Aptitude - Partnership - Discussion

7. 

A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew of his capital and B withdrew of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:

[A]. Rs. 330
[B]. Rs. 360
[C]. Rs. 380
[D]. Rs. 430

Answer: Option A

Explanation:

A : B = 4x x 3 + 4x - 1 x 4x x 7 : 5x x 3 + 5x - 1 x 5x x 7
4 5

   = (12x + 21x) : (15x + 28x)

   = 33x :43x

   = 33 : 43.

A's share = Rs. 760 x 33 = Rs. 330.
76


Deepu said: (Jan 7, 2011)  
How the ratio of A:B is brought out please can anybody explain ?

N.Srikanth said: (May 29, 2011)  
A invests for 3 months N = 4x * 3
1/4th of capital(4x)= 4x-1/4(4x) this is for (10-3) months investment
i.e Let M=(4x-(1/4)4x)*7
B investment for 3 months O =5x*3
1/5th of capital(5x)= 5x-1/5(5x) this is for (10-3) months investment
i.e P=(5x-(1/5)5x)*7
Ratio: (N+M):(O+P)

I think this will clear your doubt

Snp said: (Aug 2, 2011)  
Atlast why we have to divide by 76 ?

Umesh said: (Aug 8, 2011)  
A:B RATIO 4X : 5X.

FOR THREE MONTHS A's SHARE = 4X*3 = 12X.

FOR THREE MONTHS B's SHARE = 5X*3 = 15X.

FOR NEXT 7 MONTHS NEW RATIO = (4X-1/4*X) : (5X-1/5*X) I. E 3X:4X.

FOR 7 MONTHS A's SHARE = 3X*7 = 21X.

FOR 7 MONTHS B's SHARE = 4X*7 = 28X.

A's TOTAL SHARE =12+21 = 33X & B's = 15 +28 =43X.

TOTAL MONEY = 760
TOTAL SHARE = 33+43 =76X.

THEREFORE 76X =760 (i.e.)X= 10 (i.e.) A'S SHARE=33X =330.

Rohit Singh said: (Nov 2, 2011)  
This is called a real brain teaser.

Prashant said: (Apr 12, 2012)  
How to Solve (4X-1/4*X) : (5X-1/5*X) i.e 3X:4X.

Arockiaraj said: (Aug 31, 2012)  
How to Solve (4X-1/4*X) : (5X-1/5*X) i.e 3X:4X

Sindhuja said: (Sep 30, 2012)  
Is there any other is way to solve this sum?

Pavithran said: (Aug 18, 2013)  
Its not (4x-1/4*x) guys. Its (4x-1/4*4x).

Darshan said: (Nov 23, 2013)  
Withdrew means reducing the capital right?

Bala said: (May 26, 2014)  
Why did you take both the capital of A and B as x (instead of x and y) ?

In the question it was not mentioned that both the capitals are same know?

Nani said: (Aug 7, 2014)  
They did not take the capital as x.

The numbers were assumed to be 4x and 5x because their ratios were 4:5.

Sindhu said: (Aug 22, 2014)  
For that (4x-1/4*x):(5x-1/5*5).

We are applying like this,

Assume a=4x, b=x/4, c=5, d=x/5.
b*c/a*d.

If we apply like this we can easily get 3x:4x.

Roshni said: (Oct 2, 2014)  
Ratio = 4:5.
1/4*(4) = 1.
4-1 = 3.
Therefore 4*3 months + 3*7 months = 33.

1/5*(5) = 1.
5-1 = 4.
Therefore 5*3 months + 4*7 months = 43.
So, gain ratio is 33:43.

Total gain is 760/-
A's share is (33*760)/76 = 330.

Charmy said: (Feb 11, 2015)  
Why should we take 7?

Nupoor said: (Mar 11, 2015)  
Couldn't get any of the method? Please explain me with simple steps.

Sukumar Satyen said: (Jun 12, 2015)  
Following is Correct explanation:

Given that, Investment ratio of A and B = 4:5.

Let's assume that at 1st day, A's share = 4X and B's share = 5X.

