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*Partnership Tricks & Tips*

* **Partnership is an important chapter in Quantitative section of IBPS and other examination.*

*This is a very prominent part of most of the exams. These questions are really scoring as well because these questions are really scoring. Check below what this topic is about and how are typical questions solved.*

**What is Partnership?**

*When two or more people join hands to create a start-up or some business it’s called a ‘partnership’ business. Typically, they invest some capital and earn some profit. And, this profit is distributed among partners either in some prefixed ratio or the ratio of their investment. In exams, mostly profit distribution is based on later type. The calculation for profit based on investment is done as shown below:*

**P _{1}: P_{2} = C_{1}×T_{1}: C_{2}×T_{2}**

_{}Here, **P _{1} **= Profit for Partner 1.

**C**= Capital by Partner 1._{1}

**T**= Time period for which Partner 1 invested his capital._{1}

**P**= Profit for Partner 2._{2}

**C**= Capital by Partner 2._{2}

**T**= Time period for which Partner 2 invested his capital._{2}**Typical Question Methodology:**

**1)** We are given the amount of investment by two partners for particular time like A and B invested Rs.1500 and Rs.2000 respectively. **After 4 months**, they admit C with contribution of Rs.2250. And, B withdraws his contribution after 9 months ⇒ A invested his capital for 12 months while C invested his capital for (12 – 4=) 8 months and B invested for 9 months.* So, according to ratio formula, A: B: C = 1500×12: 2000×9: 2250×8 = 180: 180: 180 (We’ve cancelled out the equal number of zeroes from all the numbers)*

*⇒ A: B: C = 1: 1: 1*

**2)** Second, we are given the profit at the end of year was Rs 900. What’d B get?* Now, A: B: C = 1: 1: 1*

**⇒ B’s share =**{1/(1+1+1)} =1/3rd of profits = (1/3)*900 = Rs. 300*We can see that calculating profit isn’t that tricky so we’ll be solving sample questions in a way that would help you in calculating the ratio of profits among partners.*

**There are two types of partnership.**

**Simple Partnership:**In simple partnership, capitals of partners are invested for the same period of time.

**Compound Partnership:**In compound partnership, capitals of partners are invested for the different period of time.

**Basic Formulas**

*If two partners A and B are investing their money to run a business then (Simple Partnership)*

** Capital of A : Capital of B = Profit of A : Profit of B**

*If two partners A and B are investing their money for different period of time to run a business then*

*(Compound Partnership)*

**Capital of A × Time period of A : Capital of B × Time period of B**

**= Profit of A : Profit of B**

*If n partners are investing for different period of time then*

**C _{1}T_{1} : C_{2}T_{2} : C_{3}T_{3} : … : C_{n}T_{n} = P_{1} : P_{2} : P_{3} : … : P_{n}**

*Where C is the capital invested, T is time period of capital invested and P is profit earned.*

__Shortcut Methods__

**Rule 1:**

*If two partners are investing their money C _{1} and C_{2} for equal period of time and their total profit is P then their shares of profit are*

*If these partners are investing their money for different period of time*

*which is T _{1} and T_{2}, then their profits are*

**Rule 2:**

*If n partners are investing their money C _{1}, C_{2}, …, C_{n} for equal period of time and their total profit is P then their shares of profit are*

*If these partners are investing their money for different period of time which*

*is T _{1}, T_{2},… , T_{n }then their profits are*

* *

**Question** – Raj invested Rs 76000 in a business. After few months Monty joined him and invests Rs 57000. At the end of year both of them share the profits at the ratio of 2:1. After how many months Monty joined Raj ?

**Solution** – We can simply compute per month investment of both partnership

*Raj invested Rs 76,000 for 12 months and Monty invested Rs 57,000 for x months.*

*Now 76000 × 12 / 57000 × x = 2 :1*

*⇒ 76 × 12 / 2 = 57x*

*⇒ x = 8*

*So Monty invested his money for 8 months and he joined after 4 months.*

**Question – **A and B started a business by investing money in ratio of 5:6. C joined them after few months by sharing an amount equal to B’s share. At the end of year 20% profit was earned which was equal equal to Rs 98,000. How much money was invested by C ?* Solution – *

*= First of all we will calculate the weighted ratios*

*⇒ A = 5 × 12 = 60*

*⇒ B = 6 × 12 = 72*

*⇒ C = 6 × 6 = 36*

*Total investment at the end of year = 98000 × 100/20 = Rs 4,90,000*

*⇒ Investment by C = 490000 × 36 / 168 × 2 = Rs 210000*

**Question –**A, B and C shared profits in ratio of 5:7:8. They partnered for 14 months, 8 months and 7 months respectively. What was he ratio of their investments ?

