Mrunal [Aptitude] Partnership and Profit-sharing Made Easy for CSAT IBPS CAT » Mrunal

Mrunal [Aptitude] Partnership and profit-sharing made Easy for CSAT IB...

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[Aptitude] Partnership and profit-sharing made Easy for CSAT IBPS CAT 1. Case 1: Two partners join @same time Step 1: Fill up the table Step 2: Find Ratio of Actual investment Step 3: Componendo on Total Profit 2. Case 2: Two Partners join @Different Time Step 1: Fill up table Step 2: Find Ratio of Actual investment Step 3: Apply Componendo on Total Profit 3. Case 3: Three partners join @same time Step 1: Fill up table Step 2: Ratio of Actual investment Step 3: Componendo 4. Case 4: All In One Step 1: Fill up the table Step 2: Ratio of actual investment Step 3: Componendo for Mehta’s share

Case 1: Two partners join @same time Jethalal Ghada and Roshansingh Sodhi decided to start an ice-cream parlor in partnership. Their individual investment is rupees 2,70,000 and 2,10,000 respectively. At the end of first year, they make profit of Rs.80,000. Find Jethalal’s share in this profit.

Step 1: Fill up the table Make a table Name

Initial Investment Months Actual Investment=Initial x months

Jethalal 2.7lakh

12

2.7 x 12

Sodhi

12

2.1 x 12

2.1lakh

Step 2: Find Ratio of Actual investment Actual Investment Ratio of Jethalal : Sodhi = (2.7 x 12) / (2.1 x 12)

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=9:7 Therefore, whatever profit is made, they must share it in the ratio of their investment =9:7

Step 3: Componendo on Total Profit See this image for calculation

This means, whatever “total” profit is made, Jethalal should get 9/16th part of that “total” profit. Given: they made profit of Rs.80,000 Hence Jethalal’s share in profit =(9/16) multiplied with 80,000 =Rs.45000 Corporally to that, Sodhi’s share in profit = Total profit Minus Jetha’s share in profit =80000-45000 =35000 Alternatively:Sodhi’s share in profit

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Therefore Sodhi’s share in profit = 7/16th of Total profit =(7/16) x 80000 =35000 Time to complicate the case.

Case 2: Two Partners join @Different Time Jethalal starts an Ice cream parlour with initial investment of Rs.2.7 lakhs. After 3 months, Sodhi joins him with investment of Rs.2.1 lakh. At the end of first year, they make profit of Rs.95,000. Find out Jethalal’s share in this profit? Answer: Jethalal starts the business and Sodhi Joins after 3 months. It means Sodhi stayed in the business 12 minus 3 =9 months. Fill up the table

Step 1: Fill up table Name

Initial Investment Months Actual Investment

Jethalal 2.7lakh

12

=2.7 x 12

Sodhi

9

=2.1 x 9

2.1lakh

Step 2: Find Ratio of Actual investment Actual Investment Ratio of Jetha:Sodhi = (2.7 x 12) / (2.1 x 9) =12/7

Step 3: Apply Componendo on Total Profit Profit share of (Jetha:Total) = 12/(12+7)

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=12/19th part of total Given: they made profit of Rs.95000 Jethalal’s share in profit =(12/19) x 95000 =Rs.60000 And Sodhi’s share in profit = 95000 minus 60000 =35,000

Case 3: Three partners join @same time Jethalal, Sodhi and Mehta start an ice cream parlor with initial investment of Rs. 2.1lakhs, 2.7lakhs and 1.5 lakhs respectively. At the end of one year, they make profit of Rs.1.05 lakhs. Find the Share of Mehta in this profit. The method remain the same.

Step 1: Fill up table Name

Initial Investment Months

Jethalal 2.7 lakh

12

Sodhi

2.1 lakh

12

Mehta

1.5 lakh

12

The “Months” column isn’t really important, unless the partners are joining at different time (as happened in case#2) Because x12 months will cut each other when we take ratio since they’re common for each partner. So we can simply ignore that column and concentrate on

Step 2: Ratio of Actual investment Jetha : Sodhi : Mehta = 2.7 : 2.1 : 1.5 If you multiply each with 10 =27:21:15 If you divide each number with 3 =9:7:5

Step 3: Componendo Mehta’s share = 5 / (9+7+5) =(5/21) x 1,05,000 =Rs.25000

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Alternative: without simplifying the ratio Since all partners joined @ same time, the months aren’t important. We can directly use the money invested by them. Mehta’s share ratio = 1.5 lakh / (1.5 lakh + 2.1 lakh + 2.7 lakh) =1.5/6.3 Mehta’s share in total profit =(1.5/6.3) x 105000 =Rs.25000 Now let’s try a complicated problem that uses all of above cases.

Case 4: All In One Jethalal starts an icecream parlour with initial investment of 3 lakhs. 3 months later Sodhi joins him with investment of Rs.2 lakhs and stays till the end. Later on Mehta also joins them and contributes Rs.1 lakh and stays till the end. After one year, they make total profit of Rs.28,000 and Mehta is given Rs.1000 out of this profit. Find out when did Mehta join the business? Jetha started the business. Sodhi joined 3 months after Jetha. Hence Sodhi stayed in business for 12 minus 3 = 9 months. Assume Mehta stayed in business for “m” months.

Step 1: Fill up the table Name

Initial Investment Months

Actual investment =Initial investment x Months

Jethalal 3 lakhs

12

3 x 12 =36

Sodhi

2 lakhs

9

2 x 9 =18

Mehta

1 lakh

M

1 x M=M

Step 2: Ratio of actual investment As you ca see in the last column of ^that table. Jetha : Sodhi : Mehta =36:18:M

Step 3: Componendo for Mehta’s share =M / (36+18+M)

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=M/(54+M)th part of Total profit (Rs.28,000) But it is given: Mehta was paid Rs. 1000 out of total profit.

28M=1M+54 28M-1M=54 27M=54 M=54/27 M=2 months. It means Mehta stayed in the business for 2 Months. It means he joined the gang 10 months after Jethalal had started the business (10+2=12months) To learn more such tricks about mathematics and aptitude, visit Mrunal.org/aptitude

URL to article: http://mrunal.org/2012/05/aptitude-partnership-and-profitsharing.html Posted By Mrunal On 03/05/2012 @ 14:54 In the category Aptitude

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