Partnership problems shortcuts play a major role in quantitative aptitude test. It is bit difficult to score marks in competitive exams without knowing the shortcuts related to partnership problems. We might have already learned this topic in school.Even though we have been already taught this topic in our higher classes in school, we need to learn some more short cuts which are being used to solve the problems in the above topic.

The only thing we have to do is, we need to apply the appropriate short cut and solve the problems in a limited time. This limited time will be one minute or less than one minute in most of the competitive exams.

Partnership : When a business is run by two or more persons, it is known as partnership and the people who are running the business are called partners.We have the following four cases in partnership |

Case1: If all the partners invest equal amount for same time period then the profit is divided equally among them. |

Case2: If all the partners invest equal amount for different time period,then the profit is divided among them in the ratio of time period. |

Case3: If all the partners invest different amount for same time period,then the profit is divided among them in the ratio of amount invested. |

case4: If all the partners invest different amount for different time period, then the profit is divided among them in the ratio of the product of investment and time period for each partner. |

Students who are preparing to improve their aptitude skills and those who are preparing for this type of competitive test must prepare this topic in order to have better score. Because, today it is bit difficult to score marks in competitive exams without knowing shortcuts related to partnership problems. Whether a person is going to write placement exam to get placed or a student is going to write a competitive exam in order to get admission in university, they must be knowing partnership problems shortcuts. This is the reason for why people must study this topic.

As we mentioned in the above paragraph, a person who wants to get placed in a company and a students who wants to get admission in university for higher studies must write competitive exams like placement test and entrance exam. To meet the above requirement, it is very important to score more marks in the above mentioned competitive exams. To score more marks, they have to prepare this topic. Preparing this topic would definitely improve their marks in the above exams. Preparing this topic is not difficult task. We are just going to remember the stuff that we have already learned in our lower classes

Students will learn, how and when they have to apply shortcuts to solve the problems which are related to partnership. Apart from the regular shortcuts, students can learn some additional tricks in this topic partnership problems shortcuts. Already we are much clear with the four basic operations which we often use in math. They are addition, subtraction, multiplication and division. Even though we are much clear with these four basic operations, we have to be knowing some more stuff to solve the problems which are being asked from the topic in partnership in competitive exams. The stuff which I have mentioned above is nothing but the tricks and shortcuts which need to solve the problems in a very short time.

Short cut is nothing but the easiest way to solve problems related to time and distance. In competitive exams, we will have very limited time to solve each problem. Then only we will be able to attend all the questions. If we do problems in competitive exams in perfect manner with all the steps, it will definitely take much time and we may not able to attend the other questions. So we need some other way in which the problems can be solved in a very short time. The way we need to solve the problem quickly is called as shortcut.

**Here,
we are going to have some problems such that how partnership problems
shortcuts can be used. You can check your answer online and see step by
step solution.**

1. A, B and C start a partnership.The capitals of A, B and C are in the ratio 10:9:6 and the time period of A and B is in the ratio 2:3. B gets $10,800 as his share out the of a total profit of $26,000. If A's capital was there is in the business for 8 months, for how many months was C's capital in the business?

Ratio of capitals A:B:C = 10:9:6

Ratio of time period A:B:C = 2:3:x

Ratio of profit share A:B:C = 20:27:6x (as per case4)

From the above ratio, we have

B's share = 27k ===> 27k = 10800 ===> k = 400

A's share = 20X400 = 8000

C's share = (6x)X400 = 2400x

Total Profit = 26000

8000+10800+2400x = 26000 ===> 2400x = 7200 ===> x = 3

Ratio of time period A:B:C = 2:3:3

A's time period = 2k

2k = 8 months ===> k = 4

C's time period = 3k = 3X4 = 12 months

Hence, C's capital was in the business for 12 months.

Ratio of time period A:B:C = 2:3:x

Ratio of profit share A:B:C = 20:27:6x (as per case4)

From the above ratio, we have

B's share = 27k ===> 27k = 10800 ===> k = 400

A's share = 20X400 = 8000

C's share = (6x)X400 = 2400x

Total Profit = 26000

8000+10800+2400x = 26000 ===> 2400x = 7200 ===> x = 3

Ratio of time period A:B:C = 2:3:3

A's time period = 2k

2k = 8 months ===> k = 4

C's time period = 3k = 3X4 = 12 months

Hence, C's capital was in the business for 12 months.

2. A and B start a partnership by investing $24,000 and $36,000 respectively. Their agreement is to share half of the total profit equally and then share the remaining half in the ratio of their capital. If they share the entire profit in the ratio of their capitals, B would have got $2500 more than what she would have got otherwise. What is the total profit?