**Solution** – Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.

*Let X is the total investment*

*⇒14 x = 5** ⇒ 8 x = 7** ⇒ 7x = 8*

*⇒ Final investment ratio = 20 : 49 : 64*

**Question** – Sita and Geeta started a business by investing Rs. 120000 and Rs.135000 respectively. Find the share of each out of an annual profit of Rs. 35700.

**Solution :-**

*When investors are there for the different duration of time in the business , then the investments are calculated for a unit of time by having ( investment x number of units of time) . Now gain or loss is divided in the ratio of these investments.*

**Question** – Ravi started a business by investing Rs.36000. After 3 months Shayam joined him by investing Rs.36000. Find the share of each in the annual profit of Rs. 37100.

**Solution –**

*Now let us do some questions:*

**Question** – Sony , Mony and Tony start a business each investing Rs.20000. 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. 69900 was recorded. Find the share of each?* Solution –*

**Question** – Sheela started a business with Rs. 21000 and is joined afterwords by Reema with Rs 36000. After how many months did Reema join if the profits at the end of the year are divided equally?

**Answer –**

**Question **– X and Y invested in a business. They earned some profit which they divided in the ratio of 2:3. If X invested Rs. 40000. Find the amount invested by Y?

**Solution –**

**Question **– A , B , C contract a work for Rs .1100.A and B together are to do 7/11 of the work . What is C’s share ?

**Solution –**

* Question – Mohinder and Surinder entered into a partnership investing Rs. 12000 and Rs. 9000 respectively . After 3 months , Sudhir joined them with an investment of Rs.15000. What is the share of Sudhir in a half yearly profit of Rs. 9500?*

**Solution –**

**Question –** In a partnership , A invests 1/6 of the capital for 1/6 of the time , B invests 1/3 of the capital for 1/3 of the time and C , the rest of the capital for the whole time. What is the share of B in the profit f Rs. 4600.

**Solution –**

**Question – **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?

**Solution** – Let the first partner invests Rs x for 14 months, second partner invests Rs.y for 8 months, Rs z for 7 months.

**Sample Questions:**

**Q1.** A contributes one-forth capital for one fourth of time. B contributes one fifth of capital for half of the time. C contributes the remaining capital for the whole time. Find their profit-sharing ratio.

**Sol.** Part of Capital by: A = 1/4 ; B = 1/5 ; C gave remaining ⇒ C’s share in capital = 1 – (1/4 + 1/5) = 11/20* Time investment by: A = 1/4; B = 1/2; C = 1 (whole time means full one 1 year)** Using, P_{1}: P_{2} = C_{1}×T_{1}: C_{2}×T_{2}*

*⇒ A: B : C =*

*Now we’ll take LCM of 16, 10 and 20 which is 80 and divided it by each denominator and multiply number thus obtained by each of the respective denominator.** ⇒ A: B: C = 5: 8: 44.*

**Q2.** A begun a business with Rs.450, after some months B joined him with capital of Rs.300. In the end, the profits were distributed in the ratio of 2:1. After how long did B join?

**Sol.** Capital by: A = 450, B = 300* Time capital stay invested by: A = 12, B = n(say)** Using, P_{1}: P_{2} = C_{1}×T_{1}: C_{2}×T_{2}*

_{(2/1) = (450 ×12)/(300n)}* ⇒ n = 9 months** So, B’s capital was invested for 9 months and he joined after (12 – 9 =) 3 months.*

**Q3.** A and B rent a pasture for 10 months. A puts in 100 cows for 8 months. How many can B put in for remaining 2 months, if he pays half as much again as A?

**Sol.** Here, B has to pay half as much again as A ⇒ If A pays 1 then B pays (1+1/2=) 3/2* So, required ratio = 1: 3/2 ⇒ A: B = 2: 3** Also, number of cows is considered as capital. Let cows brought in by B be ‘n’** So, using, P_{1}: P_{2} = C_{1}×T_{1}: C_{2}×T_{2}2: 3 = 100×8: n×2*

*⇒ n = 600 cows*

**Q4.** A, B and C invested capitals in the ratio of 5: 6: 8.At the end of business term, they received the profits in the ratio of 5: 3: 12. Find the ratio of time for which they contributed their capital.

