Question

A and 8 started a business with Rs.1200 and Rs.1500. After some time C joined with Rs.2400. C and A got equal amount as their share of profit at the end of the year. After how many months did C join the firm?

• A. 9months
• B. 4months
• C. 6months
• D. 10 months
• E. None of these

Answer 1

The Correct Option is C

Step 1: Understand the problem.
A and B started a business with investments of Rs.1200 and Rs.1500, respectively. After some time, C joined with an investment of Rs.2400. At the end of the year, C and A received an equal share of the profit. We need to find out after how many months C joined the firm.

Step 2: Calculate the time-weighted investments.
The profit-sharing ratio is based on the product of the investment and the time for which it is invested. Let’s assume C joined after \( x \) months.

- A’s investment for 12 months: \( 1200 \times 12 = 14400 \) (as A invested for the entire year). - B’s investment for 12 months: \( 1500 \times 12 = 18000 \) (as B also invested for the entire year). - C’s investment for \( x \) months: \( 2400 \times x \) (since C joined after \( x \) months and invested for \( 12 - x \) months).

Step 3: Set up the equation.
Since A and C got equal shares of the profit, their time-weighted investments should be equal:
\( A’s \, investment = C’s \, investment \)
\( 1200 \times 12 = 2400 \times x \)
\( 14400 = 2400x \)
\( x = 14400 / 2400 \)
\( x = 6 \)

Step 4: Conclusion.
C joined the firm after 6 months.

Final Answer:
The correct option is (C): 6 months.