 Hi and how are you all today? My question says if bankers gain on a bill is 1 by 81 of the bankers discount at 5% find the discounted period of the bill. So let's solve the given question. Now here, let the discounted period be t and let the face value of the bill be s. Right? We are given the weight of interest as 5% per annum that will be equal to 5 upon 100 that can be further written as 1 upon 20 per annum. We are given that bankers gain is 1 by 81 of bankers discount. Isn't it? We know that bankers gain is equal to what? It is bankers discount minus true discount, isn't it? So we have bankers discount minus true discount equal to 1 by 81 of bankers discount. Now here BD is bankers discount and TD is true discount, don't forget. That can be further written as bankers discount minus bankers discount upon 81 is equal to true discount. We have just rearranged the given equation that on taking the LCM we have 80 upon 81 bankers discount is equal to true discount. Let this be equation number one. We know that true discount is equal to bankers discount upon 1 plus RT, right? Let this be the second equation. Now, equating the first and the second equation we get 80 upon 81 BD is equal to BD upon 1 plus RT. Let us simplify it. So we have 80 upon 81 equal to 1 upon 1 plus RT. Let us substitute the value of R that is found out above as 1 upon 20. On further solving it we have 80 upon 81 equal to 20 upon 20 plus T that can be further written as 4 into 20 plus T is equal to 81. 80 plus T, sorry 4T is equal to 81, 4T is equal to 1 and T is equal to 1 by 4 of an year. Therefore, the discounted period is one fourth of a year that is 3 months, right? So this completes the session. Hope you understood the question well and enjoyed it while we were solving it. Have a nice day.