A father left a will of 35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount invested of 10% p.a. Simple interest. How much did the elder daughter get at the time of the will?

Options

A. Rs 17.6 lakhs
B. Rs 21 lakhs
C. Rs 15 lakhs
D. Rs 20 lakhs

Answer

To solve the problem step by step, we need to determine how much the elder daughter received from the total amount of 35 lakhs, given that both daughters will receive equal amounts when they reach the age of 21.

### Step 1: Determine the time until each daughter reaches 21 years of age.
- The elder daughter is currently 16 years old. She will reach 21 in:
\[ 21 - 16 = 5 \text{ years} \]

- The younger daughter is currently 8.5 years old. She will reach 21 in:
\[ 21 - 8.5 = 12.5 \text{ years} \]

### Step 2: Calculate the total amount each daughter will receive when they reach 21 years of age.
Let the amount received by the elder daughter be \( A \) and the amount received by the younger daughter be \( B \).

Using the formula for Simple Interest:
\[ \text{Total Amount} = \text{Principal} + \text{Interest} \]
The interest can be calculated as:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

For the elder daughter:
\[ A = P_A + (P_A \times 0.10 \times 5) = P_A (1 + 0.5) = 1.5 P_A \]

For the younger daughter:
\[ B = P_B + (P_B \times 0.10 \times 12.5) = P_B (1 + 1.25) = 2.25 P_B \]

### Step 3: Set the amounts equal to each other.
Since both daughters will receive equal amounts when they turn 21:
\[ 1.5 P_A = 2.25 P_B \]

### Step 4: Express \( P_B \) in terms of \( P_A \).
From the equation:
\[ P_B = \frac{1.5}{2.25} P_A = \frac{2}{3} P_A \]

### Step 5: Use the total amount from the will.
The total amount left in the will is:
\[ P_A + P_B = 35 \text{ lakhs} \]
Substituting \( P_B \):
\[ P_A + \frac{2}{3} P_A = 35 \]
Combining the terms:
\[ \frac{5}{3} P_A = 35 \]

### Step 6: Solve for \( P_A \).
Multiplying both sides by \( \frac{3}{5} \):
\[ P_A = 35 \times \frac{3}{5} = 21 \text{ lakhs} \]

### Step 7: Calculate \( P_B \).
Now substituting \( P_A \) back to find \( P_B \):
\[ P_B = \frac{2}{3} P_A = \frac{2}{3} \times 21 = 14 \text{ lakhs} \]

### Step 8: Calculate the total amounts received by each daughter.
Now we can calculate the total amount each daughter will receive when they turn 21:
- For the elder daughter:
\[ A = 1.5 P_A = 1.5 \times 21 = 31.5 \text{ lakhs} \]

- For the younger daughter:
\[ B = 2.25 P_B = 2.25 \times 14 = 31.5 \text{ lakhs} \]

### Final Answer
Thus, the amount the elder daughter received at the time of the will is:
\[ \boxed{21 \text{ lakhs}} \]