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Partnership Questions

81. A,B started a business by investing Rs.10000/- and Rs.20000/- respectively. After 1year B withdrew Rs.5000/- and A invested Rs.5000/- more. At the end of 2 years they got total Profit Rs.6000/-. What is A's share?  




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Correct Ans:Rs.2500/-
Explanation:
A's Share = Rs.10000/- per first 1 year, Next year Rs.5000/- added
= Rs.10000/- * 1 + Rs.15000 * 1
= 25000

B's Share = Rs.20000/- per first 1 year, Next year Rs.5000/- reduced
= Rs.20000/- * 1 + Rs.15000/- * 1
= Rs.35000/-

Then, A's part : B's part= 25 :35

Total --> 60 parts -----> Rs.6000/-
1 part ------> Rs.100/-

Then, A's share = 25 parts = Rs.100/- * 25 parts = Rs.2500/-
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82. A began a business with Rs.5000/- and was joined afterwards by B with Rs.4000/-. If the profits at the end of the year were divided in the ratio 3:1, B joined the business after:? 




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Correct Ans:7 Months
Explanation:
1) Share's ratio is always equal to profit ratio
2) When two ratios are equal, then the cross products of the ratios are equal.
That is, for the proportion, a:b = c:d , a x d = b x c
A = 5000/- per 12 Months B = 4000/- per x Months 4000 * 12 : 5000 * 8 = 3 : 1
=> 6 : 5 = 3 : 1
=> 3x = 15
=> x = 5 Months
Then, B joined the business after = 12 - x ==> 12 - 5 ==> after 7 Months.
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83. A began a business with Rs,5000/- and was joined afterwards by B with Rs.4000/-. If the profits at the end of the year were divided in the ratio 3:1, How many months B was in the business? 




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Correct Ans:5 Months
Explanation:
Let the number of months B in the business = x

Given, A's investment = Rs. 5000 for 12 months
B's investment = Rs. 4000 for x months

Given Profit ratio = 3 : 1
=> Ratio of Profit = Ratio of investment
=> 3 : 1 = (5000 * 12) : (4000 * x)
=> 3 : 1 = 15 : x
=> 3/1 = 15 / x
=> x = 15 / 3
=> x = 5
Thus,number of months B in the business = 5 months
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84. A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. B's contribution in the capital is:




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Correct Ans:9000
Explanation:
Given Profit is for one year = 12 months, so the peroid of given business = 12 months.
Given, A investment = Rs. 3500 for 12 months

Given, B joined the business after 5 months, which means he is in the business for (12 - 5) = 7 months.
LetB's contribution in the capital= Rs. "x"

Given Profit Ratio = 2 : 3
A and B's Ratio of (Amount invested * No. of months in business) = A, B's Ratio of profit
=> (3500 * 12) : (x * 7) = 2 : 3
=> (500 * 12) / x = 2 / 3
=> x = (500 * 12) * 3/2
=> x = 500 * 6 * 3
=> x = 9,000

Therefore,B's contribution in the capital= Rs. "x" = Rs. 9,000
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85. A and B started a partnership business investing capital in the ratio of 3 : 5. C joined in the partnership after six months with an amount equal to that of B. At the end of one year, the profit should be distributed among A, B and C in --- proportion.




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Correct Ans:6:10:05
Explanation:
Initial investment capital ratio of A and B = 3 : 5
Hence we can assume that initial capital of A and B are 3x and 5x respectively.
Amount that C invest after 6 months = 5x (Since it is equal to B's investment)
Ratio in which profit should be distributed after 1 year = 3x * 12 : 5x * 12 : 5x * 6
=> 3 * 12 : 5 * 12 : 5 * 6
= 6 : 10 : 5
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86. A , B , C started a partnership business by investing Rs 27000 , 72000 , 81000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?




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Correct Ans:80000
Explanation:
A:B:C = 27000:72000:81000
= 3:8:9
Let the total profit= p
Then p * 9/20 = 36000
=> p = 36000 * 20/9 = 80000
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87. P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is




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Correct Ans:60000
Explanation:
Let the amount invested by Q = q
40000 : q = 2 : 3
=> 40000/q = 2/3
=> q = 40000 * (3/2) = 60000
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88. A and B starts a business investing Rs.85,000 and Rs.15,000 respectively. Find out the ratio in which the profits should be shared.




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Correct Ans:17:3
Explanation:
Here A's and B's capitals are there for an equal time. Hence
Ratio of share of profits between A and B =A's investedamount :B's investedamount
= 85000 : 15000
= 85 : 15
= 17 : 3
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89. A started a business by investing Rs.10000/-.After 1 year B joined by investing Rs.15000/- After 6 months C joined by investing Rs.24000/-. At the end of two years, they got a profit of Rs.47000/-. What is A's share?




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Correct Ans:Rs.20000/-
Explanation:
A = Rs.10000/- per 24 months
B = Rs.15000/- per 12 months
C = Rs.24000/- per 6 months

A : B : C = 10000 * 24 : 15000 * 12 : 24000 * 6
= 20 : 15 : 12

Total = 47 parts -----> Rs.47000/- (profit)
=> 1 part ------> Rs.1000/-

Then, A's share is
= 20 part = Rs.1000/- * 20 parts = Rs.20,000/-
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90. A started a business by investing Rs.5000/-. After 4 months B joined by investing Rs.4000/- After 2 months C joined by investing Rs.3000/-. At the end of the year, they got a profit of Rs.5500/-. What is A's share? 