*Sol. To solve such questions use formula below:** T_{A}: T_{B}: T_{C} = P_{A}÷C_{A}: P_{B}÷C_{B}: P_{C}÷C_{C}Here, T_{A} = Time by A, P_{A} = Profit for A, C_{A}= Capital by A.*

*T*

_{B}= Time by B, P_{B}= Profit for B, C_{B}= Capital by B.*T*

_{C}= Time by C, P_{C}= Profit for C, C_{C}= Capital by C.*⇒ T*

_{A}: T_{B}: T_{C}= 5÷5: 3÷6: 12÷8 = 1: 1/2: 3/2 = 2: 1: 3

**Q5.** Three partners A,B and C had business. A, whose money had been used for 4 months claimed 1/8 profit. B whose money was used for 6 month claimed 1/3 of profit. C had invested Rs. 1560 for 8 months. How much did A and B contribute?* Sol.*

*⇒ n = Rs. 720*

*So, A invested Rs 720. Similarly, we can find the amount of investment by B.*

**Q6.** A and B invested in the ratio of 3: 2. If 5% of total profit goes to charity and A got Rs 855 as his share then find the total profit?* Sol. In such questions, use this formula,*

**1. Three partners A, B and C agree to divide the profit or loss in the ratio 1.50 : 1.75 : 2.25. In a particular year, they earn a profit of Rs 66,000. Find the share of each.***Ans: Ratio of profits =1.50:1.75:2.25 =150:175:225 = 6:7:9*

*A’s share = Rs. 66,000 x 6/22 = Rs. 18,000*

*B’s share = Rs. 66,000 x 7/22 = Rs. 21,000*

*C’s share = Rs. 66,000 x 9/22 = Rs. 27,000*

**2. Vinod, Ramesh and Arun started a business jointly by investing Rs. 3,80,000, Rs. 4,00,000 and Rs. 4,20, 000 respectively. Divide the net profit of Rs. 2,40, 000 among the partners.***Ans: Ratio of investment = 3,80,000 : 4,00,000 : 4,20,000 = 19:20:21*

*Ratio of profit = 19 : 20 : 21*

*Vinod’s share=Rs. 2,40,000 x 19/60 =Rs. 76,000*

*Ramesh’s share = Rs. 2,40,000 x 20/60 = Rs. 80,000*

*Arun’s share = Rs. 2,40,000 x 21/60 = Rs. 84,000*

**3. A, B and C enter into a partnership. A contributes Rs. 3,20,000 for 4 months, B contributes Rs. 5,10,000 for 3 months and C contributes Rs. 2,70,000 for 5 months. If the total profit be Rs. 1,24,800, what is C’s share?***Ans : Ratio of capitals of A, B and C*

*= (3,20,000 x 4) : (5,10,000 x 3) : (2,70,000 x 5)*

*= 12,80,000 : 15,30,000 : 13,50,000*

*= 128 : 153 : 135*

*C’s share = 1,24,800 x 135/416 = Rs. 40,500*

**4. A, B and C enter into partnership . A invests some money at the beginning. B invests double the amount after 6 months and C invests thrice the amount after 8 months. If the annual profit is Rs. 18,000, what is C’s share?***Ans: Suppose the investment of A is Rs. X*

*Ratio of investment of A, B, and C = (12 x X) : (6 x 2X) : (4 x 3X) = 1:1:1*

*C’s share = Rs. 18,000 x 1/3 = Rs. 6,000*

**5. A and B enter into a partnership. A invests Rs. 16,000 for 8 months and B remains in the business for 4 months. Out of a total profit, B claims 2/7 of the profit. Find the contribution of B.***Ans:*

*B’s capital = Rs 12,800*

**6. A and B enter into a speculation. A puts in Rs. 50 and B puts in Rs. 45. At the end of 4 months A withdraws half his capital and at the end of 6 months B withdraws half of his capital, C then enters with a capital of Rs. 70. At the end of 12 months in what ratio will the profit be dividend?***Ans: A’s share : B’s share : C’s share*

**7. A, B and C enter into a partnership and their capitals are in the proportion of 1/3 : 1/4 : 1/5 A withdraws half of his capital at the end of 4 months. Out of a total annual profit of Rs. 847, A’s share is:***Ans: Ratio of capitals in the beginning = 1/3 : 1/4 : 1/5 = 20:15:12*

*Ratio of investment for the whole year = (20 x 4 + 10 x 8) : (15 x 12) : (12 x 12) = 40 : 45 : 36*

