High School

A and B started a business by investment of Rs. 45000 & Rs. x respectively. At the end of six months, C joined them with Rs. (x + 18000) on the agreement that he will take 10% of total profit for managing the business and the remaining profit distributed among them in the respective profit ratio. At the end of two years, the total profit of C is Rs. 24000 out of total profit of Rs. 60000. Then find the investment (in Rs.) of C.

A) 72000
B) 36000
C) 54000
D) 48000
E) 60000

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:

  1. Investments Overview:

    • A invests Rs. 45,000.
    • B invests Rs. x.
    • C joins after 6 months with an investment of Rs. (x + 18,000).

  2. 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.

  3. 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.

  4. 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).

  5. 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]

  6. 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.

  7. 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]

Thus, the correct investment of C is option C) Rs. 54,000.

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