Ratio of capitals A:B = 2:3

Let the total profit be "x"

Half of the total profit = x/2. If it is divided equally between A and B, A will get (x/4) and B will get (x/4)

When the profit is shared as per the agreement,

profit share of B = (x/4) + (3/5)X(x/2) = 11x/20 ----(1)

If the profit is shared in the ratio of capitals,

profit share of B = 3x/5 ----(2)

In (2), B would get $2500 more than what she gets in (1)

Therefore, (3x/5) - (11x/20) = 2500

(12x-11x)/20 = 2500

x = 50,000

Hence, the total profit is $50,000

Let the total profit be "x"

Half of the total profit = x/2. If it is divided equally between A and B, A will get (x/4) and B will get (x/4)

When the profit is shared as per the agreement,

profit share of B = (x/4) + (3/5)X(x/2) = 11x/20 ----(1)

If the profit is shared in the ratio of capitals,

profit share of B = 3x/5 ----(2)

In (2), B would get $2500 more than what she gets in (1)

Therefore, (3x/5) - (11x/20) = 2500

(12x-11x)/20 = 2500

x = 50,000

Hence, the total profit is $50,000

3. A invested 125% as much money as B, C invested 80% as much money as B. The total of all the three is $61,000. How much did C invest?

Since both A and C are compared to B, let "x" be the investment of B

From the given information, we have

Investment of A = 125% of x = 1.25x

Investment of C = 80% of x = 0.85x

Total of all the three = 61,000

1.25x + x + 0.8x = 61,000

3.05x = 61,000

x = 61000/3.05

x = 20000

Investment of C = 80% 20000 = 0.8X20000 = 16000

Hence, C invested $16000

From the given information, we have

Investment of A = 125% of x = 1.25x

Investment of C = 80% of x = 0.85x

Total of all the three = 61,000

1.25x + x + 0.8x = 61,000

3.05x = 61,000

x = 61000/3.05

x = 20000

Investment of C = 80% 20000 = 0.8X20000 = 16000

Hence, C invested $16000

4. A , B and C entered in to a partnership by investing $ 12,000, $ 15,000 and $ 18,000 respectively. A is also a working partner and getting 15% of the annual profit for his work. If B and C got $ 8,500 and $ 10,200 respectively from the annual profit as their shares, what amount did A get from the annual profit?

Ratio of capitals, A:B:C = 12000:15000:18000
= 4:5:6

In the total profit, 15% is paid to A for his work.

Remaining 85% of the total profit will be shared among A, B and C in the ratio of capitals (4:5:6)

In the remaining 85% of the total profit,

B's share = 5k = 8500 ===> k = 1700

A's share = 4k = 4X1700 = 6800

C's share = 10200

If "x" be the total profit, we have

85% of x = 6800 + 8500 + 10200

85% of x = 25500

15% of x = (25500X15)/85 = 4500

Amount received by A = 6800 + 4500 = 11300

Hence,the total amount A got from the annual profit is $11,300

In the total profit, 15% is paid to A for his work.

Remaining 85% of the total profit will be shared among A, B and C in the ratio of capitals (4:5:6)

In the remaining 85% of the total profit,

B's share = 5k = 8500 ===> k = 1700

A's share = 4k = 4X1700 = 6800

C's share = 10200

If "x" be the total profit, we have

85% of x = 6800 + 8500 + 10200

85% of x = 25500

15% of x = (25500X15)/85 = 4500

Amount received by A = 6800 + 4500 = 11300

Hence,the total amount A got from the annual profit is $11,300

5. Daniel started a business with a capital of $ 8000. After six months, David joined him with investment of some capital. If at the end of the year, each of them gets equal amount as profit, how much did David invest?

Let "x" be the investment of David

David's investment was in the business for six months.

Daniel invested $ 8000 and his investment was in the business for 12 months.

Then the profit sharing ratio must be 6x : 12X8000

Since both of them get equal profit at the end of the year, the terms of the above ratio must equal.

Therefore 6x = 12X8000 ===> x = 16000

Hence, David's invested $16,000

David's investment was in the business for six months.

Daniel invested $ 8000 and his investment was in the business for 12 months.

Then the profit sharing ratio must be 6x : 12X8000

Since both of them get equal profit at the end of the year, the terms of the above ratio must equal.

Therefore 6x = 12X8000 ===> x = 16000

Hence, David's invested $16,000

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