Aptitude - Partnership - Discussion

5. 

Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

[A]. 5 : 7 : 8
[B]. 20 : 49 : 64
[C]. 38 : 28 : 21
[D]. None of these

Answer: Option B

Explanation:

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.

Then, 14x : 8y : 7z = 5 : 7 : 8.

Now, 14x = 5       98x = 40y       y = 49 x
8y 7 20

And, 14x = 5       112x = 35z       z = 112 x = 16 x.
7z 8 35 5

x : y : z = x : 49 x : 16 x = 20 : 49 : 64.
20 5


Anju said: (Jul 2, 2011)  
Is there any easier solution for this sum?

Juhi said: (Jul 5, 2011)  
How it is possible that ratio of their investments are=ratio of their profits ?

Yogesh said: (Dec 25, 2011)  
How is 20 come can any body describe me?

Saravanan.O said: (Jan 6, 2012)  
I am not understand the answer could you please explain me?

Mahesh said: (Jan 16, 2012)  
Hello Yogesh ,LCM of x : 49x/20 : 16x/5 = 20: 49: 64

Mahesh said: (Jan 16, 2012)  
Hello saravanan ,
Formula
---------
(investment of A X duration in months) : (investment of B X duration in months) : (investment of C X duration in months) = A's Profit : B's Profit :C's Profit

Zishan said: (May 27, 2012)  
Here it use a formula. i.e explaning with example.
Suppose a invest Rs x for p months & b invest Rs why for q months. Then.
(a's share of profit) : (b's share of profit) = xp : yq.

Mohankumar said: (Oct 12, 2012)  
This is mohan,

Your answer is write there is no words i have, but your answer is more confusing and very difficult to understand this answer. can u explain me another way

Sruthi said: (Mar 18, 2013)  
We can take LCM in ratio ?

Franz said: (Jul 24, 2013)  
Yeah. We can do LCM.

Its just for compensating purpose only.

Swetha said: (Sep 14, 2013)  
Lets try this:

After equating the profits, we left with,

14x : 8y : 7z = 5 : 7 : 8.

=> x=5/14 , y=7/8, z=8/7.

take l.c.m of 14,8,7. we get 56.

x = 5/14*56 = 20.

y = 7/8*56 = 49.

z = 8/7*56 = 64.

So, investments x:y:z = 20:49:64.

B.Bhuvi said: (Oct 15, 2014)  
Calculation of LCM is best way to find the answer. It is used for compensating purpose.

Richard said: (Nov 15, 2014)  
How did you calculate LCM?

Simmo said: (Jan 14, 2015)  
Please give me easy trick to understand.

Muthumani said: (Apr 23, 2015)  
How do find 56?

Masterneeji said: (Jun 6, 2015)  
Before finding least common multiple, bring all terms to x.

Any partnership problem.

Month=m; Investment=i.

I'm 1: I'm 2 : I'm 3 = p1:p2:p3.

If any changes like 50% more add to.

Sukumar Satyen said: (Jun 10, 2015)  
This question says, "They had partnered for 14 months, 8 months and 7 months respectively".

The word "partnered" does not mean "invested". It is open to more than one interpretation. It is not having one obvious meaning.

Do you have same doubt?

Sukumar Satyen said: (Jun 13, 2015)  
Here, we have to assume that all partners had some investment, and therefore, their partnership existed.

When investments of all the partners are 'for the same time', the gain or loss or liability is distributed among the partners in the ratio of their investments.

Given that, max duration of investment is 14 months.

Therefore, A 's investment = X*14/14.
Therefore, B 's investment = Y*8/14.
Therefore, C 's investment = Z*7/14.

Let's find ratio of investments,

=> A : B : C = (X*14/14) : (Y*8/14) : (Z*7/14).
=> A : B : C = (X*14) : (Y*8) : (Z*7).
=> A : B : C = 14X : 8Y : 7Z.

=> Share of Profit at end of 14 months.

= 14X : 8Y : 7Z = 5 : 7 : 8.

Please refer to answer of this question for remaining explanation.

Thanks.

Vijay said: (Oct 20, 2015)  
Someone explain the last step for me.

Bala said: (Jan 2, 2016)  
Shortcut: Use option with formula.

Ammu said: (Jan 12, 2016)  
How did you get 5:7:8?

Suhana said: (Mar 7, 2016)  
How to find LCM?

Swagatika said: (Apr 21, 2016)  
Good explanation, Thanks @Swetha.

Jennifer said: (Apr 25, 2016)  
@Swetha.

Nice explanation. Thank you.

Mani Sankar said: (Jun 20, 2016)  
Profit = Investment * time.

