The true discount on ₹ 1760 due after a certain time at 12% per annum is ₹ 160. The time after which it is due is

### Concept & Time Calculation To find the time period, isolate it from the simple interest formula applied to the present worth. $$ \text{PW} = \text{Amount} - \text{TD} $$ $$ T = \frac{100 \times \text{TD}}{\text{PW} \times R} $$ ### Step-by-Step Solution - Given Amount = ₹ 1760 - True Discount (TD) = ₹ 160 - Rate (R) = 12% per annum - Calculate the Present Worth (PW): $$ \text{PW} = 1760 - 160 = 1600 $$ - Use the formula to find Time (T) in years: $$ T = \frac{100 \times 160}{1600 \times 12} $$ $$ T = \frac{16000}{19200} = \frac{5}{6} \text{ years} $$ - Convert years into months by multiplying by 12: $$ T = \frac{5}{6} \times 12 = 10 \text{ months} $$ ### Exam Strategy & Shortcut Observe that the TD is exactly 10% of the PW ($160 / 1600$). If the annual rate is 12%, then a 10% return requires a fraction of the year equal to $10/12$. $10/12$ of 12 months is trivially 10 months. ### Common Pitfall Leaving the final answer as a fraction of a year (5/6) and guessing incorrectly among the options instead of converting it to months. ### Final Answer Therefore, the correct answer is **10 months**.