A and B invested Rs 7999.99 and Rs 5000.03 in a business. A invested his amount for whole years and B invested for T+2 days. At the end of the year, the profit share of B is Rs 5999.93 out of total profit of Rs. 22000.01. Find the approximate value of ‘T’?

To find the approximate value of T, we can first approximate the given values to make calculations simpler:

Investment of A ≈ Rs. 8000
Investment of B ≈ Rs. 5000
Total profit ≈ Rs. 22000
Profit share of B ≈ Rs. 6000

Since the total profit is Rs. 22000 and B's profit share is Rs. 6000, we can find A's profit share as follows:

Profit share of A = Total profit - Profit share of B
Profit share of A ≈ 22000 - 6000 = Rs. 16000

The ratio of the profit shares of A and B is:

$\frac{\text{Profit of A}}{\text{Profit of B}}=\frac{16000}{6000}=\frac{8}{3}$

We know that the profit share ratio is equal to the ratio of the product of their investments and their respective time periods. A invested for a whole year (365 days) and B invested for (T + 2) days.

$\frac{\text{Investment of A}\times \text{Time of A}}{\text{Investment of B}\times \text{Time of B}}=\frac{\text{Profit of A}}{\text{Profit of B}}$

Substituting the values into the formula:

$\frac{8000\times 365}{5000\times (T+2)}=\frac{8}{3}$

Simplifying the fraction on the left side:

$\frac{8\times 365}{5\times (T+2)}=\frac{8}{3}$

Dividing both sides by 8:

$\frac{365}{5\times (T+2)}=\frac{1}{3}$

Since 365 divided by 5 is 73:

$\frac{73}{T+2}=\frac{1}{3}$

Cross-multiplying to solve for T:

$T+2=73\times 3$

$T+2=219$

$T=219-2$

$T=217$

Thus, the approximate value of T is 217.