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 option is Rs. 450.

To find how much Blake's share of the earnings exceeds Anya's share, we need to calculate the ratio of their effective investments over the total period of 1 year (12 months).

Step 1: Calculate the effective investment of each person

1. Anya's investment:
For the first 7 months, Anya invested Rs. 1200.
After 7 months, she withdrew 50% of her starting contribution.
Amount withdrawn = 50% of 1200 = Rs. 600.
Remaining investment for the remaining 5 months (12 - 7 = 5 months) = 1200 - 600 = Rs. 600.
Anya's total effective investment =
$(1200\times 7)+(600\times 5)$
$=8400+3000=\text{Rs.}11400$

2. Blake's investment:
Blake invested Rs. 3200 for the entire 12 months.
Blake's total effective investment =
$3200\times 12=\text{Rs.}38400$

3. Charles's investment:
Charles joined after 7 months with Rs. 4800, so his money was invested for 5 months.
Charles's total effective investment =
$4800\times 5=\text{Rs.}24000$

Step 2: Find the ratio of profit distribution

Ratio of profit of Anya : Blake : Charles =
$11400:38400:24000$
Dividing each term by 300:
$38:128:80$
Dividing further by 2:
$19:64:40$

Step 3: Calculate the difference between Blake's share and Anya's share

Sum of ratio parts =
$19+64+40=123$

Total earnings = Rs. 1230

Difference between Blake's ratio part and Anya's ratio part =
$64-19=45$

Difference in earnings =
$\frac{45}{123}\times 1230$
$=45\times 10=\text{Rs.}450$

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