The true discount on a bill due 9 months hence at 12% per annum is ` 540. Find the amount of the bill and its present worth.
Answer
Answer (as printed):
Explanation
Let the sum be ₹$x$. Then, $$\frac{x\times\text{R}\times\text{T}}{100+(\text{R}\times\text{T})}=\text{T.D.}\Rightarrow\frac{x\times12\times\frac{3}{4}}{100+\left(12\times\frac{3}{4}\right)}=540\Rightarrow x=\left(\frac{540\times109}{9}\right)=₹6540.$$ $$\therefore\ \text{Amount}=₹6540.$$ $$\text{P.W.}=₹(6540-540)=₹6000.$$
Explanation as extracted from the printed page; notation may be imperfect.