- 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)

To learn more such tricks about mathematics and aptitude, visit Mrunal.org/aptitude

## 28 Comments on “[Aptitude] Partnership and profit-sharing made Easy for CSAT IBPS CAT”

shud it not b m/ m+54?

even by componendo rule it shud b 54+2m/54

or here we r usin d fact that m is insignificant compared to 54…ie m<<<54…..plz elaborate

imn m/54 it shud b m/m+54…..even by componendo it shud b 54+2m/54…..or m<<<54 so ignored.plz elaborate

Yes it has to be M/M+54,

Typing mistake on my part. Thanks for notifying.

Hey mrunal..grt work…

here is a qus i came thru in ssc cgl T2

i didn’t understood the meaning of “PREMIUM” in d question…

A nd B started a bussiness with Rs20000 and Rs 35000 respectively.

dey agreed to share their profit in in d ratio of there capital..

C joins dem with d condition that A B and C willl share profit equally and pays Rs 220000 as a premium for this, to be shared between A and B.this is to be divided between A and B in the ratio of…????????

test form no -010 MN 2

Thank you

ishan its not the ratio of their capital but the ratio of LEAVING their profit..

and they leave in the ratio of 1:10

Hello,sir In the above question how the profit is shared equally?

This question is done using sacrificing ratio

(4/11-1/3):(7/11-1/3)

=1/33:10/33

=1:10

@ishan – here ration of A:B according to the investment is 20:35 ie. 4:7 and when C pays 22,0000 as premium it has to divided between A and B according to their share of capital invested. now total capital invested is 11 parts (4+7 as the ration is 4:7) out of these 11 parts A’s share is just 4 parts! hence 4/11*220000 = 80000 Rs will be the share of A and the remaining ie. 140000 will be the share of B. hope it clears your doubt.

@Naman ,but the answere is 1:10 and according to you its 4:7…

@ishan, sorry brohter.. after seeing the problem that was thought process i don’t know how the answer comes out to be 1:10…

@Ishan and Naman,

Will be like below

A and B’s total investment ratio is 20:35 means – 4:7 or we can say it will be 4/11 and 7/11 of the total profit.

Now condition given

1. C will give premium 2.2 Lac to A and B according to their share of capital invested

2. C willl share profit equally

hence as per the condition 2, if total profit is shared equally, in that case total profit deducted from A and B will be 1/3, 1/3.

hence it will be (4/11 – 1/3) : (7/11 – 1/3) = 1/33 : 10/33 = 1/10

So answer will be 1/10.

thank you

really u r great sir…….. just seated in my mind

Sir one of my ques is…

A and b started a business With rs 20000 and 35000 respectivly.they agree to share the Profit in the Ratip of capital. Now c joins the partnerhip with condition That A,b,c share Profit equally and paid 220000 as premium For This to be share bw A And B .this is to be fivide in a And B in the ratio of

A)9:10

B)10:9

C)1:10

D)10:1

Will be like below

A and B’s total investment ratio is 20:35 means – 4:7 or we can say it will be 4/11 and 7/11 of the total profit.

Now condition given

1. C will give premium 2.2 Lac to A and B according to their share of capital invested

2. C willl share profit equally

hence as per the condition 2, if total profit is shared equally, in that case total profit deducted from A and B will be 1/3, 1/3.

hence it will be (4/11 – 1/3) : (7/11 – 1/3) = 1/33 : 10/33 = 1/10

So answer will be 1/10.

Hi

in case-1 to find the share of 1st person and avoid multiple steps i prefer this m/d

they give share of 1st person is 2,70,000 and 2nd one is 2,10,000 by using ratio n prop.

2,70,000= 2,10,000 strike off zero’s now it is

27 = 21 i.e 9:7

at the end profit is 80000.

therefore 1st person share is 9*(80,000\16)= 45,000 (here 16 is total partner ratio wh have to add that i.e 9+7=16)

hence 2nd persons profit is 80000-45000=35000..

I just CNT get wats m|d yaar please xplain

i don,t understand this answer. please , explain this in other method.

hi dear its a great work you have done over here for SSC. one of friend has given information about such blog.

Kindly explain please

great work sir

SIR TAKE AN EXAPLE WHERE THE INVESTMENTS ARE IN THE RATIO

You’re awesome!

Case 4: All In One >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.

:- what’s the formula in this line? i can’t access the photo of any formula.

28M=1M+54

28M-1M=54

@Pratul Gupta

1000/28000 = M/M+18+36

=> 1/28 = M/M+54

=> M+54 = 28M

=> 54 =27M

hence => M=2

In a business Abhay invested rs600 more than pavan b’s capital remains invested for 7 1/2 months while abhay’s capital remains invested for 2months more.If the total profit is rs620,out of which Pavan get rs140 less than abhay,find the capital invested by each.

Pls solve.thank you

tried so many times but not able to open / see any images here and in all

other topics of quant . then how i will get to know the process? help me with this?