Question 1

Find true discount from banker’s gain: The banker’s gain on a bill due 1 year hence at 10% per annum is ₹20. What is the true discount?

Accepted Answer

Introduction / Context:Given BG and r t, we can find the face value and then TD. Alternatively, use the relation BG = TD * r t to get TD directly once r t is known. Given Data / Assumptions:t = 1 year, r = 10% ⇒ r t = 0.10; BG = ₹20. Concept / Approach:Use either of two paths: (1) BG = TD * r t ⇒ TD = BG / (r t) = 20 / 0.10 = ₹200 (2) BG = A * (r t)^2 / (1 + r t) ⇒ find A, then TD = A * (r t)/(1 + r t) Step-by-Step Solution: TD = 20 / 0.10 = ₹200 Verification / Alternative check:From (2): 20 = A * 0.01 / 1.10 ⇒ A = 2200; TD = 2200 * 0.10 / 1.10 = ₹200 (same result). Final Answer:Rs. 200

Question 2

Find banker’s discount from banker’s gain: The banker’s gain on a sum due 3 years hence at 12% per annum is ₹360. Compute the banker’s discount.

Accepted Answer

Introduction / Context:From BG and r t we can find the face value A, and then compute BD = A * r t. This question emphasizes the utility of the BG identity in reverse. Given Data / Assumptions:t = 3 years; r = 12% ⇒ r t = 0.36; BG = ₹360. Concept / Approach: BG = A * (r t)^2 / (1 + r t) ⇒ A = BG * (1 + r t) / (r t)^2 Then BD = A * r t Step-by-Step Solution: A = 360 * 1.36 / (0.36)^2 = 360 * 1.36 / 0.1296 = ₹3777.78 BD = A * 0.36 ≈ 3777.78 * 0.36 = ₹1360 Verification / Alternative check:TD = BD − BG ≈ 1360 − 360 = ₹1000; TD should also equal A * 0.36 / 1.36 ≈ 1000 (checks). Final Answer:Rs. 1360

Question 3

Find the rate percent from true discount and term: The true discount on ₹2562 due 4 months hence is ₹122. Determine the annual simple interest rate.

Accepted Answer

Introduction / Context:With TD, face amount A, and time t, we can solve for r t and hence for the annual rate r. The derivation is algebraic and direct from the definition of true discount. Given Data / Assumptions: A = ₹2562 TD = ₹122 t = 4 months = 1/3 year Concept / Approach: TD = A * (r t) / (1 + r t) Let x = r t ⇒ TD = A * x / (1 + x) Step-by-Step Solution: 122 = 2562 * x / (1 + x) ⇒ x = 122 / (2562 − 122) = 122 / 2440 = 0.05 r = x / t = 0.05 / (1/3) = 0.15 = 15% per annum Verification / Alternative check:TD recompute: 2562 * 0.05 / 1.05 = ₹122 (exact). Why Other Options Are Wrong:12%, 13%, 14% yield different TDs when substituted back into the formula for t = 4 months. Common Pitfalls:Using months without converting to years; always express t in years for simple interest formulas. Final Answer:15

Question 4

Present worth and true discount (simple interest): A sum of Rs 9300 is due exactly 3 years from now at a simple interest rate of 8% per annum. Compute the present worth (i.e., the amount which, if invested today at 8% simple interest, will grow to R…

Accepted Answer

Introduction / Context:This is a standard present worth (PW) and true discount (TD) question under simple interest. PW is the amount today that will accumulate to the future sum at the stated rate and time. TD is the difference between the face value due at maturity and the PW. Given Data / Assumptions: Sum due (face value) S = Rs 9300. Simple interest rate r = 8% per annum. Time to maturity t = 3 years. Concept / Approach:Under simple interest, PW = S / (1 + r * t). True Discount TD = S - PW = S * r * t / (1 + r * t). These formulas follow directly from the linear growth of simple interest with time. Step-by-Step Solution: 1) Compute 1 + r * t = 1 + 0.08 * 3 = 1.24.2) PW = 9300 / 1.24 = Rs 7500.3) TD = 9300 - 7500 = Rs 1800. Verification / Alternative check:Accruing PW for 3 years: 7500 * (1 + 0.08 * 3) = 7500 * 1.24 = 9300 ✔️, confirming the PW/TD values. Why Other Options Are Wrong:Rs 1860, 1850, 1890 do not satisfy TD = S - PW with PW computed at the stated rate and time; only Rs 1800 fits exactly. Common Pitfalls:Using compound interest (not asked), or mistakenly taking TD = S * r * t (that is the banker’s discount, not the true discount). Final Answer:True Discount = Rs 1800; Present Worth = Rs 7500 (correct option for TD is Rs 1,800).

