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Partnership Questions

21. Akshay and Bimal entered into a partnership investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months, Akshay withdrew Rs. 5,000 while Bimal invested Rs. 5,000 more. After 3 more months Chinmay joins the business with a capital of Rs. 21,000. The share of Bimal exceeds that of Chinmay, out of a total profit of Rs. 26400 after one year by ______.




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Correct Ans:Rs. 3600
Explanation:
Given, Akshay's total investment = 16000 for 3 months + 11000 for 9 months
Bimal's total investment = 12000 for 3 months + 17000 for 9 months
Chinmay joins after 6 months, and his total investment = 21000 for 6 months

Ratio of investment of Akshay, Bimal and Chinmay = [16000 * 3 + 11000 * 9] : [12000 * 3 + 17000 * 9] : [21000 * 6]
= [48000 + 99000] : [36000 + 153000] : [126000]
= 147000 : 189000 : 126000
= 147 : 189 : 126
= 7 : 9 : 6

Given Total profit = Rs. Rs. 26400
Here, Profit share of Bimal = [9/(7 + 9 + 6)] * 26400
= (9/22) * 26400
= 9 * 1200
= Rs. 10,800

and Profit share of Chinmay = (6/22) * 26400
= 6 * 1200
= Rs. 7200

Difference of Bimal and Chinmay's shares = 10,800 - 7200 = Rs. 3600
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22. Kamala and Shamala start a business with the capital of Rs.4500 and Rs.5400 respectively. After some months Shamala left the business and received one-third of the total profit, then how many months Kamala alone run the business?




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Correct Ans:7
Explanation:
Given,
Reference:
Shamala left the business and received one-third of the total profit

Kamala and Shamala profit ratio = ((4500*12) : (5400*x) ) = (2 : 1)
x = Shamala's months in the business
Find the x value:
----------->((54000) : (5400 *x) ) = (2 :1)
-----------> x = (54000/2 * 5400)
-----------> x = 5 months
----------->Shamala 5 months in the business.
Simplify the above equation, we get x.
Find Kamala alone run the business:
-----------> (12 -5) = 7 months.
Hence the answer is : 7 months
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23. A starts a business with a capital of Rs. 15000. B joins the business after 6 months and C joins the business after 9 months. At the end of the year, their respective shares were in ratio of 8: 4: 3. What is the sum of amount invested in the business by B and C together?




SHOW ANSWER
Correct Ans:37500
Explanation:
Let find the share of A,B and C:
Profit ratios of A,B and C: (8 : 4 :3)
--------->
---------> ((15000 *12) : 6B : 3C) = (8 : 4 :3)
Find the capital of B:
---------> ((15000 *12) / 6B) = (8/4)
--------> B = 15000
Find the capital of C:
---------> ((15000 *12) / 3C) = (8/3)
--------> C = 22500
Find the Total amount invested by B and C:
--------> (15000+22500) = 37500

Hence the answer is : 37500
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24. P, Q and R started a business with investments of Rs. 12000, Rs. 15000 and Rs. 18000 respectively. After 8 months from the start of the business, Q and R invested additional amounts in the ratio of 3: 5 respectively. If at the end of the year, the ratio of share of P and Q was 3: 4, then what was the additional amount invested by Q after 8 months?




SHOW ANSWER
Correct Ans:Rs. 3000
Explanation:

Let the ratio additional amount of Q and R be 3x and 5x,
The ratio of profit of P : Q : R
------> ( [12000*12]: [15000*8 + (15000 + 3x) *4]: [18000*8 + (18000 + 5x) *4])
------> (144000: (120000 + 60000 +12x): (144000+ 72000 + 20x))
------> (144000 : (180000+12x) : (216000+20x))
The ratio of share of P and Q = (3: 4)
------> (144000/(180000+ 12x)) = (3/4)
-------> Simply the equation ,we get
------> x = 1000

Q's additional investment after 8 months = (3 * x)
-------> (3*1000) = Rs. 3000

Hence the answer is : 3000
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25. Kala invested Rs. 2250 in a business and after some time Kapil also join him and invested Rs. 2500. At the end of year Kapil 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:
Kala's Profit = 6050 - 2750 = 3300 Rs.

Kapil's profit = 2750 Rs.

Ratio of the profit = (3300 : 2750)

= (6 : 5)

Because the ratio of the capital is equals to the ratio of the profit then,

(2250 × 12 : 2500 × x) = (6 : 5)
5 ( 2250 × 12) = 6 ( 2500 × x)

x = 9 months

So Kapil invested after 3 months.


