Ex. 1. A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives. Sol. 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.

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

Ex. 2. If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker's discount on the same sum for the same time and at the same rate?

Sol. B.G. = S.I. on T.D. = Rs.(120 x 15 x 1/2 x 1/100) = Rs. 9. (B.D.) - (T.D.) = Rs. 9. B.D. = Rs. (120 + 9) = Rs. 129.

Ex. 3. The banker's discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs. 1872 for the same time at the same rate. Find the time. Sol. 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.

Ex. 4. The banker's discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the sum and the rate percent. Sol. Sum =[( B.D.*T.D.)/(B.D.-T.D.)] = Rs.[(120x110)/(120-110)] = Rs. 1320. Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120. Rate =[(100 x120)/( 1320 x 2/3)% = 13 7/11%.

Ex. 5. The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker's discount and the banker's gain. Sol. T.D. =√(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.

Ex. 6. The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain. Sol. Sum = [(B.D.xT.D.)/ (B.D.-T.D.)] = [(B.D.xT.D.)/B.G.] T.D./B.G. = Sum/ B.D. =1650/165 =10/1 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.

Ex. 7. What rate percent does a man get for his money when in discounting a bill due 10 months hence, he deducts 10% of the amount of the bill? Solution: Let amount of the bill = Rs.100 Money deducted =Rs.10 Money received by the holder of the bill = Rs.100-10 = Rs.90 SI on Rs.90 for 10 months = Rs.10 Rate =[(100*10)/(90*10/12)%=13 1/3%

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Ex. 1. A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives.

Sol.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.

Ex. 2. If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker's discount on the same sum for the same time and at the same rate?

Sol.B.G. = S.I. on T.D.

= Rs.(120 x 15 x 1/2 x 1/100)

= Rs. 9.

(B.D.) - (T.D.) = Rs. 9.

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

Ex. 3. The banker's discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs. 1872 for the same time at the same rate. Find the time.

Sol.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.

Ex. 4. The banker's discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the sum and the rate percent.

Sol.Sum =[( B.D.*T.D.)/(B.D.-T.D.)]

= Rs.[(120x110)/(120-110)]

= Rs. 1320.

Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120.

Rate =[(100 x120)/( 1320 x 2/3)%

= 13 7/11%.

Ex. 5. The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker's discount and the banker's gain.

Sol. T.D. =√(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.

Ex. 6. The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain.

Sol.Sum = [(B.D.xT.D.)/ (B.D.-T.D.)]

= [(B.D.xT.D.)/B.G.]

T.D./B.G. = Sum/ B.D.

=1650/165

=10/1

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.

Ex. 7. What rate percent does a man get for his money when in discounting a bill due 10 months hence, he deducts 10% of the amount of the bill?

Solution: Let amount of the bill = Rs.100Money deducted =Rs.10

Money received by the holder of the bill = Rs.100-10 = Rs.90

SI on Rs.90 for 10 months = Rs.10

Rate =[(100*10)/(90*10/12)%=13 1/3%