Question 5

Present worth of two equal half-yearly instalments: A total of Rs 702 is to be paid in two equal instalments due at the end of 6 months and 12 months respectively. If interest is 8% per annum (simple interest), find the present worth today of the tw…

Accepted Answer

Introduction / Context:When a total amount is split into equal instalments due at different future times, the present worth (PW) is the sum of the discounted values of each instalment to today under simple interest. Given Data / Assumptions: Total due in two instalments = Rs 702 → each instalment = Rs 351. Instalment due dates: 6 months and 12 months. Simple interest rate r = 8% p.a. Concept / Approach:Under simple interest, PW = F / (1 + r * t) for each cash flow, with t in years. Sum the two present values for the total PW. Step-by-Step Solution: Instalment 1 (at 0.5 year): PW1 = 351 / (1 + 0.08 * 0.5) = 351 / 1.04 = 337.50.Instalment 2 (at 1 year): PW2 = 351 / (1 + 0.08 * 1) = 351 / 1.08 = 325.00.Total PW = 337.50 + 325.00 = Rs 662.50. Verification / Alternative check:If invested today: 337.5 grows to 351 in 6 months at 8% p.a.; 325 grows to 351 in 12 months at 8% p.a. Sum at those due dates matches required instalments, validating the PW. Why Other Options Are Wrong:Values like 650, 640, 675 do not match the exact discounting of each instalment under the given rate and timings. Common Pitfalls:Discounting both instalments with the same time; using compound interest unintentionally; or dividing Rs 702 by 1.08 only (ignoring the 6-month instalment timing). Final Answer:Rs 662.50

Question 6

From PW and true discount, find banker’s discount and banker’s gain: The present worth (PW) of a bill due sometime hence is Rs 1600, and its true discount (TD) is Rs 160. Find the banker’s discount (BD) and the extra gain (banker’s gain, BG).

Accepted Answer

Introduction / Context:Relations among present worth (PW), true discount (TD), banker’s discount (BD), and banker’s gain (BG) under simple interest are standard results used in banker’s discount problems. Given Data / Assumptions: PW = Rs 1600. TD = Rs 160. Face value S = PW + TD = 1760. Concept / Approach:Let x = r * t (rate × time). Then TD = S * x / (1 + x) and BD = S * x. Also BG = BD − TD = S * x^2 / (1 + x). We can find x from PW and TD without knowing r or t individually. Step-by-Step Solution: Since PW = S / (1 + x), we have 1600 = 1760 / (1 + x) → 1 + x = 1760 / 1600 = 1.1 → x = 0.1.BD = S * x = 1760 * 0.1 = Rs 176.BG = BD − TD = 176 − 160 = Rs 16. Verification / Alternative check:TD = S * x / (1 + x) = 1760 * 0.1 / 1.1 = 160 ✔️; BG = S * x^2 / (1 + x) = 1760 * 0.01 / 1.1 = 16 ✔️. Why Other Options Are Wrong:Rs 176, Rs 18 gives a BG inconsistent with the identity BG = BD − TD; Rs 186, Rs 16 implies x > 0.1 and contradicts PW. Common Pitfalls:Using BD = TD or mixing up PW with face value; forgetting that x = r * t and cancels in ratios. Final Answer:Banker’s Discount = Rs 176; Banker’s Gain = Rs 16

Question 7

Find the discount date from the rebate received: A bill for Rs 17,850 is nominally due on 21 May 1991. Its holder receives Rs 357 less than the amount of the bill by discounting it at 5% per annum (banker’s discount). On which date was the bill disc…

Accepted Answer

Introduction / Context:When a bill is discounted at banker’s discount, the rebate equals S * r * t where t is the time (in years) from discount date to the maturity (due date including days of grace). We can recover the time from the rebate and then count back from maturity to the discount date. Given Data / Assumptions: Face value S = Rs 17,850. Rebate BD = Rs 357 at r = 5% p.a. Nominally due on 21 May 1991; assume 3 days grace → maturity ≈ 24 May 1991. Concept / Approach:BD = S * r * t → t = BD / (S * r). Convert t to days and count backward from the maturity date to find the discount date (calendar approximation with ordinary year used). Step-by-Step Solution: t = 357 / (17850 * 0.05) = 357 / 892.5 = 0.4 year ≈ 0.4 * 365 ≈ 146 days.Maturity ≈ 24 May 1991. Counting back ~146 days lands near 29 Dec 1990 (standard textbook alignment with ordinary simple-interest day count). Verification / Alternative check:Using 360-day convention gives ~144 days, still placing the discount date very close to the last days of December 1990; 29 Dec 1990 is the accepted keyed value for this dataset. Why Other Options Are Wrong:Dec 30, 1989 is a year too early; Dec 19, 1990 yields an interval too long for the given rebate at 5% on this face value. Common Pitfalls:Forgetting 3 days of grace; using true discount instead of banker’s discount; mixing 360 vs 365 without checking reasonableness against options. Final Answer:December 29, 1990

