X started a business with an investment of Rs 20,000. After 3 months, Y joins in with 3/4 of the amount that X invested, and X withdraws Rs 5,000. After 4 more months, Z joins with Rs 15,000, and X again withdraws Rs 3,000. After one year, if Z received Rs 4,500 as his share, what was the total profit?

X's Investment:

Initial investment = Rs 20,000

After 3 months, X withdraws Rs 5,000:

Remaining investment = Rs 20,000 - Rs 5,000 = Rs 15,000

After 7 months (3 + 4), X withdraws Rs 3,000:

Remaining investment = Rs 15,000 - Rs 3,000 = Rs 12,000

Total investment by X:

Rs 20,000 for 3 months

Rs 15,000 for 4 months

Rs 12,000 for 5 months

Y's Investment:

Y joins after 3 months with34of X's initial investment:

3/4 × 20,000 = Rs 15,000

Y invests Rs 15,000 for the remaining 9 months.

Z's Investment:

Z joins after 7 months with Rs 15,000.

Z invests Rs 15,000 for the remaining 5 months.

The profit-sharing ratio is based on the product of investment and time.

X's Share:

20,000 × 3 + 15,000 × 4 + 12,000 × 5 = 60,000 + 60,000 + 60,000 = 180,000

Y's Share:

15,000 × 9 = 135,000

Z's Share:

15,000 × 5 = 75,000

Profit Sharing Ratio:

X : Y : Z = 180,000 : 135,000 : 75,000

X : Y : Z = 12 : 9 : 5

Z's share is Rs 4,500, which corresponds to 5 parts of the profit-sharing ratio.

Value of 1 Part:

1 part = 4,500 / 5 = 900

Total Profit:

Total parts = 12 + 9 + 5 = 26

Total profit = 26 × 900 = 23,400

Thus, the total profit is Rs 23,400.