The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.100 and Rs.80 respectively. What is the sum and the time?

BD = Rs.100
TD = Rs.80
R = 10%

$F=\frac{BD\times TD}{BD-TD}=\frac{100\times 80}{100-80}=Rs.400$ 

BD = Simple interest on the face value of the bill for unexpired time= FTR/100

$\Rightarrow 100=\frac{400\times T\times 10}{100}$

=> T = 2.5 years