The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time? Choose one.
A) 3 months B) 4 months C) 5 months D) 6 months E) None of these
Explanation :   Bankers Discount, BD = Simple Interest on the face value of the bill for unexpired time.   True Discount, TD = Simple Interest on the present value for unexpired time.   Simple Interest on Rs. 1600 = True Discount on Rs.1680   =&gt; Rs. 1600 is the Present Worth (PW) of Rs. 1680   =&gt; Rs. 80 is the Simple Interest of Rs.1600 at 15%   ⇒80=(1600×T×15)/100   ⇒ 80 = 16 × T × 15   ⇒ 5 = T × 15   ⇒ 1 = T × 3   =&gt; T = 1/3 year = 12/3= 
<gadget id="calculator">12/3</gadget>
<output>4</output>
4 months Answer : Option 4 months
<result>B</result>
The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?