1. A starts a business with Rs.70,000. After 2 months, B joined him with Rs.90,000. C joined them after some more time with Rs.1,40,000. At the end of the year, out of a total profit of Rs.4,25,000, C gets Rs.1,30,000 as his share. How many months after B joined the business, did C join?
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Correct Ans:4 (1/2) months
Explanation:
Given, A invested amount = Rs. 70,000 for 12 months
B invested amount = Rs. 90,000 for 10 months
and C invested amount = Rs. 1,40,000
Assume that C was there in the business for x months.
Ratio of investment of A, B, C is:
=> A : B : C = (70000 * 12) : (90000 * 10) : (140000 * x)
= (70 * 12) : (90 * 10) : (140 * x)
= (7 * 12) : (9 * 10) : (14 * x)
= (7 * 6) : (9 * 5) : (7 * x)
= 42 : 45 : 7x
Thus, share of A, B , C = 42 part, 45 part, 7x part respectively.
Given, Total profit = Rs. 4,25,000
Given C's share = Rs. 1,30,000
=> C's share = 425000 * [7x/(42 + 45 + 7x)] = 130000
=> 425 [ 7x / (87 + 7x)] = 130
=> 85 [ 7x / (87 + 7x)] = 26
=> 85 [ 7x] = 26 [ (87 + 7x)]
=> 595 x = 2262 + 182 x
=> 595 x - 182 x = 2262
=> 413 x = 2262
=> x = 5.48
=> x = 5.5 (approx)
It means C was there in the business for 5 and half months.
Given that B is in the business for 10 months.
Hence C joined after (10 - 5.5) months = 4.5 =4 and half monthsafter B joined.
2. A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
SHOW ANSWER
Correct Ans:Rs. 59000
Explanation:
Given,
A invested amount = Rs. 50,000
Interest received by A from B = 10% of half of Rs.50,000
= 10% of Rs. 25000
= Rs.2500.
Amount received by A per annum for being a working partner = 1500 x 12
= Rs.18000
Let 'P' be the part of the remaining profit amount that A receives as his share.
So,total income of A = (Rs.2500 + Rs.18000 + Rs. P ) = (Rs. 20500 + Rs. P)
Total income of B = only his share from the remaining profit amount = 'P', (Given as A and B share the remaining profit amount equally.)
Given, income of A = Twice the income of B
So, (20,500 + P ) = 2(P)
=> P = 20,500
Thus, the Total profit = 2P + Rs.18000
= 2 * (20500) + 18000
= Rs. 59000
Therefore, Total Profit = Rs. 59000
3. Rahul and Rafick start a business with investments of Rs. 2500 and Rs. 2250 respectively. After 2 months, Rahul takes out Rs.1250 from his capital. After 1 more month, Rafick takes out Rs.750 of his capital while Ramesh joins them with a capital of Rs. 3500. At the end of 6 months, they earn a profit of Rs. 2540. Which of the following is the share of each member in the profit?
SHOW ANSWER
Correct Ans:Rahul - Rs. 800, Rafick - Rs. 900, Ramesh - Rs. 840
Explanation:
Given, total period of Business = 6 months.
Rahul's investment:
Given, Rahul 's Initial Investment = Rs 2500 for 2 months.
After 2 months he withdraw Rs.1250 from his capital = Rs (2500-1250) = Rs 1250 for next 4 months.
Rafick's Investment:
Rafick's Initial Investment = Rs 2250 for 3 months
After 3 months he withdraw Rs.750 from his capital = Rs.(2250-750) = Rs.1500 for next 3 months.
Ramesh's Investment:
Ramesh invested Rs.3500 for last 3 months.
