 Hello friends, and how are you all today? My name is Priyanka and I shall be helping you with the following question says a bill was drawn in April for 2004 at eight months after date it was discounted on July 14 2004 at five percent per annum if Bankel's gain is rupees 2000 find the face value of the bill Let the face value of the bill for two rupees yes Further we are given Bankel's gain that is BG equal to rupees 200 Further we are given rate of interest as five percent per annum now let us Find out the due date of the bill that is the legal due date we are given the date of drawing the bill as 4th April 2004 so the legal due date of the bill will be for eight months 4th December 2004 Plus three days of grace though it is equal to 7th December 2004 the period of this bill was eight months further we are given Discounting date of the bill as July 14th 2004 so period of discount is for the month of July August Timber tober November and December It is in the month of July there are 17 days left the month of August there are 31 then 30 then 31 30 and then here it was Legally due date was 7th December so here month of December there are seven days so in all there are 146 days That on converting in here will give us two by five Here now we know that Bankers gain is equal to bankers discount minus True discount So we have bankers gain is given to us as 200 bankers discount is Phase value of the bill into weight that is five upon hundred that can be written as one upon 20 into period of discount that is two by five Minus again s into r into t upon 1 plus R into t What we need to do further is we just need to simplify it We have 200 equal to s upon 50 full upon 1 minus s upon 50 upon 1 plus one upon 50 further We have 200 equal to s upon 50 minus s upon 50 divided by 51 upon 50 that is 200 is equal to s upon 50 minus s upon 50 1 That is 200 is equal to LCM will be 15 to 51 and the numerator now we have 51 s minus 50 s So we have 200 into 50 into 51 equal to s which Simplifying comes out to be five black ten Thousand that is equal to s which is the face value of the bill. So therefore face value of the bill is rupees five black ten Thousand right so this completes the session. Hope you understood it well You take care of your calculations and have a very nice day ahead