Question 8

Zero-loss investment rate against banker’s discount: A bill is discounted at 5% per annum (banker’s discount) for its full term of 1 year. At what annual simple-interest rate should the proceeds be invested for the same term so that there is no loss…

Accepted Answer

Introduction / Context:When a bill is discounted at rate r for term t, the holder receives the proceeds P = S(1 − r t). To avoid loss, investing P for time t at rate i should grow exactly back to S. This determines a relationship between i and r. Given Data / Assumptions: Banker’s discount rate r = 5% p.a. Term t = 1 year. Simple interest for the re-investment. Concept / Approach:Set future value of proceeds equal to face value: (1 − r t)(1 + i t) = 1. Solve i = r / (1 − r t). For t = 1, i = r / (1 − r). Step-by-Step Solution: i = 0.05 / (1 − 0.05) = 0.05 / 0.95 = 0.052631…As a percent: 5.2631…% = 100/19 % = 5 5/19 %. Verification / Alternative check:Check: Proceeds = 0.95 S. Investing at 100/19 % for 1 year gives multiplier 1 + 1/19 = 20/19. Product: 0.95 * (20/19) = 0.95 * 1.052631… = 1.0000 = S ✔️. Why Other Options Are Wrong:5% or 10% do not satisfy the exact no-loss condition; 55/19 % ≈ 2.894% is far too low. Common Pitfalls:Using i = r instead of i = r / (1 − r t); applying compound interest instead of simple interest on the proceeds. Final Answer:100/19 % per annum (≈ 5.263%)

Question 9

Bill dated July 14, 5 months; discounted Oct 5 at 10%: A bill of ₹ 10,200 is drawn on July 14 at 5 months. It is discounted on Oct 5 at 10% per annum. Find (i) banker’s discount, (ii) true discount, (iii) banker’s gain, and (iv) the proceeds receive…

Accepted Answer

Introduction / Context:We compare banker’s discount (BD) and true discount (TD) for a bill discounted before maturity. BD is computed on the face value for the time from discount date to maturity; TD discounts the face value back at simple interest to obtain present worth; their difference is banker’s gain (BG). Given Data / Assumptions: Face value S = ₹ 10,200. Drawn July 14 at 5 months → nominal due Dec 14; add 3 days grace → maturity Dec 17. Discount date = Oct 5; rate r = 10% p.a. Concept / Approach:Time between Oct 5 and Dec 17 is 73 days. Use t = 73/365 years. BD = S * r * t. TD = BD / (1 + r * t). Proceeds = S − BD. BG = BD − TD. Step-by-Step Solution: t = 73/365 = 0.2 year.BD = 10200 * 0.10 * 0.2 = ₹ 204.TD = 204 / (1 + 0.10 * 0.2) = 204 / 1.02 = ₹ 200.BG = 204 − 200 = ₹ 4; Proceeds = 10200 − 204 = ₹ 9996. Verification / Alternative check:BG = S * r^2 * t^2 / (1 + r t) = 10200 * 0.01 * 0.04 / 1.02 = ₹ 4 ✔️. Why Other Options Are Wrong:Other tuples do not satisfy both BD and TD identities together for t = 0.2 year. Common Pitfalls:Omitting 3 days of grace; using months as 30 days blindly; forgetting that TD = BD / (1 + r t). Final Answer:BD = ₹ 204, TD = ₹ 200, BG = ₹ 4, Proceeds = ₹ 9996

Question 10

BD is 11/10 of TD after 4 years: find the annual rate: For a certain sum due 4 years hence, the banker’s discount is 11/10 times the true discount. Find the simple interest rate per annum.

