Anya and Blake initiated a collaborative venture, contributing capital worth Rs. 1200 and Rs. 3200 respectively. After a period of seven months, Anya withdrew 50% of her starting contribution, and Charles joined the venture with an investment of Rs. 4800. If the total earnings distributed at the end of the year amount to Rs. 1230, by how much does Blake's share of the earnings exceed Anya's share?

The correct answer is Rs. 450.

To find the difference between Blake's share and Anya's share of the total earnings, we need to determine the ratio of profit distribution among Anya, Blake, and Charles based on their capital investments and the duration for which the capital was invested.

The venture lasted for a total duration of 1 year (12 months).

Step 1: Calculate the effective investment (Capital × Time) for each person:

1. Anya's Investment:
Anya starts with Rs. 1200 for the first 7 months.
After 7 months, she withdraws 50% of her starting contribution. 50% of Rs. 1200 = Rs. 600.
Remaining capital for the next 5 months (12 - 7 = 5 months) = Rs. 1200 - Rs. 600 = Rs. 600.
Anya's total effective investment = (1200 × 7) + (600 × 5)

$\text{Anya's effective investment}=8400+3000=11400$

2. Blake's Investment:
Blake invests Rs. 3200 for the entire 12 months.
Blake's total effective investment = 3200 × 12

$\text{Blake's effective investment}=38400$

3. Charles's Investment:
Charles joins after 7 months with Rs. 4800, so his money is invested for the remaining 5 months.
Charles's total effective investment = 4800 × 5

$\text{Charles's effective investment}=24000$

Step 2: Determine the ratio of their profit shares:
Ratio of Anya : Blake : Charles = 11400 : 38400 : 24000
Dividing all terms by 600:

$\text{Ratio}=19:64:40$

Step 3: Calculate the total ratio units:

$\text{Total ratio units}=19+64+40=123$

Step 4: Calculate the value of 1 ratio unit:
Total earnings = Rs. 1230

$\text{Value of 1 unit}=\frac{1230}{123}=\text{Rs. 10}$

Step 5: Find the difference between Blake's share and Anya's share:
Difference in ratio units between Blake and Anya = 64 - 19 = 45 units.

$\text{Required Difference}=45\times 10=\text{Rs. 450}$

Thus, Blake's share of the earnings exceeds Anya's share by Rs. 450.