The true discount on a certain sum of money due 10 yr hence is 68 and the simple interest on the same sum for the same time and at the same rate of interest is 102. Find the sum due.

Answer

To solve the problem step by step, we will use the relationship between True Discount (TD), Simple Interest (SI), and the Sum Due (S).

### Step 1: Understand the Given Information
We know:
- True Discount (TD) = 68
- Simple Interest (SI) = 102
- Time (T) = 10 years

### Step 2: Recall the Formula
The formula for calculating the Sum Due (S) using True Discount and Simple Interest is:
\[ S = \frac{TD \times SI}{SI - TD} \]

### Step 3: Substitute the Values
Now, substituting the values we have into the formula:
- TD = 68
- SI = 102

So,
\[ S = \frac{68 \times 102}{102 - 68} \]

### Step 4: Calculate the Denominator
First, calculate the denominator:
\[ 102 - 68 = 34 \]

### Step 5: Calculate the Numerator
Next, calculate the numerator:
\[ 68 \times 102 = 6936 \]

### Step 6: Calculate the Sum Due (S)
Now we can calculate the Sum Due:
\[ S = \frac{6936}{34} \]

### Step 7: Perform the Division
Now, perform the division:
\[ S = 204 \]

### Conclusion
Thus, the sum due is **204**.