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# Note for Banker's Discount - BD by Placement Factory

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Banker's Discount Introduction As discussed in the chapter of "True Discount", i f the borrower returns the loan before the due date, he has to pay slightly less money than the amount due. This less money is the benefit given to the borrower for earlier repayment and is known as True Discount. In fact true discount is the "interest calculated on the Present Worth of the Due Amount for due periodfrom right new ". But, suppose the debtor (who has taken the loan) is not able to clear the loan before it is due, but the creditor (who has given the loan) requires money, he has no right to ask the debtor to pay back before the bill is due. The only way the creditor can raise money is to go to a bank and encash the bill. During encashment of the bill, the bank will charge a simple interest on the amount mentioned in the bill for the unexpired time. Now look at some important terms that are frequently used in this chapter. 1. Face value: The amount mentioned in the bill is called face value. 2. Banker's Discount: (B.D.) It is the simple interest on the amount mentioned in the bill (or face value) for the period from the date on which the bill was encashed and the legally due date. "Banker's Discount is slightly more than True Discount ' 3. Banker's Gain (B.G.): The difference between Banker's Discount (B.D) and True Discount (TD) is known as Banker's Gain. Note: 1. Banker's Discount, True Discount and Banker's Gain are on the unexpired (unutilised) time of the bill and face value (or actual amount) of the bill. 2. In Arithmetic 'Discount' always means 'True Discount' unless Banker's Discount is expressly meant. Banker's Discount is generally denoted by BD. Important Results (i) Banker's Discount (BD) = Simple interest on bill for its unexpired time Bill amount (A) x Rate (R) x Unexpired Time (T) (ii) 100 Banker's Gain (BG) = Simple interest on True DisT.DxRxT count(TD)= (iif) 1 Q ( ) = Banker's Discount (B.D) - True Discount (TD.) True Discount ( T D . ) = Bill Amount (A) - Present Worth (PW) = Simple Interest on Present Worth (PW) PWxRxT 100 Rule 1 To find the Banker's Discount when Bill Amount (A), Time (T) and Rate (R) are given. AxRxT Banker's Discount = 100 Illustrative Example EK Find the banker's discount on a bill of Rs 2550 due 4 months hence and 6% per annum. Soln: Applying the above formula, we have 2550x6x4 = Rs 51 Banker's Discount = ... 100x12 Exercise 1. 2. 3. The true discount on a bill of Rs 1860 due after 8 months is Rs 60. Find the banker's discount. a)Rs62 b)Rs52 c)Rs60 d) None of these Find the banker's discount on a bill of Rs 12750 due 2 months hence and 3% per annum. a) Rs 63.75 b)Rs61.75 c)Rs 64.75 d)Rs 63.25 The true discount on a bill of Rs 3720 due after 4 months is Rs 120. Find the banker's discount. a)Rsl22 b)Rsl34 c) 124 d) None of these Answers 1. a; Hint: Amount = Rs 1860; True Discount * Rs 60 • Present Worth = Rs 1860 - Rs 60 - Rs 1800

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PRACTICE BOOK ON QUICKER MATHS 716 Answers SI on Rs 1800 for 8 months = Rs 60 1. d; Hint: Present Worth = Rs 1860 - Rs 60 = Rs 1800 \ 100x60 (TD) % = 5% Rate = BG = 1800x 60x60 Z Present Worth 1800 = Rs2 2. a 3. c; Hint: Present Worth = 540 - 90 = Rs 450 Banker's Discount = 1860x5x-2- = R 62 100 Banker's Gain = S .-. Banker's discount = 90 + 18 = Rs 108 [See Note]. 3.c 2. a (TD) Rule 2 A(RT) (TD)' , or, 100(100 + RT) PW ' 2 1 f t f t / l f t n 36x36 = Rsl.62. PW ^ 800 .