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 20,00 how much money will each son get ?

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Define the Total Money
Let the total money the man has be represented as \( X \).

### Step 2: Calculate the Wife's Share
The wife receives half of the total money:
\[ \text{Wife's share} = \frac{1}{2}X \]

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

### Step 4: Calculate the Sons' Share
Two-thirds of the remaining money is distributed among the three sons equally:
\[ \text{Sons' share} = \frac{2}{3} \times \frac{1}{2}X = \frac{1}{3}X \]
Since there are three sons, each son gets:
\[ \text{Each son's share} = \frac{1}{3}X \div 3 = \frac{1}{9}X \]

### Step 5: Calculate the Remaining Money After Sons' Share
After distributing the sons' share, the remaining money is:
\[ \text{Remaining money after sons' share} = \frac{1}{2}X - \frac{1}{3}X \]
To subtract these fractions, find a common denominator (which is 6):
\[ \frac{1}{2}X = \frac{3}{6}X \quad \text{and} \quad \frac{1}{3}X = \frac{2}{6}X \]
Thus,
\[ \text{Remaining money} = \frac{3}{6}X - \frac{2}{6}X = \frac{1}{6}X \]

### Step 6: Calculate Each Daughter's Share
This remaining money is distributed equally among four daughters:
\[ \text{Each daughter's share} = \frac{1}{6}X \div 4 = \frac{1}{24}X \]
According to the problem, each daughter receives Rs. 20,000:
\[ \frac{1}{24}X = 20,000 \]

### Step 7: Solve for Total Money \( X \)
To find \( X \), multiply both sides by 24:
\[ X = 20,000 \times 24 = 480,000 \]

### Step 8: Calculate Each Son's Share
Now, substitute \( X \) back to find each son's share:
\[ \text{Each son's share} = \frac{1}{9}X = \frac{1}{9} \times 480,000 = 53,333.33 \]

### Final Answer
Each son will receive Rs. 53,333.33.

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