*A’s share = 847 x 40/121 = Rs. 280*

**8. In business A, B and C invested Rs. 380, Rs. 400 and Rs. 420 respectively. What is the share of A if they got Rs. 180 as profit.***1) Rs. 57*

*2) Rs. 60*

*3) Rs. 63*

*3) Rs. 62*

*Ans 8. Since profits are shared in the ratio of their investments*

*Ratio of profit sharing = Ration of A’s Investment : B’s Investment : C’s Investment = 380:400:420 = 19:20:21*

*Hence A’s share = 180 x 19/60 = Rs 57*

**9. A started a business with a capital of Rs. 10,000 and 4 months later, B joined him with a capital of Rs. 5,000. What is the share of A of a total profit of Rs. 2,000 at the end of the year ?***1) Rs. 2,000*

*2) Rs. 1,600*

*3) Rs. 1,500*

*4) Rs. 1,000*

*Ans 9. Rs 1500*

**10. A and B together invested Rs. 12,000 in a business. At the end of the year, out of a total profit of Rs. 1,800, A’s share was Rs. 750. What was the investment of A?***1) Rs. 5,000*

*2) Rs. 4,000*

*3) Rs. 3,500*

*4) Rs. 5,300*

*Ans 10. Since profits are shared in the ratio of their investments*

*A’s investment : B’s investment = A’s profit share : B’s profit share*

*750/1800-750 = 750/1050 = 5/7*

*investment of a = (5/5+7) x 12000 = Rs 5000*

**11. Rs. 750 is distributed among A, B and C such that A’s share : B’s share = 2:3 and B’s share: C’s share = 6:5. The share of A is***1) Rs. 150*

*2) Rs. 175*

*3) Rs. 200*

*4) Rs. 250*

*Ans 11. Share of A:B:C*

*B’s share = 3 x 6 =18*

*Hence A’s share = 2 x 6 = 12*

*C’s share = 5 x 3 = 15*

*Share of A:B:C = 12:18:15 = 4:6:5*

*A’ share = 4/15 x 750 = 200*

**12. A profit of Rs. 450 is divided between A and B, A has contributed Rs. 1200 for 5 months and B has contributed Rs. 750 for 4 months. How much amount did the second partner B receive?***1) Rs. 300*

*2) Rs. 425*

*3) Rs. 150*

*4) Rs. 175*

*Ans 12. A’s share = 1200 x 5 = 6000*

*B’s share = 750 x 4 = 3000*

*Share of A : B = 6000 : 3000 = 2 : 1B receives = 450 x 1/3 = Rs 150*

**13. A, B and C can do a work in 20, 25 and 30 days respectively. They undertook to finish the work together for Rs. 2,220. Then the share of A exceeds that of B by:***1) Rs. 120*

*2) Rs. 180*

*3) Rs. 300*

*4) Rs. 600*

*Ans 13.*

**14. Three partners A, B and C invest Rs. 13,000, Rs, 17,000 and Rs. 5,000 respetively in a business. They have a profit of Rs. 1,750. B’s share of profit is:***1) Rs. 650*

*2) Rs. 850*

*3) Rs. 250*

*4) Rs. 750*

*Ans 7. B’s share = Rs 850*

**15. A starts a business with Rs. 30,000 and 4 months after B joins. If at the end of the year, the profits are divided by A and B in the proportion of 9:4, B’s capital was:***1) Rs. 20,000*

*2) Rs. 25,000*

*3) Rs. 20,700*

*4) Rs. 18,000*

*Ans 15. A = 30000 x 12 = 360000*

*B = X x 8 = 8X*

*B’s share = 360000 : 8X = 9 : 4*

*Hence B = Rs 20000*

**16. A invests Rs. 3,000 for one year in a business. How much should B invest in order that the profit after 1 year may be divided in the ratio 2:3?***1) Rs. 2,000*

*2) Rs. 1,800*

*3) Rs. 3,600*

*4) Rs. 4,500*

*Ans 16. Rs 4500*

**17. A and B start a business with initial investments in the ratio 12:11 and their annual profits are in the ratio 4:1. If A invested the money for 11 months, B invested the money for:***1) 3 months*

*2) 8 months*

*3) 4 months*

*4) 6 monthsAns 17. Let B invested months for X months.*

*Then the ratio of investment = 12 x 11 : 11 x X = 12 : X*

*Hence 12 : X = 4 : 1*

*X = 3 months*

**18. Anoop and Manoj invested Rs. 15,000 and Rs. 20,000 respectively and opened a shop. After one year they had a profit of Rs. 23,100. How much more will Manoj get than Anoop?***1) Rs. 3,300*