Their investment ratio = Rahul: Rafick : Ramesh
= (2500x2 + 1250x4) : (2250x3 + 1500x3) : (3500x3)
= ( 5000 + 5000) : ( 6750 + 4500) : ( 10,500)
= (10,000) : (11,250) : (10,500)
= 1000 : 1125: 1050
= 40 : 45 : 42 = Profit ratio of Rahul: Rafick : Ramesh
Given, Total profit for 6 months = Rs.2540
Therefore, Rahul's share = Rs. [40/(40+45+42)] * 2540
= Rs.(40/127) * 2540
= 101600 / 127
= Rs 800
Rafick's share = Rs.(45/127) * 2540
= 114300 / 127
= Rs.900
Ramesh's share = Rs.(42/127) * 2540
= 106680 / 127
= Rs.840
Thus Profit for: Rahul - Rs. 800, Rafick - Rs. 900, Ramesh - Rs. 840
4. In a business, A invested 1/3rd of total investment in 1/3rd of the period of investment, B invested 1/4th of total investment in 1/4th of the period of investment and remaining was invested by C in the remaining period. Then the ratio's between their shares is:
SHOW ANSWER
Correct Ans:16:9:25
Explanation:
Formula used:- Ratio between A, B, C shares = [A's amount invested X A's period in business] : [B's amount invested X B's period in business] : [C's amount invested X C's period in business]
Given,
A's amount invested = (1/3)of the total invested amount
B'samount invested = (1/4)of the total invested amount
C's amount invested = Remaining of the total invested amount
= 1 - (A's amount invested +B'samount invested)
= 1 - (1/3 + 1/4)
= 1 - [(4+3)/12)]
= 1 - [7/12]
= 5/12
ThereforeC's amount invested =5/12of the total invested amount
Also Given that,
A'speriod of investment =(1/3)of the total investment period
B'speriod of investment =(1/4)of the total investment period
C'speriod of investment =Remaining of the totalinvestment period
= 1 - (A'speriod +B'speriod)
= 1 - (1/3 + 1/4)
= 1 - [(4+3)/12)]
= 1 - [7/12]
= 5/12
ThereforeC'speriod of investment =5/12of the totalinvestment period
Now,Ratio between A, B, C shares = [A's amount invested X A's period in business] : [B's amount invested X B's period in business] : [C's amount invested X C's period in business]
= [1/3 X 1/3] : [1/4 X 1/4] : [5/12 X 5/12]
= [1/9] : [1/16] : [25/144]
=[16/144] : [9/144] : [25/144]
= 16 : 9 : 25
5. In a business A invested 3 times that of B and the period of investment of A is 2 times that of B. Then their profit ratio is:
SHOW ANSWER
Correct Ans:6:1
Explanation:
share's ratio = A : B = 3 : 1
Time ratio = A : B = 2 : 1
Then, profit ratio = A : B = 3*2 : 1*1 = 6 : 1
6. A and B invested in a business in the ratio 2:3 and the ratio of their period of investment is 4:5. Then their profit ratio is:
SHOW ANSWER
Correct Ans:8:15
Explanation:
share's ratio = A : B = 2 : 3
Time ratio = A : B = 4 : 5
Then, profit ratio = A : B = 2*4 : 3*5 = 8 : 15
7. A,B invested Rs.20,000/- and Rs.25,000/- respectively in a business. The 20% of profits goes to charities. The rest being divided in proportion to their capitals out of a total profit of Rs.9000/-. The A's share is:
SHOW ANSWER
Correct Ans:Rs.3200/-
Explanation:
A = Rs.20,000/- & B = Rs.25,000/-
==> A : B = 20 : 25
==> 4 : 5
Total profit = Rs.9000/-
20 % of profit goes to charities ===> Rs.9000/- - Rs.1800/- = Rs.7200/-
remaining amount = Rs.7200/-
Total parts = 9
9 parts -----> Rs.7200/-
1 part ------> Rs.800/-
A's share ===> Rs.800/- * 4 parts = Rs.3200/
8. A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join?
SHOW ANSWER
Correct Ans:4 months
Explanation:
Given, A invested amount = Rs. 40,000for 12 months
B invested amount = Rs. 60,000for 10 months
and Cinvested amount = Rs. 1,20,000
Assume that C was there in the business for x months.
Ratio of investment of A, B, C is:
=>A : B : C = (40000 * 12) : (60000 * 10) : (120000 * x)
= (40 * 12) : (60 * 10) : (120 * x)
= 40 : (5 * 10) : (10 * x)
= 8 : 10 : 2x
= 4 : 5 : x
Thus, share of A, B , C = 4 part, 5 part, x part respectively.
Given, Total profit = Rs. 3,75,000
Given C's share = Rs. 1,50,000
=>C's share = 375000 * [x/(4 + 5 +x)] = 150000
=> 375 [x/(9+x)] = 150
=> 5 [x/(9+x)] = 2
=> 5x = 2(9+x)
=> 5x = 18 + 2x
=> 3x = 18
=> x = 18/3
=> x= 6
It means C was there in the business for 6 months.
