If BD and TD on a sum due certain time hence at a certain rate are ? 72 and ? 60 respectively, find the sum.

Answer

To solve the problem, we need to find the sum (principal) given the Banker’s Discount (BD) and True Discount (TD). The formulas we will use are based on the relationships between these discounts.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Banker Discount (BD) = ₹72
- True Discount (TD) = ₹60

2. **Use the Formula for Sum:**
The relationship between Banker Discount (BD), True Discount (TD), and the Sum (S) is given by the formula:
\[ S = \frac{BD \times TD}{BD - TD} \]

3. **Substitute the Values into the Formula:**
Substitute BD and TD into the formula:
\[ S = \frac{72 \times 60}{72 - 60} \]

4. **Calculate the Denominator:**
Calculate the difference between BD and TD:
\[ 72 - 60 = 12 \]

5. **Calculate the Numerator:**
Calculate the product of BD and TD:
\[ 72 \times 60 = 4320 \]

6. **Divide the Numerator by the Denominator:**
Now, divide the product by the difference:
\[ S = \frac{4320}{12} \]

7. **Final Calculation:**
Perform the division:
\[ S = 360 \]

### Conclusion:
The sum (principal) is ₹360.

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