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Correct Ans:Rs.3000/-
Explanation:
A = Rs.5000/- per 12 months
B = Rs.4000/- per 8 months
C = Rs.3000/- per 6 months

A : B : C= (5000 * 12) : (4000 * 8) : (3000 * 6)
= 30 : 16 : 9

Total = 55 parts -----> Rs.5500/- (profit)
=> 1 part ------> Rs.100/-

Then, A's share is = 30 part = Rs.100 * 30 parts = Rs.3000/-
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91. A started a business by investing Rs.4000/-. After 4 months B joined by investing Rs.5000/- At the end of the year, there was a profit of Rs.8800/-. What is A's share?




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Correct Ans:Rs.4800/-
Explanation:
A = Rs.4000/- per 12 months B = Rs.5000/- per 8 months
= 4000 * 12 : 5000 * 8 = 6 : 5 Total = 11 parts -----> Rs.8800/- (profit)
= 1 part ------> Rs.800/-
Then, A's share is
= 6 part = Rs.800/- * 6 parts = Rs.4800/-
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92. A,B and C started a business in which A invested Rs.2000/- for 1 year, B invested Rs.3000/- for 1 1/2 years, C invested Rs.4000/- for 2 years. At the end of the profit received by them is Rs.14500/-. What is C's share?




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Correct Ans:Rs.8000/-
Explanation:
A = Rs.20000/- per 12 months B = Rs.30000/- per 18 months C = Rs.40000/- per 24 months
= 20000 * 12 : 30000 * 18 : 40000 * 24 = 4 : 9 : 16 Total = 29 parts -----> Rs.14500/- (profit)
= 1 part ------> Rs.500/-
Then, C's share is
= 16 part = Rs.500/- * 16 parts = Rs.8000/-
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93. A,B and C started a business in which A invested Rs.20000/- for 2 year, B invested Rs.30000/- for 3 years, C invested Rs.40000/- for 4 years. At the end of the profit received by them is Rs.11,600/-. What is B�s share?




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Correct Ans:Rs.3600/-
Explanation:
A = Rs.20000/- per 2 year B = Rs.30000/- per 3 years C = Rs.40000/- per 4 years
= 20000 * 2 : 30000 * 3 : 40000 * 4
= 4 : 9 : 16
Total = 29 parts -----> Rs.11600/- (profit)
= 1 part ------> Rs.400/-
Then, B's share is
=> 9 part = Rs.400/-
=> 400 * 9 parts = Rs.3600/-
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94. A invested Rs 76000 in a business. After few months, B joined him with Rs 57000. The total profit was divided between them in the ratio 2 : 1 at the end of the year. After how many months did B join?




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Correct Ans:4
Explanation:
Assume that B joins for x months . Then
A : B = 76000 * 12 : 57000 * x = 2:1
=> 76 * 12 : 57x = 2:1
=> 76 * 12/57x = 2/1 = 2
=> x = (76 * 12)/(57 * 2) = (76 * 4)/(19 * 2) = 8
Hence B was there in the business for 8 months, and joined after 12-8 = 4 months
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95. In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs 157300 was their profit, how much amount did B receive?




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Correct Ans:48400
Explanation:
Assume that investment of C = x
Then, investment of A = 2x
Investment of B = 4x/3
A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3
B's share = 157300 * 4/(6+4+3) = 157300 * 4/13
= 12100 * 4 = 48400
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96. If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4650 , R will receive




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Correct Ans:900
Explanation:
Let P's capital = p, Q's capital = q and R's capital = r
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 4650 * (6/31) = 150 * 6 = 900
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97. P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them. What is Q's share?




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Correct Ans:144
Explanation:
The ratio of their initial investment = 1/2 : 1/3 : 1/4
= 6 : 4: 3
Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively
P:Q:R = (6x * 2 + 3x * 10) : 4x * 12 : 3x * 12
= (12 + 30) : 4 * 12 : 3 * 12
=(4 + 10) : 4 * 4 : 12
= 14 : 16 : 12
= 7 : 8 : 6
B's share = 378 * (8/21) = 18 * 8 = 144
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98. A,B and C started a business in which A invested Rs.10000/- for 1 year, B invested Rs.20000/- for 2 years, C invested Rs.30000/- for 3 years. At the end, the profit received by them is Rs.5600/-. What is C's share? 




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Correct Ans:Rs.3600/-
Explanation:
Given,A invested Rs.10,000/- for 1 year, B invested Rs.20,000/- for 2 years, C invested Rs.30,000/- for 3 years.
Therefore, the ratio of investment of A, B, C = Ratio of (Amount invested * No. of months in Business)
= (10,000 * 12) *: (20,000 * 24) : (30,000 * 36)
= (1 * 12) : (2 * 24) : (3 * 36)
= 1 : 4 : 9

Thus,Total parts of share = 1 + 4 + 9 = 14
C's part of share = 9
Given,total profit = Rs. 5600

Hence, C's share = Rs. (9/14) * 5600 = Rs. 3600
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99. A,B started a business in which A invested Rs.10000/- for 1 year, B invested Rs.20000/- for 2 years. At the end of the profit received by them is Rs.5000/-. What is A's share?




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Correct Ans:Rs.1000/-
Explanation:
A = Rs.10000/- per 1 year B = Rs.20000/- per 2 years
= 10000 * 1 : 20000 * 2 = 1 : 4 Total = 5 parts -----> Rs.5000/- (profit)
= 1 part ------> Rs.1000/-
Then, A's share is
= 1 part = Rs.1000/-
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100. A,B and C started a business by investing Rs.1400/- , Rs.4200/- and Rs.7000/- respectively. Total profit is Rs.8100/-. Find the C's share? 




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Correct Ans:Rs.4500/-
Explanation:
Ratio of investment of A, B and C = 1400 : 4200 : 7000
= 1 : 3 : 5

Given,Total profit = Rs.8100

Then, C's share = 5/ (1 + 3 + 5) * 8100
= (5 /9) * 8100
= Rs. 4500
=> C's share =Rs. 4500
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