Let's denote the total worth of Pratik's property as $x$.

• One-third of the property is left for his son, so the son's share is $\frac{1}{3} \times x$.
• One-fourth of the property is left for his daughter, so the daughter's share is $\frac{1}{4} \times x$.
• The remainder of the property is left for his wife, and we know this amount is worth 10 lakh.

Now, we can set up the equation to find $x$:

1. The total property is divided into three parts:

   • Son's share: $\frac{1}{3} \times x$
   • Daughter's share: $\frac{1}{4} \times x$
   • Wife's share: $\frac{1}{3} \times x + \frac{1}{4} \times x + 10 \text{ lakh} = x$

2. First, find the fraction of the property that is already allocated (to the son and daughter): $\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ So, the son and daughter together have $\frac{7}{12}$ of the property.

3. Therefore, the wife’s share is the remainder: $1 - \frac{7}{12} = \frac{5}{12}$ Thus, the wife’s share is $\frac{5}{12}$ of the total property, and we are given that this share is worth 10 lakh: $\frac{5}{12} \times x = 10 \, \text{lakh}$

4. To find $x$, solve for $x$: $x = \frac{10 \, \text{lakh} \times 12}{5}$ $x = 24 \, \text{lakh}$

So, the total worth of Pratik's property is 24 lakh.

Would you like any further explanation or have any questions about the solution? Here are some related questions:

1. How do you handle fractions in property division problems?
2. What are some different methods for solving equations involving fractions?
3. How can this problem be solved using algebraic expressions instead of fractions?
4. How would the solution change if the wife’s share were given in percentage instead of a fixed amount?
5. Can this approach be used for more than three divisions of property?

Tip: When solving problems involving fractions of a whole, always remember that the sum of the fractions of all parts should equal 1 (or 100%) of the total.