-. BD = TD + BG = Rs36 + Rsl.62 = Rs37.62 5. b; Hint: Difference between the banker's discount and the true discount = Banker's gain. 4. c; Hint: BG = To find the Banker's Gain (BG) when Bill Amount (A), rime (T) and Rate (R) are given. (I) Banker's Gain = 90x90 — = Rs 18 450 D T N where TD = True Discount, PW = Present Worth 8100x5x-x5xl 4 4 required answer = AxRxT (11) True Discount (TD) = 100 + R T Illustrative Example Rule 3 Ex: Find the banker's gain on a bill of Rs 2550 due 4 months hence at 6% per annum. Soln: Applying the above formula, we have To find theface value (or bill amount) when Banker's Discount (BD) and Time (T) are given. Face value (A) = 2550x 6x Banker's Gain = 100 100+ Rs 1.25. 100 100 + 5x 6x 2550x4 100x102 IOOXBD RxT Illustrative Example = Rel. Ex: I f the B . D on a bill at 4% per annum is Rs 60, find the face value of 6 months bill. Soln: Applying the above formula, we have Note: Banker's Gain = BD - TD [ie if you calculate TD, you can find the Banker's Gain by subtracting TD from BD. 100x60 Face value = 4x- Rs3000 12 Exercise 1. 2. 3. 4. 5. The true discount on a bill of Rs 1860 due after 8 months is Rs 60. Find the banker's gain. a)Rsl.5 b)Rs2.5 c)Rs4 d)Rs2 Find the banker's gain on a bill of Rs 6900 due 3 years hence at 5% per annum simple interest. a)Rsl35 b)Rsl25 _c)Rsl85 d)Rsl45 The true disocunt on a bill of Rs 540 is Rs 90. The banker's discount is: a)Rs60 b)Rsl50 c)Rsl08 d)Rsll0 The present worth of a certain bill due sometime hence is Rs 800 and the true discount is Rs 36. Then, the banker's discount is: a)Rs37 b)Rs 34.38 c)Rs 37:62 d)Rs 38.98 Find the difference between the banker's discount and the true discount on Rs 8100 for 3 months at 5%. a)Rs0.125 b)Rsl.25 c)Rs!2.5 d) None of these Exercise 1. 2. 3. I f the B.D on a bill at 8% per annum is Rs 120, find the face value of 1 year bill. a) Rs 3000 b) Rs 750 c)Rsl500 d)Rs2250 If the B.D on a bill at 5% per annum is Rs 135, find the face value of 9 months bill. a)Rs3600 b)Rs3650 c)Rs2750 d)Rs3250 If the B.D on a bill at 6% per annum is Rs 63, find the face value of 3 months bill. a)Rs415<) b)Rs4200 c)Rs4250 d) None of these Answers !.c 2.'a 3.b

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i Banker's Discount 717 5% being given that the banker's gain is Rs 90. a)Rs550 b)Rs650 c)Rs690 d)Rs600 The banker's gain on a bill due 1 year 4 months hence at Rule 4 To find the Banker's Discount if True Discount, Rate and Time are given. Banker's Discount True Discount 1 + Rate x Time = TD 1 + 2. 7^-% per annum simple interest is Rs 16. Find the sum. RT Illustrative Example a)Rsl760 b)Rsl560 c)Rsl660 d)Rsl860 The banker's gain on a bill due 1 year hence at 5% is Re 1. The true discount is: Ex: a)Rsl5 Too 100 If the TD on a certain sum due 9 months hence at 4% is Rs 20. What is the BD on the same sum for the same time and at the same rate? Soln: Applying the above formula, we have BD=20 1 + 4x9 = Rs 20.60. 12x100 Exercise 1. 2. 3. If the true discount on a certain sum due 6 months hence at 6% is Rs 36, what is the banker's discount on the same sum for the same time and at the same rate? a) Rs 37.80 b)Rs 27.08 c)Rs 37.08 d) None of these The banker's discount on a bill due 6 months hence at 6% is Rs 37.08. Find the true discount. a)Rs38 b)Rs32 c)Rs36 d)Noneofthese ,1 If the TD on a certain sum due 1 — years hence at 8% is 3. d)Rs5 90x100 1. c; Hint: True Discount = ——2— Rs 600 3x5 .-. Banker's Discount = True Discount + Banker's Gain = Rs600 + Rs90 = Rs690 16x100 2. a; Hint: TD = j p= = Rs 160 —x — 3 2 = BD = Rsl60 + Rs 16 = R s l 7 6 Sum = 176x100 = Rsl760 4 15 —x — 3 2 3.b; Hint: TD = BGxlOO 1x100 RxT 5x1 [See Rule 3] = Rs20. Rule 6 To find the Banker's Discount when True Discount and the Face Value are given. Banker's Discount Answers 1. c , 100 1 A A 3708 .-. TD 103 AxTD ~~ Bill Amount or Face Value-True Discount A-TD Illustrative Example Rule 5 Ex: To find Banker's Gain (BG) when True Discount (TD), Rate (R) and Time (T) are given. Banker's Gain (BG) True Discount x Rate x Time 100 Bill Amount or Face Value x True Discount = Rs36 3. c If the true discount on a bill for Rs 480 is Rs 80. Find the bankers' discount. Soln: Applying the above formula, we have TD x R x T ~ Banker's Discount 100 Illustrative Example Exercise Ex: 1. If the TD on a certain sum due 4 years hence at 4% is Rs 250. What is the Banker's gain (BG) on the same sum for the same time and at the same rate? Soln: Applying the above theorem, we have 2. 