 Hello friends and how are you all doing today? The question says a bill for Rs. 5,050 is drawn on April 13, 2005. It is discounted on July 4, 2005 at 5% per annum. If the bankers gain in the transaction is Rs. 50,000, find the nominal date of majority of the bill. Here we are given the face value of the bill that is S as it reads 5,050. Date of drawing of the bill is given to us as April 13, 2005. Rate of interest that we take as R is given to us as 5% per annum which can be written as 5 upon 100. Also we are given bankers gain as 50. Now we need to proceed with the solution. We can write bankers gain as bankers discount minus true discount also. So it is equal to 50%. Now we know that the formula for bankers discount is SRT. So SRT minus SRT upon 1 plus RT that is the true discount is equal to 50 upon 100. Further on taking SRT common we have 1 minus 1 upon 1 plus R which is further equal to SRT 1 plus RT minus 1 upon 1 plus RT equal to 50 upon 100. Further simplifying we reached this step. Now we have S5050R as 5% and we need to find out time. So let us simplify it. We have 5050 into 25 upon 10000 into T square upon 100 plus 5T upon 100 equal to 5 upon 100. Now we have 5050 into 25 gives us upon we have multiplied this denominator by 100. Now further we have 126250T square into 100 equal to 50000 plus 2500T that is after cross multiplying. Now we have 12625000T square minus 2500 minus 50000 equal to 0. Now on dividing the whole equation by 2500 we have 5050T square minus it was having T with it minus T minus 20 equal to 0.