- Case 1: Two partners join @same time
- Case 2: Two Partners join @Different Time
- Case 3: Three partners join @same time
- Case 4: All In One
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.
Make a table
|Name||Initial Investment||Months||Actual Investment=Initial x months|
|Jethalal||2.7lakh||12||2.7 x 12|
|Sodhi||2.1lakh||12||2.1 x 12|
Actual Investment Ratio of Jethalal : Sodhi
= (2.7 x 12) / (2.1 x 12)
Therefore, whatever profit is made, they must share it in the ratio of their investment =9:7
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
Corporally to that, Sodhi’s share in profit
= Total profit Minus Jetha’s share in profit
Alternatively:Sodhi’s share in profit
Therefore Sodhi’s share in profit = 7/16th of Total profit
=(7/16) x 80000
Time to complicate the case.
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?
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
|Name||Initial Investment||Months||Actual Investment|
|Jethalal||2.7lakh||12||=2.7 x 12|
|Sodhi||2.1lakh||9||=2.1 x 9|
Actual Investment Ratio of Jetha:Sodhi
= (2.7 x 12) / (2.1 x 9)
Profit share of (Jetha:Total)
=12/19th part of total
Given: they made profit of Rs.95000
Jethalal’s share in profit
=(12/19) x 95000
And Sodhi’s share in profit
= 95000 minus 60000
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.
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
Jetha : Sodhi : Mehta
= 2.7 : 2.1 : 1.5
If you multiply each with 10
If you divide each number with 3
= 5 / (9+7+5)
=(5/21) x 1,05,000
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)
Mehta’s share in total profit
=(1.5/6.3) x 105000
Now let’s try a complicated problem that uses all of above cases.
|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.
|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|
As you ca see in the last column of ^that table.
Jetha : Sodhi : Mehta =36:18:M
=M / (36+18+M)
=M/(54+M)th part of Total profit (Rs.28,000)
But it is given: Mehta was paid Rs. 1000 out of total profit.
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)
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