P = I * T,

I = P / T,

x:y:z = 5/14 : 7/8 : 8/7,

=> 20:49:64.

Venkat said: (Aug 12, 2016)  
Can anyone expalin me this problem.

Koperunchelli said: (Aug 28, 2016)  
I am not getting this, Anyone explain clearly & shortly?

Poonam said: (Sep 20, 2016)  
Lets try this:

After equating the profits, we left with,

14x : 8y : 7z = 5 : 7 : 8.

=> x=5/14 , y=7/8, z=8/7.

take l.c.m of 14,8,7. we get 56.

x = 5/14*56 = 20.

y = 7/8*56 = 49.

z = 8/7*56 = 64.

So, investments x:y:z = 20:49:64.

Kishan said: (Sep 21, 2016)  
Thanks @Swetha.

Rajvanshi said: (Oct 12, 2016)  
Let initial A's, B's, C's investment is Rs x, y, z respectively.
Let the Profit is "P".

A : B : C = 14x : 8y : 7z (INVESTMENTS).

A's profit = P * 14x/(14x + 8y + 7z);
B's profit = P * 8y/(14x + 8y + 7z).

Now, A : B (Profit ratio is given) = 5/7.
Equating the both sides we get answers.

Rajesh said: (Oct 14, 2016)  
How 20:49:64 will come? Can anyone explain me clearly?

Monir said: (Oct 17, 2016)  
Your method is easy. Thanks @Poonam.

Ryan said: (Nov 20, 2016)  
@Pooonam.

Your method is easy to understand the solution, Thanks.

Sandy.J said: (Dec 20, 2016)  
From the soln 20:49:64.

20 is divided by 5, 49 divided by 7 and 64 is divided by 8.
From that, we get 5 : 7 : 8. Try this method, it is simple to solve.

Pavan said: (Feb 14, 2017)  
Apply the simple formula for this.

Profit(P) = capital investment (C) * time(T).
So,
C = P/T,
All the problems of partnership solved using this formula.

Saurabh Patil said: (Mar 4, 2017)  
Superb explanation, thank you all.

Swetha said: (Mar 7, 2017)  
Superb explanation @Poonam.

Thank you.

Swati said: (Jun 18, 2017)  
@Swetha & @Poonam thanks.

Aakash said: (Jul 19, 2017)  
Best explanation, Thanks @Poonam.

Mahesh said: (Aug 10, 2017)  
Hi @Swetha.

Nice.

But why 56 multiplied with those ratios?

Shraddha said: (Sep 6, 2017)  
Here we can use options.

Investment = 20x*14: 49x*8: 64x*7.
Investment ratio = profit ratio.
If we solve this ratio then we get 5:7:8 which is exactly equal to the given profit ratio.

Felix Ikpabi said: (Dec 10, 2017)  
First divide each profit ratio by its corresponding investment period for the particular partner, that is;

5/14, 7/8, 8/7.
Now take LCM of the denominators 14,8,7 which is 56 then,
Finally, divide this 56 by each denominator and multiply the answer obtained by the corresponding numerator and write the value separately, do this for the three fraction and see
{56/14*5}=20, {56/8*7}=49, and {56/7*8}=64.

Jothi said: (Jan 6, 2018)  
Really very useful. Thank you for the explanation.

Mir Rokon Uddin said: (Mar 10, 2018)  
According to me, the question is missing accurate information. They should have used what ratio of their monthly investment instead of their investment. The ratio of their total investment is same as the ratio of profit sharing (5:7:8).

Pardu said: (Apr 23, 2018)  
Thank you @Swetha.

Sharon Thomas said: (May 17, 2018)  
@Swetha.

Nice, Very well explained.

Sagar said: (Sep 27, 2018)  
5/14:7/8:8/7 take LCM of 14,8,7 is 56.

Multiply it 5/14 * 56 = 20.

Felix said: (Oct 1, 2018)  
There is a concept related to profit, investment and time, which is given by;

Profit = investment * time.
==>investment = profit/time.

Adik said: (Dec 24, 2018)  
Yes, agree @Sandy.J.

The Answer is 5 :7: 8.

Elumalai said: (Feb 14, 2019)  
In the income statement of Asha and Ravenna, the ratio of their income of the year 2017 was 5: 4. The ratio of Asha's income of the year 2018 to that of 2017 is 3: 5 and the ratio of Ravenna's income of the year 2018 to that of 2017 is 3: 2. If 10, 242 is the sum of the income of Asha and Ravenna in the year 2018, then find the income of Ravenna for the year 2017?

Can anyone solve this?

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