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26. Amar invested Rs 55000 in a cosmetic shop for the whole year. After 4 months of Amar, Sachin joined him and invested Rs 70000. Next year Amar invested Rs 10000 more and Sachin withdrew Rs 10000 and at the end of two years profit earned by Amar is Rs 32375. Find the total profit if they distributed half of the total profit equally and rest in the capital ratio.     




SHOW ANSWER
Correct Ans:62900
Explanation:
Amar invested Rs 55000 for a year and Rs 65000 for the next year.

Sachin invested Rs 70000 for 8 months and Rs 60000 for the next year.
Capital Ratio = (Invested Amount* Unit of time )of each persons

Capital Ratio = 55000 * 12 + 65000 * 12 : 70000 * 8 + 60000 * 12

= 660000 +780000 : 560000 + 720000

= 1440000 : 1280000 = 9 : 8

Let total profit = Rs x

Amar and Sachin distributed half of the total profit equally
So, Amar and Sachin get (Rs x/2)/2 each ie.,(x/4)each.

Now rest of the total profit is distributed in the capital ratio.
So, rest of total profit = x - 2(x/4) = x/2 which is divided in capital ratio.
Hence, Amar get = *(x/2)(9/17)
Also, Sachin get = (x/2) * (8/17)

Given, profit earned by Amar = Rs 32375
Now, total profit earned by Amar = (x/4) +{(x/2) * (9/17)}
35x/68 = 32375
x = 62,900 = total profit

Hence the answer is 62900
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27. Harvinder and Deepak invest in a business, Rs 8000 and Rs 8250 for 11 months and 9 months respectively. If Deepak earn Rs 2500 less profit than Harvinder. Find difference between amount invested and profit earn by Harvinder?




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Correct Ans:Rs. 8000
Explanation:
Ratio of profit earned by Harvinder and Deepak
= 8000 * 11 : 8250 * 9
= 32 : 27
Let profit earned by Harvinder and Deepak are 32x and 27x respectively.
32x - 27x = 2500
x = 500
Profit earned by Harvinder = 32x = 16000
Required difference = 16000 - 8000 = Rs. 8000
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28. Rita and Jyoti opened a beauty parlor by contributing Rs. 36000 and Rs. 48000 respectively. Rita, being a runner of parlor, charges 20% of total profit as salary of herself and rest profit is distributed between them in their investment ratio. If profit of Jyoti is Rs. 6400 then what is the profit of Rita ?




SHOW ANSWER
Correct Ans:Rs. 7600
Explanation:
Let total Profit = T
Ratio of Rita's investment and Jyoti's investment
= 36000 : 48000 = 3 : 4
We know Jyoti's profit
4/7 * (80% * T) = 6400
4/7 * 80T/100 = 6400
T = 20 * 100 * 7 = 14000
Profit of Rita = (20% of T) + [(80% of T) * 3/7]
= (20*14000)/100 + [(80*14000)/100 * 3/7]
= 2800 + (8 * 200 * 3)
= 2800 + 4800 =Rs. 7600
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29. A, B and C enter into a partnership in the ratio 1 : 1/2 : 1/3. After 6 months A increases his share by 50% and B decreases 33(1/3)% of his initial invest. Find out the ratio of profit of A, B and C in the end of year. 




SHOW ANSWER
Correct Ans:15 : 5 : 4
Explanation:
let the investment of A, B and C = x, x/2, x/3
= 6x, 3x, 2x respectively.
50% of A = 1/2 * 6x = 3x
and 33(1/3)% of B = 1/3 * 3x = x
The ratio of profit of A, B and C in the end of year,
A's profit => (6x * 6) + (6x + 3x)*6 = 36x + 54x = 90x
B's profit => (3x * 6) + (3x - x)*6 = 18x + 12x = 30x
C's profit => 2x*12 = 24x
A : B : C = 90x : 30x : 24x = 15 : 5 : 4
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30. A puts Rs 80 and B puts Rs 45 in a game. At the end of 4 months, A withdrew half of his money and at the end of 6 months B also withdrew half of his money. Now C also wants to play and puts Rs 75 and remains until the end of the year. In what ratio the profit will be divided among them?




