Vijay decides to leave 100 acres of his land to his three daughters Vijaya, Sunanda and Ansuya in the proportion of one-third, one-fourth and one-fifth respectively. But Vijaya suddenly expires. Now how should Vijay divide the land between Sunanda and Anusuya?

Options

A. `(500)/(9),(400)/(9)`
B. `(450)/(8),(350)/(8)`
C. `(420)/(7),(280)/(7)`
D. `(320)/(7),(380)/(7)`

Answer

To solve the problem of how Vijay should divide his 100 acres of land between his two daughters, Sunanda and Anusuya, after Vijaya's demise, we can follow these steps:

### Step 1: Determine the total parts of the land distribution
Vijay initially intended to divide the land among his three daughters in the ratios of:
- Vijaya: \( \frac{1}{3} \)
- Sunanda: \( \frac{1}{4} \)
- Anusuya: \( \frac{1}{5} \)

To find a common basis for these fractions, we need to find the least common multiple (LCM) of the denominators (3, 4, and 5).

**Hint:** To find the LCM, consider the multiples of each denominator and find the smallest number that appears in all lists.

### Step 2: Calculate the LCM of the denominators
The LCM of 3, 4, and 5 is 60.

Now, we can convert each fraction to have a denominator of 60:
- Vijaya's share: \( \frac{1}{3} = \frac{20}{60} \)
- Sunanda's share: \( \frac{1}{4} = \frac{15}{60} \)
- Anusuya's share: \( \frac{1}{5} = \frac{12}{60} \)

### Step 3: Calculate the total parts
Now, we add these parts together:
\[ \text{Total parts} = 20 + 15 + 12 = 47 \]

### Step 4: Determine the shares of Sunanda and Anusuya
Since Vijaya has passed away, we only consider Sunanda and Anusuya's shares:
- Sunanda's share: \( \frac{15}{60} \)
- Anusuya's share: \( \frac{12}{60} \)

### Step 5: Calculate the total land for Sunanda and Anusuya
The total land available for Sunanda and Anusuya is:
\[ \text{Total land} = 100 \text{ acres} \]

### Step 6: Calculate the new shares
To find out how much land each daughter receives, we need to find their respective shares out of the total parts (15 + 12 = 27 parts).

- Sunanda's new share:
\[ \text{Sunanda's share} = \left( \frac{15}{27} \right) \times 100 = \frac{1500}{27} \approx 55.56 \text{ acres} \]

- Anusuya's new share:
\[ \text{Anusuya's share} = \left( \frac{12}{27} \right) \times 100 = \frac{1200}{27} \approx 44.44 \text{ acres} \]

### Final Result:
Thus, the land should be divided as follows:
- Sunanda receives approximately 55.56 acres.
- Anusuya receives approximately 44.44 acres.