Arun spends `(2)/(13)th` of his salary on the education of his children, Tarun and Varun. He spends Rs 13,006 on Varun's education, which is `(2)/(3)` rd of his total expenditure on education. What is Arun's total salary?

Options

A. Rs 84,539
B. Rs `126,808.50`
C. Rs `134,278.50`
D. Rs 102,346

Answer

To find Arun's total salary, we can break down the problem step by step.

### Step 1: Define the variables
Let Arun's total salary be \( x \).

### Step 2: Calculate the total expenditure on education
According to the problem, Arun spends \( \frac{2}{13} \) of his salary on the education of his children. Therefore, the total expenditure on education can be expressed as:
\[ \text{Total Expenditure on Education} = \frac{2}{13} x \]

### Step 3: Relate Varun's expenditure to the total expenditure
It is given that Arun spends Rs 13,006 on Varun's education, which is \( \frac{2}{3} \) of his total expenditure on education. We can set up the equation:
\[ \frac{2}{3} \times \text{Total Expenditure on Education} = 13006 \]
Substituting the expression from Step 2 into this equation gives:
\[ \frac{2}{3} \times \left(\frac{2}{13} x\right) = 13006 \]

### Step 4: Solve for \( x \)
Now, we can simplify and solve for \( x \):
\[ \frac{4}{39} x = 13006 \]
To isolate \( x \), multiply both sides by \( \frac{39}{4} \):
\[ x = 13006 \times \frac{39}{4} \]

### Step 5: Calculate the value of \( x \)
Now, we perform the multiplication:
\[ x = 13006 \times \frac{39}{4} = 13006 \times 9.75 = 126,060.50 \]

### Final Step: Conclusion
Thus, Arun's total salary is:
\[ \text{Total Salary} = Rs. 126,060.50 \]