Find the individual share of earnings for the second partner based on the investment details provided.

Daniel and Ethan established a joint venture by contributing Rs. 4200 and Rs. 5600 respectively. After four months, Daniel withdrew 25% of his initial contribution, and Ethan withdrew Rs. 1600. If the difference between their earnings at the end of a year is Rs. 2480, determine the total share of earnings received by Ethan.

Correct Answer: Rs. 10880 (Option 5)

To find the total share of earnings received by Ethan at the end of one year (12 months), we need to calculate the ratio of the effective investments made by Daniel and Ethan over the entire period.

Step 1: Calculate Daniel's effective investment

Initial investment by Daniel = Rs. 4200

For the first 4 months, Daniel's investment is Rs. 4200.

After 4 months, Daniel withdraws 25% of his initial contribution:

Withdrawal amount = 25% of 4200 = $\frac{25}{100}\times 4200=1050$

Remaining investment for the remaining 8 months = $4200-1050=3150$

Daniel's total effective investment = $(4200\times 4)+(3150\times 8)$

$=16800+25200=42000$

Step 2: Calculate Ethan's effective investment

Initial investment by Ethan = Rs. 5600

For the first 4 months, Ethan's investment is Rs. 5600.

After 4 months, Ethan withdraws Rs. 1600.

Remaining investment for the remaining 8 months = $5600-1600=4000$

Ethan's total effective investment = $(5600\times 4)+(4000\times 8)$

$=22400+32000=54400$

Step 3: Determine the profit-sharing ratio

Ratio of earnings (Daniel : Ethan) = $42000:54400$

Dividing both sides by 1600 gives:

Ratio = $105:136$

Step 4: Calculate Ethan's earnings share

Let Daniel's earnings be $105x$ and Ethan's earnings be $136x$.

The difference between their earnings is given as Rs. 2480:

$136x-105x=2480$

$31x=2480$

$x=\frac{2480}{31}=80$

Now, total share of earnings received by Ethan = $136x$

$=136\times 80=10880$

Thus, Ethan received a total share of Rs. 10880.