The true discount on a bill due 9 months hence at 16% per annum is ₹ 189. The amount of the bill is

### Concept & Formula To find the total amount of the bill, compute the present worth from the true discount and add them together. $$ \text{PW} = \frac{100 \times \text{TD}}{R \times T} $$ $$ \text{Amount} = \text{PW} + \text{TD} $$ ### Step-by-Step Solution - Given True Discount (TD) = ₹ 189 - Rate (R) = 16% - Time (T) = 9 months = $\frac{9}{12}$ years = $\frac{3}{4}$ years - Find the Present Worth (PW): $$ \text{PW} = \frac{100 \times 189}{16 \times (\frac{3}{4})} $$ $$ \text{PW} = \frac{18900}{12} = 1575 $$ - Calculate the Amount: $$ \text{Amount} = 1575 + 189 = 1764 $$ ### Exam Strategy & Shortcut Using the direct relationship for Amount: $$ \text{Amount} = \text{TD} \times \frac{100 + (R \times T)}{R \times T} $$ $$ \text{Amount} = 189 \times \frac{100 + 12}{12} = 189 \times \frac{112}{12} $$ Cancel common terms: $189 \times (\frac{28}{3}) = 63 \times 28 = 1764$. This saves calculating the intermediate PW step. ### Common Pitfall Selecting option (c) ₹ 1575, which is merely the present worth, rather than the final amount of the bill. ### Final Answer Therefore, the correct answer is **₹ 1764**.