Answer :
To solve this problem, we need to determine the investment of C, given the details of profit sharing in the business venture involving A, B, and C.
Here's a step-by-step breakdown of the situation:
Investments Overview:
- A invests Rs. 45,000.
- B invests Rs. x.
- C joins after 6 months with an investment of Rs. (x + 18,000).
Profit Distribution:
- Total profit over 2 years is Rs. 60,000.
- C takes 10% of the total profit for managing, which equals Rs. 6,000.
- Therefore, the remaining profit to be distributed among A, B, and C is Rs. 60,000 - Rs. 6,000 = Rs. 54,000.
C's Total Profit Calculation:
- Total profit received by C is given as Rs. 24,000.
- Out of this, Rs. 6,000 is for management.
- The remaining Rs. 18,000 is from the profit-sharing.
Profit Share Calculation:
- Profits are distributed in proportion to the product of investment and time.
- A's contribution is Rs. 45,000 for 24 months.
- B's contribution is Rs. x for 24 months.
- C's contribution is Rs. (x + 18,000) for 18 months (because C joined after 6 months).
Calculation for C's Investment:
- The profit ratio for C can be expressed as:
[tex]\text{C's ratio} = \frac{(x + 18,000) \times 18}{45,000 \times 24 + x \times 24 + (x + 18,000) \times 18}[/tex] - C's profit from sharing is Rs. 18,000:
[tex]\frac{(x + 18,000) \times 18}{45,000 \times 24 + x \times 24 + (x + 18,000) \times 18} \times 54,000 = 18,000[/tex]
- The profit ratio for C can be expressed as:
Solving for x:
- Simplifying and solving the equation will help us find the value of [tex]x[/tex].
- After calculations, the value of [tex]x[/tex] is found to be Rs. 36,000.
C's Investment:
- Substituting the value of [tex]x[/tex] into [tex]x + 18,000[/tex], we get C's investment:
[tex]C = x + 18,000 = 36,000 + 18,000 = 54,000[/tex]
- Substituting the value of [tex]x[/tex] into [tex]x + 18,000[/tex], we get C's investment:
Thus, the correct investment of C is option C) Rs. 54,000.