The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain?

Sum = (B.D. x T.D.) / (B.D. - T.D.) = (B.D. x T.D.) / B.G.
∴ T.D. / B.G. = Sum / B.D. = 1650/165 = 10/1
i.e., if B.G. is Re. 1, T.D. = Rs. 10 or B.D. = Rs. 11
∴ if B.D. is Rs. 11, T.D. = Rs. 10
If B.D. is Rs. 165, T.D. = Rs. (10/11) x 165 = Rs. 150
Also, BG = Rs. (165 - 150) = Rs. 15