 Hello students, let's work out the following problem. It says that true discount and the bankers gain on a certain bill of exchange due after a certain period of time are respectively Rs 700 and Rs 17.50. Find the face value of the bill. So let's now start the solution. We have to find the face value of the bill. So let the face value of the bill be Rs s and let the bill be due after n years. Now the true discount is given by the formula s into r into t upon 1 plus r into t where r is the rate of interest and s is the face value of the bill and it is given to be Rs 700. Also bankers gain is given by the formula s into r into t upon 1 plus r into t into r into t and this is given to be Rs 17.50. Let's name this as 1 and this as 2 so we have s into r into t upon 1 plus r into t is 700 so from 1 and 2 we have 700 into r into t is equal to 17.50 so this implies r into t rt is equal to 17.50 upon 700 so this implies rt is equal to 17.50 divided by 700 is equal to 0.025. Now we will substitute the value of rt in 1 now put rt is equal to 0.025 in 1 so we have s into 0.025 upon 1 plus 0.025 is equal to 700 so this implies s into 0.025 is equal to 700 into 1 plus 0.025 so this implies s is equal to 700 plus 700 into 0.025 upon 0.025 so this is again equal to 700 plus 17.5 divided by 0.025 this is again equal to 717.5 upon 0.025 divided by 717.50 by 0.025 we have 2807 plus 28700 hence the face value of the bill is equal to rupees 28700 so this completes the question and the session by for now take care have a good day