If the true discount on a sum due 2 years hence at 14% per annum be ₹ 168, the sum due is

### Concept & Formula The true discount (TD) is the simple interest on the present worth (PW) for the given time and rate. The sum due (Amount) is the present worth plus the true discount. $$ \text{PW} = \frac{100 \times \text{TD}}{R \times T} $$ $$ \text{Amount} = \text{PW} + \text{TD} $$ ### Step-by-Step Solution - Given True Discount (TD) = ₹ 168 - Rate (R) = 14% per annum - Time (T) = 2 years - First, calculate the Present Worth (PW): $$ \text{PW} = \frac{100 \times 168}{14 \times 2} = \frac{16800}{28} = 600 $$ - The Present Worth is ₹ 600. - Now, calculate the sum due (Amount): $$ \text{Amount} = \text{PW} + \text{TD} = 600 + 168 = 768 $$ ### Exam Strategy & Shortcut Realize that the true discount (₹ 168) is exactly 28% (14% × 2) of the present worth. Thus, $\text{PW} = 168 / 0.28 = 600$. Adding the TD back gives $600 + 168 = 768$. ### Common Pitfall Mistaking the "sum due" for the "present worth" and stopping the calculation at 600. Always add the true discount to find the final sum due. ### Final Answer Therefore, the correct answer is **₹ 768**.