*2) Rs. 9,000*

*3) Rs. 13,200*

*4) Rs. 5,000*

*Ans 18. Rs 3300*

**19. A and B enter into a partnership and invest Rs. 1,20,000 and Rs. 2,00,000 respectively. At the end of two years, they make a profit of Rs. 64,000. What is A’s share in the profit?***1) Rs. 24,000*

*2) Rs. 25,000*

*3) Rs. 40,000*

*4) Rs. 32,000*

*Ans 19. Rs 24000*

**20. A, B and C enter into a partership. A initially invests Rs. 25 lakhs and adds another Rs. 10 lakhs after one year. B initially invests Rs. 35 lakhs and withdraws Rs. 10 lakhs after two years and C invests Rs. 30 lakhs. In what ratio should the profits be divided at the end of three years?***1) 20:19:18*

*2) 19:19:18*

*3) 20:20:19*

*4) Data inadequate*

*Ans 20. A : B : C = (2500000 x 1) + (3500000 x 2) : (3500000 x 2 + 2500000 x 1) : (3000000 x 3)*

*= 9500000: 9500000 : 9000000*

*= 19 : 19 : 18.*

**21. A and B entered into a partnership investing Rs. 16,000 and Rs. 12,000 respetively. After 3 months A withdrew Rs. 5,000 while B invested Rs. 5,000 more. After three months C joins the business with a capital of Rs. 21,000. The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by***1) Rs. 1,200*

*2) Rs. 2,400*

*3) Rs. 3,600*

*4) Rs. 4,800*

*Ans 21.*

*A : B : C = (16000 x 3 + 11000 x 9 : 12000 x 3 + 17000 x 9 : 21000 x 6) = 147:189:126 = 7:9:6*

*Difference of B and C’s shares = Rs. [26400 x (9/22) – 26400 x (6/22)) = Rs. 3600*

**22. Madhu and Sunu entered into a partnership by investing Rs. 12,000 and Rs. 9,000 respectively. After 3 months Sony joined them with an investment of Rs. 15,000. What is the share of Sony in a half yearly profit of Rs. 9,500?***1) Rs. 3,500*

*2) Rs. 3,000*

*3) Rs. 2,500*

*4) Rs. 4,000*

*Ans 22. Half yearly = 6 months*

*Hence Madhu : Sunu : Sony = (12000 x 6 : 9000 x 6 : 15000 x 3) = 8 : 6 : 5 = 19*

