Hari babu left one-third of his property to his son, one-fourth to his daughter and the remainder to his wife.If his wife share is 18000, What was the worth of his total property?

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the total property
Let the total worth of Hari Babu's property be represented as \( x \).

### Step 2: Determine shares for son and daughter
According to the problem:
- The son receives \( \frac{1}{3} \) of the total property, which is \( \frac{1}{3}x \).
- The daughter receives \( \frac{1}{4} \) of the total property, which is \( \frac{1}{4}x \).

### Step 3: Calculate the remainder for the wife
The remainder of the property, which goes to the wife, can be calculated as follows:
\[ \text{Wife's share} = x - \left(\frac{1}{3}x + \frac{1}{4}x\right) \]

### Step 4: Find a common denominator
To simplify the expression, we need to find a common denominator for \( \frac{1}{3} \) and \( \frac{1}{4} \). The least common multiple (LCM) of 3 and 4 is 12. Thus, we can rewrite the fractions:
\[ \frac{1}{3}x = \frac{4}{12}x \quad \text{and} \quad \frac{1}{4}x = \frac{3}{12}x \]

### Step 5: Substitute back into the equation
Now, substituting these values back into the equation for the wife's share:
\[ \text{Wife's share} = x - \left(\frac{4}{12}x + \frac{3}{12}x\right) = x - \frac{7}{12}x \]
This simplifies to:
\[ \text{Wife's share} = \frac{5}{12}x \]

### Step 6: Set up the equation
We know from the problem that the wife's share is \( 18,000 \):
\[ \frac{5}{12}x = 18,000 \]

### Step 7: Solve for \( x \)
To find \( x \), we can multiply both sides by \( \frac{12}{5} \):
\[ x = 18,000 \times \frac{12}{5} \]

### Step 8: Calculate the total property value
Calculating the right side:
\[ x = 18,000 \times 2.4 = 43,200 \]

### Conclusion
The total worth of Hari Babu's property is \( 43,200 \).

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