SHOW ANSWER
Correct Ans:128 : 81 : 90
Explanation:
A's share : B's share : C's share =
[(80*4) + ((80/2)*8)] : [(45*6) + ((45/2)*6)] : [75*6]
= [320 + 320)] : [270 + 135)] : [450]
= 640 : 405 : 450
= 128 : 81 : 90
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31. A, B and C started a business with investments of Rs. 12000, Rs. 15000 and Rs. 18000 respectively. After 8 months from the start of the business, B and C invested additional amounts in ratio 2 : 5 respectively. If at the end of the year, the ratio of share of A and B was 3 : 4, then what was the additional amount invested by B after 8 months?




SHOW ANSWER
Correct Ans:Rs. 3000
Explanation:
Given, ratio of additional amount invested by B and C = 2 : 5
Let the additional amount invested by B and C be 2x and 5x respectively.
The ratio of profit of A, B, C = (12000*12) : [(15000*8) + 4(15000 + 2x)] : [(18000*8) + 4(18000 + 5x)]
= 144000 : (120000 + 60000 + 8x) : (144000 + 72000 + 20x)
= 144000 : (180000 + 8x) : (216000 + 20x)

Given the ratio of share of A and B = 3/4
----> A/B = 144000/(180000 + 8x) = 3/4
----> 144000 * 4 = 3 * (180000 + 8x)
----> 576000 = 540000 + 24x
----> 36000 = 24x
----> x = 1500
Therefore the additional amount invested by B after 8 months = 2x
= 2 * (1500)
= Rs. 3000
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32. A and B started a business with Rs 700 and Rs 600 respectively. After 4 months, C replaces B with X% of B"™s capital. After 1 year C"™s share out of the total profit 24000 is 5600. Find the value of X.




SHOW ANSWER
Correct Ans:68.50%
Explanation:
Partnership of A, B, C in business is given by
A : B : C = (700*12) : (600*4) : [(600*X)/100]*8
= (700*12) : (600*4) : 6X*8
= 8400 : 2400 : 48X
= 175 : 50 : X
Now, C's share = X/(225 + X)
Given C's share out of total profit 24000 = 5600
[X/(225 + X)] * 24000 = 5600
30*[X/(225 + X)] = 7
30X = 7(225 + X)
30X - 7X = 225*7
23X = 225*7
X =(225*7)/23 = 68.47 %
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33. Vicky started a business with an amount of Rs. 21000. But after some time, Beryl joined the business by investing amount of Rs. 36000. If the yearly profit of the firm divided equally between them. Then after how many months Beryl joined the business?




SHOW ANSWER
Correct Ans:5
Explanation:
We assume that after the period of (m) month Beryl joined the business.
Investment of Vicky = 21000 * 12
Investment of Beryl = 36000 * (12 - m)
The yearly profit of the firm divided equally between them,
21000 * 12 = 36000 * (12 - m)
7 = 12 - m
m = 12 - 7 = 5
So, Beryl joined after 5 months.
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34. B received Rs. 2800 as profit out of a total profit of Rs. 10,850 for his investment. B had invested Rs. 9600, C had invested Rs. 10,800. Time for which A, B and C had invested is in the ratio 2 : 3 : 5. Find out the amount invested by A. Only A, B and C had invested in this business.




SHOW ANSWER
Correct Ans:Rs. 14400
Explanation:
Let the investment made by A be ‘A’.
Given, B invested Rs. 9600, C invested Rs. 10,800.
Time for which A, B and C invested the amount is in the ratio 2 : 3 : 5.
Ratio of profits = Ratio of investment made
Ratio of profit = A * 2 : 9600 * 3 : 10800 * 5
Ratio of profit = A : 14400 : 27000
Given, B received Rs. 2800 as profit out of a total profit of Rs. 10,850 for his investment.
[14400/(A + 14400 + 27000)] * 10850 = 2800
55800 = A + 14400 + 27000
A = Rs. 14400
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35. P, Q, R enter into a partnership. P initially invests 25 lakh and adds another 10 lakh after one year. Q initially invests 35 lakh and withdraws 10 lakh after 2 years. R's investment is Rs 30 lakh. In what ratio should the profit be divided at the end of 3 years?




SHOW ANSWER
Correct Ans:(19:19:18)
Explanation:
Ratio of (amount invested * No. of months in Business) by P, Q, and R = Ratio of Profit of P, Q, and R
= (25 lakh for one year + 35 lakh for 2 years) : (35 lakh for 2 years + 25 lakh for one year) : (30 lakh for 3 years)
= (25 * 12 + 35 * 24) : (35 * 24 + 25 * 12) : (30 * 36)
= 5*12 (5 + 7*2) : 5*12 (7*2 + 5) : 5*12(6*3)
= (5 + 14) : (14 + 5) : 18
= 19 : 19 : 18
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36. In a business, A invested Rs. 25,000 and B invested Rs. 24,000. As his salary A got 1/50th of the total profit of Rs. 60,000 after which the remaining amount was shared among A and B in the ratio of their shares in profit. Find the difference in the shares of both.




