Aptitude - Partnership - Discussion

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.

@All.

I'll tell the simplest answer which is;

1) the given ratio of capital is 4:5.
After 3 months they withdraw,
Mean 4:5 = 760 is invested for three months.
A3 : B3
So (4*3):(5*3)=760 --> eq(1).

After three months they withdraw 1:4 and 1:5.
The mean part of 1:4 of 4 is 1.
1/4*4=1.

And part of 1:5 of 5 is also 1.
1/5*5 = 1.

Now subtract the withdrawal capital from A and B which is 1:1
A=> 4-1 = 3.
B=> 5-1 = 4.

And add into the eq(1).
A3:(A-withdraw)*7 = 12+21
B3:(B-withdraw)*7 = 15+28.
33:43 = 760,
76x = 760,
x = 10.

Now A's share is;
33 * 10 = 330.

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.

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

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).

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.

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?

@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.

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.

@Mary.

Get the ratios of salaries of Anil, Bhuvans, and Chandras from the info you mentioned (45:18:14=77).
Given the total amount 77000/77*18=18000.
Hence B's salary is 18k.