- 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

# 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 | 2.1lakh | 12 | 2.1 x 12 |

## Step 2: Find Ratio of Actual investment

Actual Investment Ratio of Jethalal : Sodhi

= (2.7 x 12) / (2.1 x 12)

=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 9/16^{th} 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

Therefore Sodhi’s share in profit = 7/16^{th} 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 | 2.1lakh | 9 | =2.1 x 9 |

## 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)

=12/19^{th} 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

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)

=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)

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