-    Clearly, Manish invested his capital for 12 months, Vibhor for 9 months and Vivek for 3 months.
  So, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3)
  = 540000 : 540000 : 270000 = 2:2:1.
  ∴ Manish’s share = Rs. [16500 x 2/5] = Rs. 6600;
  Vibhors share = Rs. [16500 x 2/5] = Rs. 6600;
  Vivek’s share = Rs. [16500 x 1/5] = Rs. 3300.

To find the share of Vivek in the profit, we need to calculate the ratio of the investment of each person and the time period for which they invested in the business. The ratio of profit sharing for Manish, Vibhor, and Vivek is calculated as follows:

Manish's investment = Rs. 45,000 (He invested for the entire year)

Vibhor's investment = Rs. 60,000 (He invested for 9 months)

Vivek's investment = Rs. 90,000 (He invested for 6 months)

To find the ratio of profit sharing, we can multiply the investment by the time period for each person:

Manish's ratio = 45,000 × 12 = 5,40,000

Vibhor's ratio = 60,000 × 9 = 5,40,000

Vivek's ratio = 90,000 × 6 = 5,40,000

The total ratio of profit sharing is:

Manish + Vibhor + Vivek = 5,40,000 + 5,40,000 + 5,40,000 = 16,20,000

The share of Vivek can be calculated by dividing his ratio by the total ratio and then multiplying the result by the total profit:

Vivek's share = (Vivek's ratio / Total ratio) × Total profit

Vivek's share = (5,40,000 / 16,20,000) × 16,500

Vivek's share = 5,500

Therefore, the share of Vivek in the profit is Rs. 3300 (Option A).

To summarize, the steps to find the share of Vivek in the profit are:

• Calculate the investment and time period for each person.
• Find the ratio of profit sharing for each person by multiplying their investment and time period.
• Calculate the total ratio of profit sharing by adding the ratios of all persons.
• Find the share of Vivek by dividing his ratio by the total ratio and multiplying the result by the total profit.

If you think the solution is wrong then please provide your own solution below in the comments section .