The banker's gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount

is:

T.D = (B.G * 100) / (Rate * Time)

(24*100) / (10 * 2)

= 120.

P.W = (100 *T.D) / (Rate * Time)

= (100 * 120) /(10 * 2)

= 600

Sum = (B.D * T.D) / (B.D) -(T.D)

= (120 * 110) / (120 -110)

= 1320

S.I on Rs 1800 = T.D on Rs 1872

P.W of Rs 1872 is Rs 1800

Rs 72 is S.I on Rs 1800 at 12%

Time = (100 * 72)/(12 * 1800)

= 1/3 years = 4 months

B.G = S.I On T.D

      = Rs. (120 * 15 * 1/2 * 1/100)

      = Rs.9

B.D - T.D = Rs.9

B.D = Rs.(120 +9) = Rs.129

T.D. =Ö(P.W.*B.G)

B.G. =(T.D.)2/ P.W.      

       = Rs.[(110x110)/ 1100]

       = Rs. 11.

B.D.= (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.

S.I. on Rs. 1800 = T.D. on Rs. 1872.

P.W. of Rs. 1872 is Rs. 1800.

Rs. 72 is S.I. on Rs. 1800 at 12%.

Time =[(100 x 72)/ (12x1800)]year

        =1/3year = 4 months.

   Sum = [(B.D.xT.D.)/ (B.D.-T.D.)]

              = [(B.D.xT.D.)/B.G.]

T.D./B.G.  = Sum/ B.D.

   =1650/165

               =10

Thus, if B.G. is Re 1, T.D. = Rs. 10.

If B.D.is Rs. ll, T.D.=Rs. 10.

If B.D. is Rs. 165, T.D. = Rs. [(10/11)xl65]

            =Rs.150

 And, B.G. = Rs. (165 - 150) = Rs, 15.

Face value of the bill = Rs. 6000.

Date on which the bill was drawn = July 14 at 5 months. Nominally due date =                  December 14.

Legally due date = December 17.

Date on which the bill was discounted = October 5.

Unexpired time  : Oct.               Nov.                Dec.

                                 26  +               30  +              17     = 73 days  =1/ 5Years

 B.D. = S.I. on Rs. 6000 for 1/5 year

= Rs.   (6000 x 10 x1/5 x1/100)= Rs. 120.

T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]

            =Rs.(12000/102)=Rs. 117.64.

B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36.

Money received by the holder of the bill = Rs. (6000 - 120) = Rs. 5880.