Question:medium

P, Q and E start a joint venture, where in they make an annual profit. P invested one-third of the capital for one-fourth of the time, Q invested one-fourth of the capital for one-half of the time and R invested the remainder of the capital for the entire year. P is a working partner and gets a salary of `10,000 per month. 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. If in a year P earns ` 60,000 more than Q, then how much does P earn?

Updated On: Jan 13, 2026
  • 1,00,000
  • 1,20,000
  • 1,35,000
  • 1,50,000
  • 1,80,000
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The Correct Option is D

Solution and Explanation

The correct answer is option (D):
1,50,000

Here's how to solve this problem step-by-step:

1. Understand the Problem: We have a joint venture with three partners. The profit distribution is complex, considering both investment amounts and time, along with a salary for P. We need to find P's total earnings.

2. Define Variables and Assumptions:

* Let the total capital be C.
* Let the total time be 12 months (a year).
* Let the profit after P's salary be P_net.
* P's salary = 10,000 * 12 = 120,000

3. Calculate Individual Investments and Time:

* P invested: (1/3)C for (1/4)*12 = 3 months
* Q invested: (1/4)C for (1/2)*12 = 6 months
* R invested: (1 - 1/3 - 1/4)C = (5/12)C for 12 months

4. Profit Proportionality:

* The problem states the profit is directly proportional to (investment * (time)^2). So, the profit share is proportional to:
* P: (1/3)C * (3)^2 = 3C
* Q: (1/4)C * (6)^2 = 9C
* R: (5/12)C * (12)^2 = 60C

5. Profit Distribution Ratio:

* The profit-sharing ratio (after P's salary) is 3C:9C:60C, or 1:3:20.
* The total ratio units = 1 + 3 + 20 = 24

6. Express Profit Shares:

* Let the total net profit (P_net) be x.
* P's share of P_net = (1/24) * x
* Q's share of P_net = (3/24) * x
* R's share of P_net = (20/24) * x

7. Relate Earnings and the Salary:

* P's total earnings = P's share of the net profit + P's salary = (1/24) * x + 120,000
* Q's total earnings = Q's share of the net profit = (3/24) * x

8. Set up the Equation based on the Problem Information:

* P earns 60,000 more than Q:
(1/24) * x + 120,000 = (3/24) * x + 60,000

9. Solve for x (Total Net Profit):

* (2/24) * x = 60,000
* x = 60,000 * (24/2) = 720,000

10. Calculate P's Total Earnings:

* P's total earnings = (1/24) * 720,000 + 120,000
* P's total earnings = 30,000 + 120,000 = 150,000

11. Answer: P earns 150,000.
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