000 * 5 + 260000 * 7 = 2,82,000

Now, the ratio ofinvestmentofSony, Mony, Tony =2,05,000 :2,12,000 :2,82,000
= 205 : 212 : 282

Given, Total profit = 69,900

Then,share of Tony = [282 / (205 + 212 + 282)] *69,900
=[282 / 699] *69,900
= 28,200 rupees
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