Q.The banker's discount on a bill due 9 months hence at 8% per annum is ₹600. Find the face value of the bill.

The banker's discount is simple interest on the face value, so reverse the interest formula to recover the face value. …

Given $BD = 600$, $r = 8\%$, $t = \dfrac{9}{12} = 0.75$ year, so $rt = 8 \times 0.75 = 6$.

Since $BD = \dfrac{F\,r\,t}{100}$, rearrange for $F$:

$F = \dfrac{100 \times BD}{r\,t} = \dfrac{100 \times 600}{6} = \dfrac{60000}{6} = 10000.$ …

Using $t = 9$ months as-is, or applying the true-discount formula (denominator $100 + rt$) when the data given is the banker's …