Let's break down the given information step by step:

1. P invested one-third of the capital for one-fourth of the time.
2. Q invested one-fourth of the capital for one-half of the time.
3. R invested the remainder of the capital for the entire year.
4. P is a working partner and receives a salary of `10,000 per month.
5. The profit after paying P's salary is directly proportional to the sum each one has put and also to the square of the number of months for which each has put their sum in the venture.
6. In a year, P earns `60,000 more than Q.

Let's assign variables to the unknowns:
Let P's investment be x, Q's investment be y, and R's investment be z.
Let P's time be t.

From the given information, we can form the following equations:

1. P = (1/3) * (x) * (1/4) * (t)
2. Q = (1/4) * (x) * (1/2) * (t)
3. R = (1 - (1/3) - (1/4)) * (x) * (t)

Now, let's calculate the profit for each partner after deducting P's salary:

Profit for P = (P - 10000) * (x) * (t)^2
Profit for Q = (Q) * (y) * (t)^2
Profit for R = (R) * (z) * (t)^2

Given that P earns `60,000 more than Q in a year, we can form the equation:

(P - 10000) * (x) * (t)^2 - (Q) * (y) * (t)^2 = 60000

Now, we need to solve these equations to find the values of x, y, and P.

Please note that the given text is in English.

Question

Let's break down the given information step by step:

1. P invested one-third of the capital for one-fourth of the time.
2. Q invested one-fourth of the capital for one-half of the time.
3. R invested the remainder of the capital for the entire year.
4. P is a working partner and receives a salary of `10,000 per month.
5. The profit after paying P's salary is directly proportional to the sum each one has put and also to the square of the number of months for which each has put their sum in the venture.
6. In a year, P earns `60,000 more than Q.

Let's assign variables to the unknowns:
Let P's investment be x, Q's investment be y, and R's investment be z.
Let P's time be t.

From the given information, we can form the following equations:

1. P = (1/3) * (x) * (1/4) * (t)
2. Q = (1/4) * (x) * (1/2) * (t)
3. R = (1 - (1/3) - (1/4)) * (x) * (t)

Now, let's calculate the profit for each partner after deducting P's salary:

Profit for P = (P - 10000) * (x) * (t)^2
Profit for Q = (Q) * (y) * (t)^2
Profit for R = (R) * (z) * (t)^2

Given that P earns `60,000 more than Q in a year, we can form the equation:

(P - 10000) * (x) * (t)^2 - (Q) * (y) * (t)^2 = 60000

Now, we need to solve these equations to find the values of x, y, and P.

Please note that the given text is in English.

Knowee AI · Accepted Answer