Let's assume that Total investment period was for 10 months and after that business ceased to exist....equation (1).

Therefore, we will calculate A's total investment for 10 months.

= A's investment for 3 months + A's investment for 7 months.

= 4X*3/10+(4X-4X/4)*7/10.
= 12X/10+21X/10.
= 33X/10.

Using equation (1), we will calculate B's total investment for 10 months.

= B's investment for 3 months + B's investment for 7 months.

= 5X*3/10+(5X-5X/5)*7/10.
= 15X/10+28X/10.
= 43X/10.

PROFIT should be shared on basis of Total Investment for time period of 10 months, alike following ratio: -.

33X/10:43X/10.....equation (2).

Let's calculate A's Share.

= 33X/10/[(33X/10)+(43X/10)]*760.
= 33X/10/[76X/10)]*760.
= 33X*760/76X.

= Rs. 330.

Note:

First, We can also write equation (1) as 33:43 and solve for A's share.

Second, If A (or B) 's investment be one-time, then X will be larger. If A (or B) 's investment be recurring every month, then X will be smaller, until 3 months from execution of Partnership agreement.

Thanks.

Priya14 said: (Jul 9, 2015)  
Where does this 7 came? Explain me please.

Shubham said: (Aug 2, 2015)  
@Priya.

7 is came after subtracting 3 from 10 (months).

Jiten said: (Oct 7, 2015)  
How 1/4 will come? Please tell me anyone.

Praveen said: (Jul 7, 2016)  
4x*3+3x*7 : 5x*3+4x*7,

=> 12x+21x : 15x+28x,

=> 33x : 43x,

=> 33 : 43,

A's share = 33/76*760 = 330,

330 is the answer.

Gaurav said: (Jul 28, 2016)  
Thanks for the great explanations.

Banke Bihari said: (Aug 10, 2016)  
Thank you @N.Srikanth.

Karthik said: (Aug 18, 2016)  
The total number of ratio = 33 + 43 = 76.

Sourabh said: (Aug 30, 2016)  
@Karthik.

But there will be, upon 10 in all the numbers.

Ekta said: (Sep 26, 2016)  
How 7 came? not getting that please explain me.

Yogesh said: (Oct 26, 2016)  
Assume total capital is Rs. 900.
And divide into the ratio of 4 : 5.
After that A's capital = 400 and B's capital = 500.
Then after deducted 1/4 and 1/5 from the respective capital.
we get the ratio of 3 : 4.
And divide Rs. 760 in the ratio of 3 : 4 then you can get 330 (approx).

Ashiq said: (Feb 9, 2017)  
Here, it will be (4x-1/4*4x) : (5x-1/5*5x) = 3x : 4x.

Sumit said: (Mar 15, 2017)  
Why 4x is multiply with 1/4?

Nikhil Kulkarni said: (Apr 21, 2017)  
I didn't get it. Please help me to get the answer.

Sweety said: (May 1, 2017)  
Thanks for the given explanation.

Asha said: (Jul 31, 2017)  
After reducing the capital why we again multiply with 4x i.e (4x-1/4*4x).

Mary said: (Apr 2, 2018)  
Can anybody solve this?

2/5th of Anil salary is equal to Bhuvans salary and 7/9th of Bhuvans salary is equal to Chandra's salary. If the sum of the salary of all of them is 77000. Then how much is Bhuvans salary?

Saran said: (Jun 12, 2018)  
@Mary.

Anil's sal=x;
Bhuvan's sal=y;
Chandra's sal=z;

As given in the que 2/5x=y;
7/9y=z;
x+y+z=77000;
5/2y+y+7/9y=77000;

After taking the lcm
45y+y+14y=77000*18,
60y=1386000,
y=23100.

So, this is the answer.

Prasanthi Gudipati said: (Jul 22, 2018)  
Capitals=a:b=4:5.

let their investments as 4x,5x.
A:B=4x*10-(4x*(1/4)*7):5x*10-(5x*(1/5)*7),
= 40x-7x:50x-7x,
=33x:44x.

A's share= {33/(33+44)}*760=330.
So option A is correct answer.

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