A man has divided his total money in his will in such a way that half of it goes to his wife, `2/3`rd of the remaining among his three sons equally and the rest among his four daughters equally. If each daughter gets Rs. 20,000. how much money will each son get ?

Options

A. Rs. 50,333.33
B. Rs. 48,233.33
C. Rs. 53,333.33
D. Data inadequate

Answer

Let's solve the problem step by step.

### Step 1: Define the total amount of money
Let the total amount of money the man has be denoted as \( x \).

### Step 2: Calculate the amount given to the wife
According to the will, half of the total money goes to the wife. Therefore, the amount given to the wife is:
\[ \text{Amount to wife} = \frac{1}{2} x \]

### Step 3: Calculate the remaining amount after giving to the wife
After giving half to the wife, the remaining amount is:
\[ \text{Remaining amount} = x - \frac{1}{2} x = \frac{1}{2} x \]

### Step 4: Calculate the amount given to the sons
Two-thirds of the remaining amount is given to the three sons. Therefore, the amount given to the sons is:
\[ \text{Amount to sons} = \frac{2}{3} \times \frac{1}{2} x = \frac{1}{3} x \]

### Step 5: Calculate the amount remaining after giving to the sons
The amount left after giving to the sons is:
\[ \text{Remaining amount after sons} = \frac{1}{2} x - \frac{1}{3} x \]
To perform this subtraction, we need a common denominator:
\[ \frac{1}{2} x = \frac{3}{6} x \quad \text{and} \quad \frac{1}{3} x = \frac{2}{6} x \]
Thus,
\[ \text{Remaining amount after sons} = \frac{3}{6} x - \frac{2}{6} x = \frac{1}{6} x \]

### Step 6: Calculate the amount given to the daughters
The remaining amount is divided equally among four daughters. Therefore, the amount each daughter receives is:
\[ \text{Amount to each daughter} = \frac{1}{4} \times \frac{1}{6} x = \frac{1}{24} x \]

### Step 7: Set the amount each daughter receives to Rs. 20,000
According to the problem, each daughter receives Rs. 20,000. Therefore, we can set up the equation:
\[ \frac{1}{24} x = 20,000 \]

### Step 8: Solve for \( x \)
To find the total amount \( x \), we multiply both sides by 24:
\[ x = 20,000 \times 24 = 480,000 \]

### Step 9: Calculate the amount given to the sons
Now that we have the total amount, we can find out how much money goes to the sons:
\[ \text{Amount to sons} = \frac{1}{3} x = \frac{1}{3} \times 480,000 = 160,000 \]

### Step 10: Calculate how much each son gets
Since this amount is divided equally among three sons, the amount each son receives is:
\[ \text{Amount to each son} = \frac{160,000}{3} \approx 53,333.33 \]

### Final Answer
Each son will get approximately Rs. 53,333.33.

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