Akram Ali left an amount of ₹ 340000 to be divided between his two sons aged 10 years and 12 years such that both of them would get an equal amount when each attain 18 years age. What is the share of elder brother if the whole amount was invested at `10%` simple interest:

Options

A. 12000
B. 16000
C. 160000
D. 180000

Answer

To solve the problem of how to divide the ₹ 340,000 between Akram Ali's two sons, we need to consider the ages of the sons and the time until they both reach 18 years old.

### Step-by-Step Solution:

1. **Identify the Ages and Time Until 18:**
- The younger son is currently 10 years old and will be 18 in 8 years.
- The elder son is currently 12 years old and will be 18 in 6 years.

2. **Calculate the Time Difference:**
- The younger son will wait 8 years to reach 18.
- The elder son will wait 6 years to reach 18.
- The difference in waiting time is 8 years (younger) - 6 years (elder) = 2 years.

3. **Determine the Shares Based on Time:**
- The amount of money each son will receive should be proportional to the time they have to wait until they reach 18.
- The younger son waits for 8 years, and the elder son waits for 6 years.
- The ratio of their waiting times is 6:8, which simplifies to 3:4.

4. **Calculate the Total Parts:**
- The total parts of the ratio are 3 + 4 = 7 parts.

5. **Determine the Share of Each Son:**
- Total amount = ₹ 340,000.
- Share of the younger son = (3/7) * 340,000 = ₹ 145,714.29 (approximately).
- Share of the elder son = (4/7) * 340,000 = ₹ 194,285.71 (approximately).

6. **Final Calculation of the Elder Brother's Share:**
- The elder brother's share is approximately ₹ 194,285.71.

### Summary:
- The elder brother will receive approximately ₹ 194,285.71 when both sons attain the age of 18.