250x4x5 Banker's Gain = — — = Rs 50. 3. Exercise 1. c)Rs25 Answers Rs 25. What is the BD on the same sum for the same time and at the same rate? a) Rs 27.50 b)Rs 28.50 c)Rs28 d)Rs 27.25 2. c; Hint: 37.08 = TD b)Rs20 Find the banker's discount on a bill due 3 years hence at 1 480x80 480x80 480-80 400 = Rs96 I f the true discount on a bill for Rs 560 is Rs 60. Find the bankers' discount. a)Rs67.2 b)Rs68 c)Rs68.5 d)Rs67.5 If the true discount on a bill for Rs 450 is Rs 50. Find the bankers' discount. a) Rs 66.25 b)Rs 56.25 c)Rs 56.50 d) None of these If the true discount on a bill for Rs 670 is Rs 70. Find the bankers' discount. a)Rs88 b)Rs76 c)Rs78 d)Rs80

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PRACTICE BOOK ON QUICKER MATHS 718 Answers I.a 2.b 3.c Rule 7 To find present worth, when Banker's Gain (BG), Time (T) and Rate (R) are given: 3. H.NJ Present worth = Banker's Gain x RT Illustrative Example 4. EK The banker's gain on a bill due 4 years hence at 5% is Rs 40. Find the present worth of the bill. Soln: Applying the above formula, we have hence is Rs 165. Find the true discount and the banker's gain. a)Rsl50,Rsl5 b)Rsl60,Rs5 c)Rsl45,Rs20 d) None of these The present worth of a certain bill due some time hence is Rs 1600 and the true discount on the bill is Rs 160. Find the banker's discount and the extra gain the banker would make in the transaction. a)Rsl76,Rsl8 b)Rsl86,Rsl6 c)Rsl76,Rsl6 d) None of these The present worth of a sum due sometimes hence is Rs 576 and the banker's gain is Re 1. The true discount is: a)Rsl6 b)Rsl8 c)Rs24 d)Rs32 Answers 100x100 Present Worth = 4 0 x 20x20 = 25 x40 = Rsl000. l.a;Hint:TD= V P W X B G 110x110 (TP) or, BG = = Rs 11 PW 1100 .-. BD = BG + TD = R s ( l l + 110) = Rsl21. Exercise 1. 2. 3. The banker's gain on a bill due 2 years hence at 5% is Rs 8, find the present worth of the bill. a)Rs800 b)Rs650 c)Rs750 d)Rs850 The banker's gain on a bill due 2 years hence at 6% is Rs 36. Find the present worth of the bill. a)Rs2400 b)Rs2550 c)Rs2440 d)Rs2500 The banker's gain on a bill due 3 years hence at 5% is Rs 45. Find the present worth of the bill. a)Rs2000 b)Rs2200 c)Rs2250 d) None of these BDxTD 2. a; Hint: Sum = B D - T D TD Sum BDxTD BG 1650 10 BG 1 BD 165 i.e., if BG is Re 1, TD = Rs 10 or BD = Rs 11 .-. If BD is Rs 11, TD = Rs 10 Answers 10 If BD is Rs 165,TD = Rs „ 100x100 1. a; Hint: Present Worth = 8 x — — = R s goo 10x10 3. a 2.d xl65 11 Rs 150 Also BG = Rs (165- 150) = Rsl5. 3. c; Hint: 160= V l 6 0 0 x B G Rule 8 160x160 To find True Discount when present worth and Banker's Gain are given. •• True Discount'= ^ P W x B G .-. Banker's Discount = 160 + 16 = Rs 176. [ v BD=TD+BG]. Illustrative Example Ex: The present worth and the banker's gain on a bill is Rs 160000 and Rs 25 respectively. Find the discount of the bill. Soln: Applying the above formula, we have True Discount = Vl60000x25 =400x5 = Rs2000. Exercise 1. 2. 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 extra gain the banker would make in the transaction. a)Rsll,Rsl21 b)Rs21,Rsl31 c) Rs 12, Rs 122 d) None of these The banker's discount on Rs 1650 due a certain time B G = - 7 6 ^ = R s 1 6 4. c;Hint:TD= ^ ( P W x B G ) = ^(576x1) =Rs24. Rule 9 Tofind the sum or Bill Amount when the banker's discount and the true discount are given. Bill Amount (A) = Ban ker's Discount x True Discount . Discount - True Discount B a nk e r s Banker's Discount x True Discount Banker's Gain Illustrative Example Ex: The bankers discount and the true discount on a certain sum is Rs 50 and Rs 40. Find the sum.