Given that B is in the business for 10 months.
Hence C joined after (10 - 6) months = 4 monthsafter B joined.
9. A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 After six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
SHOW ANSWER
Correct Ans:Rs.7500/
Explanation:
A : B : C = 20000 * 24 : 15000 * 24 : 20000 * 18 = 20 * 4 : 15 * 4 : 20 * 3
= 4 * 4 : 3 * 4 : 4 * 3
= 4:3:3
B's Share = 25000 * 3/10 = 7500/-
10. Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
SHOW ANSWER
Correct Ans:21 : 32
Explanation:
Here capital is not the same.
Suresh invest 20000 for initial 6 months and 15000 for the next 6 months.
Hence his term of ratio
=( 20000 × 6 + 15000 × 6)
Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.
Hence his term of ration
= (30000 × 4 : 50000 × 4)
Suresh : Kiran = ( 20000 × 6 + 15000 × 6) : (30000 × 4 : 50000 × 4)
= (20 × 6 + 15 × 6) : (30 × 4 + 50 × 4)
= (20 × 3 + 15 × 3) : (30 × 2 : 50 × 2)
= 105:160
= 21:32
11. A, B started a business by investing Rs.3000/- and Rs.5000/-. A is working and B is sleeping partner. A gets 10% of profits for managing, the rest being divided in proportion to their capitals out of a total profit of Rs.8,000/-. Then find the A's total.
SHOW ANSWER
Correct Ans:Rs.3500/-
Explanation:
Given, A's invested amount = Rs.3000/-
B's invested amount = Rs.5000/-
Then, A's share : B's share = 3 : 5
=>Total parts = 3 + 5 = 8
Given, Total profit = Rs.8000/-
From which A gets 10%
so, 10 % of 8000 = 800/-
A's Salary = Rs.800/-
Remaining profit amount = Rs.7200/-
Total parts = 8
8 parts -----> Rs.7200/-
1 part ------> Rs.900/-
A's share ===> Rs.900/- * 3 parts = Rs.2700/-
A's total = A's share + A's salary
= Rs.2700 + Rs.800
= Rs.3500/-
12. A,B started a business by investing Rs.4000/- and Rs.5000/-. A is working and B is sleeping partner. A gets 10% of profits for managing, the rest being divided in proportion to their capitals out of a total profit of Rs.9,000/-. The money received by B is:?
SHOW ANSWER
Correct Ans:Rs.4500/-
Explanation:
Given
A = Rs.4000/- B = Rs.5000/- Then, A : B = 4 : 5
Total profit = Rs.9000/-
10 % of 9000 = Rs.900/-
A's Salary = Rs.900/-
Remaining amount = Rs 8100/-
Total parts = 9 => 4 + 5
9 parts -----> Rs.8100/-
1 part ------> Rs.900/-
B's share = 5 parts
= 5 parts -----> 900 * 5
= Rs.4500/-
The money received by B is Rs 4500.
13. In a business, A,B invested Rs.8,000/-,Rs.4,000/- respectively. After 6 months A increases his share by 50% and B withdraws 1/5th of his capital. At the end of the year the total profit is Rs.11,600/-. Then what is A's share?
SHOW ANSWER
Correct Ans:Rs.8000/-
Explanation:
A's Share = Rs.8000/- per first 6 month + Next 6 months Rs.4000/- added
= 8 * 6 + 12 * 6 = 48 + 72 = 120
B's Share = Rs.5000/- per first 6 months + Next 6 months Rs.4000/- reduced
= 5 * 6 + 4 * 6 = 30 + 24 = 54
Then,A's part= 120 : B's part= 54
A : B = 20 : 9
Total = 29 parts -----> Rs.11600/-
= 1 part ------> Rs.400/-
Then, A's share is
= 10 parts = Rs.400/- * 20 parts = Rs.8000/-
14. In a business, A,B invested Rs.8,000/-,Rs.4,000/- respectively. After 6 months A increases his share by 50% and B decreases his share by 50%. At the end of the year the total profit is Rs.52,000/-. Then what is A’s share?
