A and B started a business with investments of Rs 4000 and Rs 3000 respectively. After 6 months, B withdrew from the business. At the end of the year, the total profit was Rs 660. Find the share of profit (in Rs) received by A.

To find the share of profit received by A, we need to determine the ratio of the investments of A and B over their respective periods of investment.

First, let's look at the investments and the duration for which each partner invested their money:
Investment of A = Rs. 4000 for 12 months (since A stayed in the business for the entire year).
Investment of B = Rs. 3000 for 6 months (since B withdrew after 6 months).

The ratio of their profit shares is equivalent to the ratio of the product of their investment amounts and investment durations:
Profit Share Ratio of A : B = (Investment of A × Time period of A) : (Investment of B × Time period of B)

Substituting the values:
Ratio = (4000 × 12) : (3000 × 6)
Ratio = 48000 : 18000

Simplifying the ratio by dividing both parts by 6000:
Ratio = 8 : 3

The total ratio parts = $8+3=11$ parts.

The total profit at the end of the year is Rs. 660.

Now, we can calculate A's share of the profit:
A's share = $\frac{8}{11}$ of the total profit
A's share = $\frac{8}{11}\times 660$
A's share = $8\times 60$
A's share = Rs. 480

Therefore, the share of profit received by A is Rs. 480.