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?  Choose the correct choice from the following answers:
A) Sum = Rs.400 and Time = 5 years
B) Sum = Rs.200 and Time = 2.5 years
C) Sum = Rs.400 and Time = 2.5 years
D) Sum = Rs.200 and Time = 5 years
E) None of these
Explanation :   BD = Rs.100   TD = Rs.80   R = 10%   F = BD ×TD/(BD – TD)=100×80/(100–80)=100×80/20=Rs. 400   BD = Simple Interest on the face value of the bill for unexpired time =FTR/100   ⇒100 = (400×T×10)/100   ⇒100 = 4 × T × 10 ⇒10 = 4 × T   ⇒ T = 10/4= 
<gadget id="calculator">10/4</gadget>
<output>5/2 = around 2.5</output>
2.5 years Answer : Option Sum= Rs.400 and Time = 2.5 years
<result>C</result>
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?