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.

The correct answer is Rs. 10880.

Step-by-step breakdown:

To find the share of earnings for Ethan, we first need to calculate the effective investment of Daniel and Ethan over the period of one year (12 months).

1. Calculating Daniel's total equivalent investment for 12 months:

Daniel's initial investment = Rs. 4200.

He invested this amount for the first 4 months.

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

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

$\text{Remaining investment for Daniel}=4200-1050=3150$

This remaining amount of Rs. 3150 stayed invested for the remaining 8 months (12 - 4 = 8 months).

So, Daniel's total effective investment is:

$\text{Daniel's Investment}=(4200\times 4)+(3150\times 8)$

$\text{Daniel's Investment}=16800+25200=42000$

2. Calculating Ethan's total equivalent investment for 12 months:

Ethan's initial investment = Rs. 5600.

He invested this amount for the first 4 months.

After 4 months, Ethan withdrew Rs. 1600.

$\text{Remaining investment for Ethan}=5600-1600=4000$

This remaining amount of Rs. 4000 stayed invested for the remaining 8 months.

So, Ethan's total effective investment is:

$\text{Ethan's Investment}=(5600\times 4)+(4000\times 8)$

$\text{Ethan's Investment}=22400+32000=54400$

3. Ratio of their earnings:

The ratio of earnings between Daniel and Ethan is proportional to the ratio of their effective investments:

$\text{Daniel : Ethan}=42000:54400=420:544=105:136$

4. Calculating Ethan's share of earnings:

Let Daniel's share be 105x and Ethan's share be 136x.

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

$136x-105x=2480$

$31x=2480$

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

Now, calculate Ethan's total share of earnings (136x):

$\text{Ethan's Share}=136\times 80=10880$

Thus, the total share of earnings received by Ethan is Rs. 10880.