Question

A started a business with Rs. 50000. After three months, B joins with an investment of Rs. 60000 and A withdraws Rs. 10000 out of his capital. Three months later, B brought in Rs. 20000 more. At the end of the year, what should be the ratio in which they A and B share the profits?

• A. 22:15
• B. 13:22
• C. 17:22
• D. 15:22

Answer 1

The Correct Option is C

To determine the ratio in which A and B should share the profits, we need to calculate the effective capital contribution of both A and B over the entire year. 

1. A initially invests Rs. 50000. After three months, A withdraws Rs. 10000, leaving Rs. 40000 in the business. The effective investment of A is calculated as:
   • For the first 3 months, A's investment is Rs. 50000. Hence, the capital for these months is: \(50000 \times 3 = 150000\).
   • After 3 months, A withdraws Rs. 10000, reducing the investment to Rs. 40000 for the next 9 months. Thus: \(40000 \times 9 = 360000\).
2. B joins after 3 months with Rs. 60000 and invests an additional Rs. 20000 after another 3 months. The effective investment for B is:
   • B's initial investment of Rs. 60000 remains for 3 months at first: \(60000 \times 9 = 540000\).
   • B adds Rs. 20000 more after 3 months, making it Rs. 80000 for the remaining 6 months: \(80000 \times 6 = 480000\).
3. Now, calculate the ratio of their effective capitals: \(\text{Ratio} = \frac{510000}{1020000}\).
4. Simplifying this ratio gives: \(\frac{510}{1020} = \frac{17}{34} = \frac{17}{22}\).
5. Therefore, the ratio in which A and B should share the profits is 17:22.

This matches the given correct answer, which confirms our calculations.