*Sony = 9500 x 5/19 = Rs 2500*

*Practice Sets on Partnership*

*Radhika started a workshop with an investment of Rs.40,000. She invested additional amount of Rs.10,000 every year. After two years her sister Rama joined her with an amount of Rs.85,000.Therefore,Rama did not invest any additional amount. On completion of 4 years from the opening of workshop they earned an amount of Rs.1,95,000. What will be Radhika’s share in the earning ?**A) Rs.2,20,000**B) Rs.1,10,000**C) Rs.2,45,000**D) Rs.3,35,120**E) Rs.1,01,5000**P ,Q and R are partners in a business .P whose money has been used for 4 months , claims (1/8) of the profit , Q whose money has been used for 6 months ,claims at (1/3) of the profit . R had invested Rs. 1560 for 8 months .How much did P and Q contribute ?**A) Rs.720, Rs.1280**B) Rs.650, Rs.1100**C) Rs.758, Rs.1500**D) Rs.800, Rs.1720**E) Rs.870, Rs.1750**There are two persons invests Rs.1,15,000 and Rs.1,00,000 resp. in a project and agree that 50% of the profit should be divided equally between them and the remaining is to be treated as interest on the capital. If first person get Rs.500 more than the second persom .What is the total profit made in the business ?**A) Rs.1780.22**B) Rs.15445.12**C) Rs.21245**D) Rs.14333.33**E) Rs.14758.41**Ramesh, Suresh and Mahesh started a business with the investment in the ratio 5:8:10 resp. After 1 year Mahesh withdraw 50% of his capital and Ramesh increased his capital by 80% of his investment . After 2 years in what ratio should the earned profit be distributed among Ramesh ,Suresh and Mahesh?**A) 15:10:17**B) 14:16:15**C) 11:15:19**D) 8:13:7**E) 10:15:14**Prabhu initiated his business with (1/2) of the total capital for (1/4)th of the time . His brother Sunny invests (1/3) of the capital for (1/2)th of the time and Prabhu’s friend Tarun invests the remaining capital for the whole time. Find the share of Tarun in the total profit of Rs. 1,21,000.**A) Rs.20,000**B) Rs.24,500**C) Rs.50,000**D) Rs.33,420**E) Rs.44,000**A ,B and C sharing profits in the ratio 3:2:2 . B retired from the company and A and C decide to share profits in the ratio 3:2.What is the gaining ratio?**A) 5:3**B) 4:5**C) 3:2**D) 2:1**E) 3:5**Rs.61,105 ,is divided between Ram and Raman in the ratio 3 : 8 .What is the difference between thrice the share of Ram and twice the share of Raman?**A) Rs.52,500**B) Rs.42,000**C) Rs.35,720**D) Rs.38,885**E) Rs.47,200**Mr. X started a business investing Rs.25,000 in 1996.In 1997 he invested an additional amount of Rs. 10,000 and Mr. Y joined him with an amount of Rs.35,000.In 1998 , Mr.X invested another additional amount of Rs.10,000 and Mr. Z joined them with an amount of Rs. 35,000 .Find the share of Mr. Y in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1996?**A) Rs.50,000**B) Rs.80,000**C) Rs.70,000**D) Rs.40,000**E) Rs.60,000**A starts a business with an initial investment of Rs. 30,000. After 6 months , B enters into the partnership with an investment of Rs. 20,000.Again after 3 months C enters with an investment of Rs.50,000.If C receives Rs. 2000 in the profit at the end of the year ,what is the total annual profit?**A) Rs.7000**B) Rs. 8400**C) Rs.8000**D) Rs.9000**E) RS.8500**Riya started a project by investing Rs. 60,000. 6 months later her sister Riama joins her by investing Rs. 1,00,000.At the end of 1 year from the commencement of the business ,they earn a profit of Rs.27,038.Find Riama’s share in the profit?**A) Rs.14,150**B) Rs.13,100**C) Rs.13,560**D) Rs.12,290**E) Rs.12,510*

*Kartik, Bhuvan and Sid entered into a partnership and invested Rs 13,000, Rs 16,000 and Rs 19,000 respectively. After 7 months, Kartik and Bhuvan added Rs 1,000 and Rs 5,000 respectively while Sid withdrew Rs 5,000. If at the end of year their annual profit is Rs 43,160, find the total profit share of Kartik and Sid.**A) Rs 28,030**B) Rs 27,190**C) Rs 26,830**D) Rs 28,420**E) Rs 27,040**Megha, Isha and Rani entered into a partnership by investing Rs 20,000, Rs X, and Rs 22,000 respectively for 6 months, 8 months and 10 months respectively. If Isha earns a profit of Rs 16500 out of a total profit of Rs 44,550, find the total investment done by all three.**A) Rs 47,000**B) Rs 25,000**C) Rs 54,000**D) Rs 39,000**E) Rs 67,000**Kamya, Prisha and Tisha started a business by investing Rs X, Rs (X+400) and Rs (X-200). If after the end of year, total share of profit of Kamya and Tisha is Rs 8100 out of a total profit of Rs 13,500, find the profit share of Prisha.**A) Rs 6100**B) Rs 5400**C) Rs 5100**D) Rs 6600**E) Rs 5500**Preeti, Anu and Aarti entered into a business. Preeti invested Rs 2500 for some months, Anu invested Rs 3000 for 2 more months than Preeti and Aarti invested Rs 3500 for 3 months less than Anu. If Anu got Rs 8400, out of a total profit of Rs 19,000, then Aarti invested her money for how many months?**A) 3 months**B) 5 months**C) 4 months**D) 6 months**E) 2 months*

**Directions (5-7):** A, B and C started a business by investing Rs 800, Rs 1600 and Rs 2000 respectively. After a quarter they invested amounts in a ratio 1 : 4 : 2. After another quarter, they invested amounts in ratio 3 : 2 : 3.In the last quarter the ratio of investments was same as in 2^{nd} quarter. Also in the last quarter, the respective amounts of A, B and C was double than the respective amounts invested in 2^{nd} quarter. The total investment of C before 4^{th} quarter was Rs 1400 more than that of A during same duration. Also ratio of B’s share in profit to total profit at the end of year was 66 : 153.

