Importance of Geometry in various exams
Partnership is a topic that is less frequently seen in MBA exams. Hence, it is of less importance than other topics. Although, partnership is studied because MBA aspirants should have the diagnostic skill to understand how to manage a shared business and to answer the basic what, why, and how’s of running/investing in a business. There are two types of Partnership concepts that MBA exams cover which are: – Simple and Compound partnerships.
Below, the frequency of questions on partnership that appeared in previous MBA exams is given:
The list of concepts that are covered in Partnerships is as follows: –
Rule: – If two investors A and B invest amount Rs. P and Rs Q respectively, the profit/loss generated at that time will be:
A’s (profit/loss):B’s (profit/loss) = P:Q
Rule: – Let C denote the capital invested and T denote the time the capital is being invested. Then Profit P is being shared in the following proportion:
P1:P2 = C1 x T1: C2 x T2
where, (C1, T1) is for the first investor, and (C2, T2) is for the second investor
Some of the sample questions on partnerships that can be useful for preparation are: –
1. Peter started a business with 20, 000. John joined him 4 months later with 30, 000. After 2 months Peter withdrew 5,000 of his capital and 2 more months later, John brought in 20, 000 more. At the end of the year what should be the ratio in which they should share the profits?
Here, even for each individual, the capital was not the same for the entire period his money was in the business. So, the term of the ratio for a person will be the sum of products of investment multiplied by time period for different parts of the year.
Peter has 20, 000 for 6 months, and then since he withdrew 5,000, he had only 15, 000 for the rest of the 6 months. His term of the ratio will be
(20, 000 * 6) + ( 15, 000 * 6) = 2,10,000
John joined with 30,000 which remained unchanged for 4 months and then he brought in 20, 000 more. So he had 50, 000 for 4 months only as he joined 4 months after the business began. His term of the ratio will be
(30, 000 * 4) + (50, 000 * 4) = 3, 20, 000
Hence, the ratio of shares of the profit will be 2,10, 000 : 3, 20, 000 = 21: 32.
2. Ram, Krishna, and Arjun start a business with 30K, 40K, and 50K respectively. Ram stays for the entire year. Krishna leaves the business after two months but rejoins after another 4 months but only with 3/4th of his initial capital. Arjun leaves after 3 months and rejoins after another 5 months but with only 4/5 of his capital. If the year-end profit is 27,900, how much more than Krishna did Arjun get?
The ratio of the investments of Ram, Krishna, and Arjun is:
(30,000*12): (40,000*2+3/4 *40,000 *6): (50,000*3+ 4/5*50,000*4)
⇒ (360,000) : (2,60,000) : (3,10,000)
Let’s Ram’s share is 36x, Arjun’s share is 31x and Krishna’s share is 26x, then the difference is 31x -26x = 5x.
Hence the amount, Arjun get more than Krishna is: 5x/93x * 27, 900 = 1500
3. A started a business with 40, 000. After 2 months B joined him with 60, 000. C joined them after some more time with 1, 20,000. At the end of the year, out of a total profit of 3, 75, 000, C gets 1,50, 000 as his share. How many months after B joined the business did C join?
The ratio of the shares of profits is : (40, 000 *12) : (60, 000 * 10) : (1,20, 000 * T), where T is the number of months that C was with the business
= 24: 30 : 6T = 4: 5: T
Hence, C share = T/ (T+9)
This is equivalent to 1,50, 000 out of 3,75,000
⇒ T/ (T+9) = 0.4
⇒ T= 6
So, C was with the business for 6 months. Hence C joined the business 4 months after, B
joined the business.
4. A, B, C starts a partnership. The capital of A, B, C are in the ratio of 10:9:6, and the time period of A: B is in the ratio of 2:3. B gets 10, 800 shares out of a total profit of 26, 000. If A’s capital was in the business for 8 months, for how many months was C’s capital there?
Given, A was in the business for 8 months, therefore, B must be in the business for 12
months. As A:B = 2:3
Let the months for C’s capital presence is x.
⇒ 80:108: 6x
B’s share in profit = 108/(188+6x )* 26,000
This is equivalent to 10,800
108/(188+6x )* 26,000= 10,800
5. X and Y invest 21,000 and 17,500 respectively in a business and at the year they make a profit of 26,400. Find their individual shares in the profit.
Since, both their investments are there in the business for the same duration (1 year), profits will be shared in the ratio of their investments i.e. 21,000: 17,500 = 6: 5.
∴ X share = 6/11 * 26,400= 14, 400
Y share= 5/11 * 26,400= 12,000
Students need to look into problems that use multiple concepts to find a solution. Try to answer questions from the advanced level of previous CAT papers, mock tests, and materials. And try to attempt these questions in a time-based manner. Taking too much time for advanced questions will be disadvantageous in cracking the exam. Finally, students need to practice as many questions as they can to get a hold of the concepts and find solutions fast. Practice will always help the student to crack the exam