The true discount on ₹ 2562 due 4 months hence is ₹ 122. The rate percent is

### Concept & True Discount Logic The true discount is the simple interest on the Present Worth. We can find the Present Worth by subtracting the true discount from the total amount due. $$ \text{PW} = \text{Amount} - \text{TD} $$ $$ R = \frac{100 \times \text{TD}}{\text{PW} \times T} $$ ### Step-by-Step Solution - Given Amount = ₹ 2562 - True Discount (TD) = ₹ 122 - Time (T) = 4 months = $\frac{4}{12}$ years = $\frac{1}{3}$ year - Find the Present Worth (PW): $$ \text{PW} = 2562 - 122 = 2440 $$ - Now substitute PW, TD, and T into the rate formula: $$ R = \frac{100 \times 122}{2440 \times (\frac{1}{3})} $$ $$ R = \frac{12200}{\frac{2440}{3}} = \frac{12200 \times 3}{2440} $$ $$ R = 5 \times 3 = 15\% $$ ### Exam Strategy & Shortcut Instead of writing complex fractions, observe that 122 is exactly 1/20th (or 5%) of 2440. If the interest for 1/3 of a year is 5%, the interest for a full year is $5\% \times 3 = 15\%$. ### Common Pitfall Forgetting to convert months into years. Using T = 4 instead of T = 1/3 will yield a drastically incorrect, tiny rate percentage. ### Final Answer Therefore, the correct answer is **15%**.