P, Q and R started a business each investing Rs. 20,000. After 5 months, P withdrew Rs. 5,000, Q withdrew Rs. 4,000 and R invested Rs. 6,000 more. At the end of the year, a total profit of Rs. 34,950 was recorded. Find the share of P.

Given:

Initial investment by P, Q, and R = Rs. 20,000 each

Total profit at the end of the year = Rs. 34,950

Concept:

The share of the profit is directly proportional to the product of the capital invested and the period of

the investment.

Solution:

⇒ Initial investment by P, Q, and R = Rs. 20,000 for 5 months each

For the next 7 months:

P's investment ⇒ Rs. (20,000 - 5,000) = Rs. 15,000

Q's investment ⇒ Rs. (20,000 - 4,000) = Rs. 16,000

R's investment ⇒ Rs. (20,000 + 6,000) = Rs. 26,000

Calculating their capital time (C × T) products:

P's investment for the year ⇒ (20,000 × 5) + (15,000 × 7) = 100,000 + 105,000 = 205,000

Q's investment for the year ⇒ (20,000 × 5) + (16,000 × 7) = 100,000 + 112,000 = 212,000

R's investment for the year ⇒ (20,000 × 5) + (26,000 × 7) = 100,000 + 182,000 = 282,000

Total capital time product summed up ⇒ 205,000 + 212,000 + 282,000 = 699,000

The share of the profit for an individual:

Share of P = (P's capital time product / Total capital time product) × Total Profit

⇒ (205,000 / 699,000) × 34,950

⇒ (205 / 699) × 34,950

⇒ Rs. 10,250

Hence, the share of P from the total profit is Rs. 10,250