A invested Rs. 4000 in a business. At the end of 4 months from the start of the business, B joined with an investment of Rs. 8400 and A left. If the total annual profit was Rs. 13,... A invested Rs. 4000 in a business. At the end of 4 months from the start of the business, B joined with an investment of Rs. 8400 and A left. If the total annual profit was Rs. 13,000, what was A's share in profit? Read more

Steps to Solve

1. Determine the investment duration for each partner

   A invested Rs. 4000 for a total of 12 months (1 year).
   Since B joined at the end of 4 months, B's investment of Rs. 8400 was active for 8 months (i.e., 12 - 4 months).

2. Calculate effective investment months for A and B

   For A:
   $$ \text{A's effective investment} = 4000 \times 12 = 48000 $$

   For B:
   $$ \text{B's effective investment} = 8400 \times 8 = 67200 $$

3. Calculate the total effective investment

   Combine both effective investments:
   $$ \text{Total effective investment} = 48000 + 67200 = 115200 $$

4. Determine A's share of the profit

   A's share of the profit is based on the ratio of A's effective investment to the total effective investment:
   $$ \text{A's share of profit} = \frac{\text{A's effective investment}}{\text{Total effective investment}} \times \text{Total profit} $$

   Substituting the numbers:
   $$ \text{A's share of profit} = \frac{48000}{115200} \times 13000 $$

5. Calculate the portion

   Evaluate the fraction:
   $$ \text{A's share of profit} = \frac{1}{2.4} \times 13000 \approx 5416.67 $$

   Therefore,
   $$ \text{A's share of profit} = \frac{48000 \times 13000}{115200} = 2250 $$