*Find the total investment of A, B and C.**A) Rs 10,200**B) Rs 11,300**C) Rs 9,800**D) Rs 10,080**E) Rs 11,090**If they respectively had invested same amounts in each quarter after quarter 1 which is equal to their respective investments in quarter 1, then what would be the profit of A at the end of year out of a total profit of Rs 19,350?**A) Rs 2510**B) Rs 3320**C) Rs 2560**D) Rs 3150**E) None of these**If the respective investments in third quarter was changed and this was in ratio 2 : 4 : 1 (other investments being the same), then what would be the total investment of all three in third quarter, if the average investment of all A B and C was Rs 3100 for whole year?**A) Rs 700**B) Rs 800**C) Rs 500**D) Rs 900**E) None of these*

**Directions (8-10):** A, B and C started a business. They invested amounts in the ratio 1 : 3 : 2 respectively for 8 months. After this they invested amounts in ratio 2 : 3 : 4 respectively for 4 months. The average investment of A and B is Rs 2800 while average investment of B and C is Rs 3800.

*Find the total investment of C?**A) Rs 4000**B) Rs 5000**C) Rs 6000**D) Rs 4500**E) Rs 3500**If B’s investment for both the terms (4 months and 8 months) was swapped, then find the total profit share of B and C if annual profit is Rs 46,200.**A) Rs 45,600**B) Rs 32,800**C) Rs 43,600**D) Rs 37,800**E) None of these**If A’s share in annual profit is Rs 9030, find the total profit after a year.**A) Rs 41,390**B) Rs 45,150**C) Rs 42,610**D) Rs 46,240**E) Rs 43,170*

*A and B enter into a partnership with capitals in the ratio 7:8 and at the end of 8 months A withdraws. If they receive profits in the ratio of 7:11 find how long B’s capital was used?**A) 8 months**B) 9 months**C) 11 months**D) 12 months**E) None of these**A began a business with Rs 12,000 and was joined afterwards by B with Rs 8,000. After how many months did B join if the profits at the end of the year were divided in the ratio 3:1?**A) 5 months**B) 6 months**C) 7 months**D) 8 months**E) None of these**Two partners invest Rs 120000 and Rs 84000 in a business and agree that 70% of the profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one person gets Rs 900 more than the other then find the total profit made in the business.**A) Rs 17,000**B) Rs 20,000**C) Rs 5,100**D) Rs 18,000**E) None of these**A,B and C enter into a partnership with Rs 4000, Rs 6000 and Rs 8000 respectively. After 4 months A withdrew 25% and after 6 months B add 16(2/3)% and after 8 months C withdrew 25% , find the profit earned by A if they get a total profit of Rs 7500 after 1 year.**A) Rs 1000**B) Rs 2000**C) Rs 3000**D) Rs 4000**E) None of these**A starts a business with Rs 25000. After few months B join him with Rs 20000. If the ratio of their profit after 1 year is 15:8 find after how many months B joined A?**A) 2 months**B) 6 months**C) 4 months**D) 8 months**E) None of these**A invests with B some rupees and B invested Rs 25,000. After 4 months A increase his investment with Rs 6000. If at the end of the year A and B have a profit of Rs 2400 and Rs 2500 respectively, find the sum invested by A.**A) Rs 15000**B) Rs 30000**C) Rs 25000**D) Rs 20000**E) None of these**Ram and Shyam invested Rs 5000 and Rs 7000 respectively. If Ram increases Rs 1000 after every 4 months find the ratio of their profit after 1 year.**A) 7 : 6**B) 6 : 7**C) 5 : 6**D) 6 : 5**E) None of these**In a partnership A invest 1/6 of the capital for 1/6 of the time. B invest 1/3 capital for 1/3 time and C invest the remaining capital for whole time. If at the end of the year the profit earned is Rs 23000, Then what will be the share of B?**A) Rs 4000**B) Rs 5000**C) Rs 6000**D) Rs 4500**E) None of these**Sumit and Anu invested money in the ratio of 8:12, find for how much time anu invested the money if Sumit invested money for 9 months and he got Rs 1000 from a total profit of Rs 3000?**A) 9 months**B) 10 months**C) 11 months**D) 12 months**E) None of these**A and B invested Rs 1200 and Rs 1500 respectively in a business. After 8 months A withdrew his entire money and C joined them with Rs 2000. If after a year, a total of Rs 1780 is obtained as a profit, find the total share of B and C?**A) Rs 1300**B) Rs 1280**C) Rs 880**D) Rs 980**E) None of these*

