Discussion
The true discount on a bill due 9 months hence at 12% per annum is Rs. 540. Find the present worth of the bill.
Answer: D
True discount is simple interest on the present worth, so the present worth follows directly.
With \( T = \dfrac{9}{12} = 0.75 \) year at 12%:
\[ k = \frac{12 \times 0.75}{100} = 0.09 \]
\[ \text{PW} = \frac{\text{TD}}{k} = \frac{540}{0.09} = \text{Rs. } 6000 \]
The bill itself is \( 6000 + 540 = \text{Rs. } 6540 \). Dividing the discount by \( k \) always lands on the present worth; the face value needs the discount added back.
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