SHOW ANSWER
Correct Ans:Rs.4000/-
Explanation:
A's Share = Rs.8000/- per first 6 months + Next 6 months Rs.4000/- added = 80 * 6 + 120 * 6 = 480 + 720 = 1200 B's Share = Rs.4000/- per first 6 months + Next 6 months Rs.2000/- reduced = 40 * 6 + 20 * 6 = 240 + 120 = 360
Then,A's part= Rs.1200 : B's part= 360
A : B = 10 : 3 Total = 13 parts -----> Rs.5200/-
= 1 part ------> Rs.400/-
Then, A's share is
= 10 parts = 400/- * 10 parts = Rs.4000/-
15. In a business, A,B invested Rs.50,000/-,Rs.60,000/- respectively. After 4 months A adds Rs.25000/- to his initial investment and B withdrew Rs.20,000/- from his initial investment. At the end of the year the total amount of profit they received is Rs.2,89,000/-. Then what is A's share?
SHOW ANSWER
Correct Ans:Rs.170000/-
Explanation:
A's investment= Rs.50000/- per first 4 month + Next 8 months Rs.25000/- added
= 50,000 * 4 + 75,000 * 8
= 2,00,000 + 6,00,000
= 8,00,000
B's investment= Rs.60000/- per first 4 months + For Next 8 months Rs.20000/- reduced
= 60,000 * 4 + 40,000 * 8
= 2,40,000 + 3,20,000
= 5,60,000
Then, Ratio of share of A and B = 8,00,000 :5,60,000
= 80 : 56
= 10 :7
=> A : B = 10 : 7
=>Total = 17 parts
Given total profit = Rs.2,89,000
17 parts -----> Rs.2,89,000/-
=> 1 part ------> (Rs. 2,89,000 / 17) = Rs.17,000/-
Then, A's share = Rs.17000/- * 10 parts = Rs.1,70,000/-
16. Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
SHOW ANSWER
Correct Ans:72000
Explanation:
Ratio of the profits = 25000 * 12 : 60000*8
= 25 * 12 : 60 * 8 = 5 * 3 : 12:2 = 5 : 4 * 2
= 5:8
Let the total profit = x.
Then Kamal received 10x/100 = x/10 as commission for managing the business
Remaining profit = x- x/10 = 9x/10 which is shared in the ration 5:8
Kamal's share = x / 10 + (9x /10) (5/13) = 58000
=> x + 9x(5/13) = 580000
=> x(1 + 45/13) = 580000
=> x ( 58/13) = 580000
=> x ( 1/13) = 10000
=> x = 130000
Kiran's share = 130000 - 58000 = 72000.
17. A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
SHOW ANSWER
Correct Ans:8 months
Explanation:
Let B joins for x months.
Given, A's capital = Rs. 85,000 for 12 months
B's capital = Rs. 42,500 for x months
Given, Ratio of profit = 3 : 1
=> Ratio of investment =Ratio of profit
=> (85000 * 12) : (42500 * x) = 3 : 1
=>(850 * 12) : (425 * x) = 3 : 1
=> (2 * 12) : (x) = 3 : 1
=> 24 / x = 3/1
=> x = 24/3
=> x = 8
Therefore, No. of months "B" in the business = 8 months
18. A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?
SHOW ANSWER
Correct Ans:1500
Explanation:
Assume that the total profit is x.
Since 5% goes for charity, 95% of x will be divided between A and B in the ratio 3: 2
Given, A's share is Rs. 855
=> A's profit = (95x/100) * (3/5) = 855
=> (95x/100) * (3/5) = 855
=> 19x * 3 = 855 *100
=> 57 x = 85500
=> x = 1500
Hence the total profit = Rs. 1500
19. 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. What is the share of B in the profit.
SHOW ANSWER
Correct Ans:2660
Explanation:
A is a working member and for that, he receive 5% of the profit
= 5% of 7400 = 5 *7400/100 = 370
Remaining amount = 7400-370 = 7030
Ratio of their investments = (6500 * 6) : (8400 * 5) : (10000 * 3)
= (65 * 6) : (84 * 5) : (100 * 3) = (13 * 6) : 84 : (20*3) = (13 * 2) : 28 : 20
= 13 : 14 : 10
Share of B in the profit = 7030 * (14/37) = 190 * 14 = 2660
20. A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
SHOW ANSWER
Correct Ans:45
Explanation:
Given
A : B: C = 10 oxen for 7 months: 12 for 5 months ,15 for 3 months
= 2 * 7 : 12 * 1 : 3 * 3 = 14 : 12 : 9
Amount that C should pay
= 175 * ( 9 / 35 ) = 5 * 9 = 45
Amount should C pay as his share of rent = Rs 45.
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