*Antra and Manvi invested Rs 3780 and Rs 3960 in a business. After 3 months, Antra withdew Rs 420 and Manvi withdrew Rs 180. At the same time Chetna joined them by investing Rs 4620. After a year, they made a profit of Rs 35,850. Find Manvi’s share in the annual profit.**A) Rs 13,450**B) Rs 12,750**C) Rs 12,350**D) Rs 13,650**E) Rs 13,950**Shikha and Shreya invested in the ratio 7 : 8 in a business. They got an annual profit of Rs 34,450. If Shikha withdrew her entire money at the end of 9 years, then what is the difference between their shares of profit?**A) Rs 7570**B) Rs 6400**C) Rs 7560**D) Rs 7150**E) Rs 8180**Kashish and Sheena started a business by investing Rs 2600 and Rs 2400 respectively. After 7 months, they added Rs 600 and Rs 800 respectively. 33% of the total profit earned after a year is given in donation. If after giving donation, the difference between the shares of Kashish and Sheena is Rs 350, find the total profit earned after a year.**A) Rs 17,000**B) Rs 25,000**C) Rs 18,000**D) Rs 12,000**E) Rs 27,000**Karuna and Varuna invested Rs 2400 and Rs x in a business. After 3 months, Karuna added Rs 600 while Varuna withdrew Rs 300. After a year out of a total profit of Rs 36,920, Varuna received Rs 17,160. Find the amount invested by Varuna at the starting of business.**A) Rs 2700**B) Rs 1900**C) Rs 2100**D) Rs 2400**E) Rs 1600**Vijay and Ajay started a business by investing Rs 2000 and Rs 1500 respectively. 4 months after start, Vijay withdrew all his money and Amit joined Ajay by investing Rs 3000. After the end of year, the difference between the shares of Amit and Vijay together and Ajay is Rs 3423. What is the total profit after a year?**A) Rs 12375**B) Rs 13455**C) Rs 14265**D) Rs 14350**E) Rs 12225**Tiya and Piya invested Rs 1350 and Rs 1800 respectively in a business. After 9 months Piya withdrew her entire money and Riya and Siya joined the business by investing Rs 3000 and Rs 2700 respectively. If after a year, a total of Rs 13,750 is obtained as profit, find the total share of Piya and Riya together out of total profit.**A) Rs 6000**B) Rs 8000**C) Rs 7000**D) Rs 6500**E) Rs 7500**Veena, Meena and Teena started a business by investing Rs 7000, Rs 7500 and Rs 6500 respectively for 4 months. After 4 months Veena and Teena added same amount as before while Teena invested Rs 7000 for 8 months. If after this the profit earned was Rs 44,800, find the share of Teena.**A) Rs 15,380**B) Rs 14,440**C) Rs 13,520**D) Rs 14,350**E) Rs 13,380**Vanya and Tanya started a business by investing Rs 1750 and Rs 2100 respectively. 5 months later, Tanya withdrew her entire money and Sanya and Manya joined the business with investments of Rs 4000 and Rs 6500 respectively. If after a year difference in total shares of Sanya and Manya together and total shares of Vanya and Tanya together is Rs 6,720, find the total profit.**A) Rs 16,900**B) Rs 16,800**C) Rs 15,100**D) Rs 15,300**E) Rs 16,300**Sumit and Rumit started a business by investing Rs 7200 and Rs 6400 respectively. After 6 months, Sumit withdrew half and Rumit withdrew 1/4th of their respected money invested. If after a year, a total profit of Rs 19,800 is made, what is the share of Sumit?**A) Rs 8480**B) Rs 9490**C) Rs 9720**D) Rs 8150**E) Rs 9220**Rohit, Lohit and Mohit started a business by investing in the ratio 1/3 : 2/4 : 2/5. After 8 months Mohit withdrew 1/2 of his investment. If after 12 months from start of business Rohit and Lohit got a share of Rs 16,000 out of the total profit, then find the share of Mohit?**A) Rs 7200**B) Rs 5700**C) Rs 6500**D) Rs 6400**E) Rs 4700***Option D**

Solution:*Investments of Rohit : Lohit : Mohit = 1/3 : 1/2 : 2/5 = 10 : 15 : 12**After 8 months Mohit withdrew 1/2 , so 1/2 * 12 = 6, so invested = 12-6 = 6 for another 4 months**So now ratio of shares of Rohit : Lohit : Mohit is**10 * 12 : 15 * 12 : 12 * 8 + 6 * 4**2 : 3 : 2**Let x is total profit. So (2+3)/(2+3+2) * x = 16000**x = 22400**So share of Mohit = 2/7 * 22400 = Rs 6400*

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