A bill is discounted at 10% per annum. If banker's discount is allowed, at what rate percent should the proceeds be invested so that nothing will be lost?

Solution(By Examveda Team)

Let the amount = Rs. 100
Then BD = Rs.10 (∵ banker's discount, BD is the simple Interest on the face value of the bill for unexpired time and bill is discounted at 10% per annum)
Proceeds = Rs. 100 - Rs. 10 = Rs. 90
Hence we should get Rs. 10 as the interest of Rs. 90 for 1 year so that nothing will be lost
$$\eqalign{ & \Rightarrow 10 = \frac{{90 \times 1 \times R}}{{100}} \cr & \Rightarrow R = \frac{{10 \times 100}}{{90}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{100}}{9} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\,\% \cr} $$