SHOW ANSWER
Correct Ans:Rs. 2,400
Explanation:
Given: A invested Rs. 25,000; B invested Rs. 24,000.

Ratio of shares of A and B = 25000 : 24000 = 25 : 24
As his salary A got 1/50th of the total profit of Rs 60,000,
A's salary = (1/50)*60000 = Rs. 1200
Therefore remaining profit = 60000 - 1200 = Rs. 58,800

So, B's share = (24/49)*58800 = Rs. 28,800
A's share = 1200 + (58800 - 28800) = Rs. 31,200
Therefore, difference in shares = 31200 - 28800 = Rs. 2,400
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37. Reema and Sima are two friends working in a insurance company get their monthly salaries in the ratio of 4 : 5. After 4 months, Reema got promotion and her salary increases by 25%. After a year, if total salary obtained by them in a year is Rs. 174,000 then find monthly salary of Sima before increment.




SHOW ANSWER
Correct Ans:Rs.7,500
Explanation:
Given: Reema and Sima, monthly salary ratio = 4 : 5

Let the monthly salary of Reema and Sima be 4X and 5X respectively.

Annual salary of Reema = (4X x 4) + (4X x (125/100) x 8)
= 16X + 40X = 56X

Annual salary of Sima = (5X x 12) = 60X

If total salary obtained by them in a year is Rs 174,000,
Annual salary of Reema + Annual salary of Sima = 174000
56X + 60X = 174000
116X = 174000
X = 1500

Therefore, monthly income of Sima before increment = 5X
= 5(1500)
= Rs. 7500
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38. A and B started a business by investing 35000 and 21000 respectively. The number of months for which B invested into the business was 4 less than the number of months for which A invested. If the ratio of the profit of A to B was 5:2 then find the ratio of the months invested by A to B. 




SHOW ANSWER
Correct Ans:3 : 2
Explanation:
Let assume A invested for X months and B invested for (X - 4) months.
WKT, Ratio of Profit = {A capital * time} : {B capital * time}
Ratio of profit = [35000 * X] : [21000 * (X - 4)]
5 : 2 = 5X : 3(X - 4)
5/2 = 5X/3(X - 4)
15(X - 4) = 10X
15X - 60 = 10X
5X = 60
X = 12 months

Therefore, A = 12 months
B = X - 4 = 12 - 4 = 8 months
Hence, ratio of the months invested by A to B = 12 : 8 = 3 : 2
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39. Arun started a business investing Rs. 38,000. After 5 months Bakul joined him with a capital of Rs. 55,000. At the end of the year the total profit was Rs. 22,000. What is the approximate difference between the share of profits of Arun and Bakul? 




SHOW ANSWER
Correct Ans:Rs. 1856
Explanation:
Given: Arun invested Rs. 38,0000 for 12 months;
Bakul invested Rs. 55,000 for 7 months

WKT, Ratio of Profit = {Arun's capital * time} : {Bakul's capital * time}
Ratio of profit = (38000 x 12) : (55000 x 7)
= 456 : 385

Therefore, required difference = [(456 - 385)/841]*22000
= (71/841)*22000
= Rs. 1856
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40. P, Q and R started a business in a partnership with investment of Rs 12000, Rs 26000 and Rs 32000 respectively. After 4 months P leaves. After 6 months from start Q leaves and P joins with an amount equal to his earlier investment. After 10 months from start R leaves and Q joins with his prior investment. At the end of the year they earn a profit of Rs 53622. Find the share of Q in the annual profit. 




SHOW ANSWER
Correct Ans:Rs. 17,212
Explanation:
Share of P = [(12000 x 4) + (12000 + 6)]
Share of Q = [(26000 x 6) + (26000 x 2)]
Share of R = [32000 x 10]
WKT, Ratio of Profit = {P's capital * time} : {Q's capital * time} : {R's capital * time}
Ratio of Profit = [(12000 x 4) + (12000 x 6)] : [(26000 x 6) + (26000 x 2)] : [32000 x 10]
= [12000 x 10] : [26000 x 8] : [32000 x 10]
= 15 : 26 : 40

Therefore, the share of Q in the annual profit = (26/81)*53622
= Rs. 17,212
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