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’?

The correct answer is 217.

We round the messy values to their nearest clean numbers for calculation:

A's investment = Rs 8000 (for a full year = 365 days)
B's investment = Rs 5000 (for T + 2 days)
B's profit share = Rs 6000
Total profit = Rs 22000

Step 1: Find B's share ratio in total profit.

B's profit ratio = \frac{6000}{22000}=\frac{3}{11}

Step 2: Set up the profit-sharing equation.

In a partnership, profit is shared in the ratio of Capital × Time. So:

A's share value = 8000\times 365=\mathrm{2,920,000}

B's share value = 5000\times (T+2)

B's fraction of total profit is:

\frac{5000\times (T+2)}{2920000+5000\times (T+2)}=\frac{3}{11}

Step 3: Cross-multiply and solve.

Let x=5000\times (T+2)

11x=3\times (2920000+x)

11x=8760000+3x

8x=8760000

x=\mathrm{1,095,000}

Step 4: Find T.

5000\times (T+2)=\mathrm{1,095,000}

T+2=\frac{1095000}{5000}=219

T=219-2=217

Therefore, the approximate value of T = 217 days.