Accepted Answer

Introduction / Context:Relationships between BD and TD often reduce to simple equations in x = r * t (rate × time). For any sum S, BD/TD = 1 + r * t under simple interest conventions. Given Data / Assumptions: BD = (11/10) * TD. t = 4 years; r = ? Concept / Approach:BD/TD = 1 + r * t. Hence 11/10 = 1 + r * 4 → r = (11/10 − 1) / 4 = (1/10) / 4 = 1/40 = 2.5% p.a. Step-by-Step Solution: 1 + r * 4 = 11/10 → r = (0.1)/4 = 0.025 = 2.5%. Verification / Alternative check:Let S be any positive amount; choosing S cancels in the ratio; result is invariant. Why Other Options Are Wrong:5%, 5.5%, 1.5% do not satisfy the exact ratio for t = 4 years. Common Pitfalls:Using BD − TD instead of BD/TD; forgetting that BD/TD is independent of S. Final Answer:2.5% per annum

Question 11

From PW = Rs 1100 and TD = Rs 110: find BD and banker’s gain: A bill has present worth Rs 1100 and true discount Rs 110. Compute the banker’s discount (BD) and the extra gain (banker’s gain, BG).

Accepted Answer

Introduction / Context:As before, let x = r * t. Then PW = S / (1 + x), TD = S * x / (1 + x), BD = S * x, and BG = BD − TD = S * x^2 / (1 + x). With PW and TD given, all quantities follow directly. Given Data / Assumptions: PW = 1100; TD = 110 → S = 1210. Concept / Approach:From PW = S / (1 + x) and TD = S * x / (1 + x) = PW * x, we get x = TD / PW = 110 / 1100 = 0.1. Hence BD = S * x and BG = BD − TD. Step-by-Step Solution: x = 0.1; S = 1210.BD = 1210 * 0.1 = Rs 121.BG = BD − TD = 121 − 110 = Rs 11. Verification / Alternative check:TD = Sx/(1 + x) = 1210*0.1/1.1 = 110 ✔️; BG = Sx^2/(1 + x) = 1210*0.01/1.1 = 11 ✔️. Why Other Options Are Wrong:Other pairs do not satisfy both the TD identity and the BG definition simultaneously. Common Pitfalls:Confusing TD with BD; using S instead of PW to compute x. Final Answer:BD = Rs 121 and BG = Rs 11

Question 12

BD is 11/10 of TD after 2 years: find the annual rate: For a certain amount due 2 years hence, the banker’s discount equals 11/10 of the true discount. Find the simple interest rate per annum.

Accepted Answer

Introduction / Context:Use the identity BD/TD = 1 + r * t. The face value cancels; only r * t matters. Given Data / Assumptions:BD/TD = 11/10; t = 2 years. Concept / Approach:1 + r * 2 = 11/10 → r = (1/10) / 2 = 1/20 = 5% per annum. Step-by-Step Solution: r = 0.05 = 5% p.a. Verification / Alternative check:Plugging back: 1 + r t = 1 + 0.05*2 = 1.10 = 11/10 ✔️. Why Other Options Are Wrong:1%, 10%, 12% yield BD/TD values not equal to 11/10. Common Pitfalls:Using TD/BD instead of BD/TD or mixing years and months. Final Answer:5% per annum

Question 13

Find BD when TD on a Rs 540 bill is Rs 90: On a bill of Rs 540, the true discount is Rs 90. What is the banker’s discount (for the same term and rate)?

Accepted Answer

Introduction / Context:Given TD and face value S, we can infer x = r * t using PW or directly via TD = PW * x and PW = S − TD. Given Data / Assumptions:S = 540; TD = 90. Concept / Approach:PW = S − TD = 540 − 90 = 450. Then x = TD / PW = 90 / 450 = 0.2. BD = S * x. Step-by-Step Solution: BD = 540 * 0.2 = Rs 108. Verification / Alternative check:TD = BD / (1 + x) = 108 / 1.2 = 90 ✔️. Why Other Options Are Wrong:120, 102, 106 do not satisfy the needed ratio with TD = 90. Common Pitfalls:Taking BD = TD; forgetting to compute PW first. Final Answer:Rs 108

Question 14

Find BD from PW = Rs 1296 and TD = Rs 72: The present worth of a certain bill is Rs 1296 and its true discount is Rs 72. What is the banker’s discount?

Accepted Answer

Introduction / Context:Compute x = r * t from PW and TD, then BD = S * x with S = PW + TD. Given Data / Assumptions:PW = 1296; TD = 72 → S = 1368. Concept / Approach:x = TD / PW = 72 / 1296 = 1/18. Then BD = S * x = 1368 * (1/18). Step-by-Step Solution: BD = 1368 / 18 = Rs 76. Verification / Alternative check:TD = BD / (1 + x) = 76 / (19/18) = 72 ✔️. Why Other Options Are Wrong:72 is the TD (not BD); 74, 4 do not satisfy the identities. Common Pitfalls:Confusing BD and TD; forgetting to add PW + TD to get S. Final Answer:Rs 76

Question 15

Given banker’s gain, find present worth: The banker’s gain on a sum due 3 years hence at 10% per annum is Rs 36. Find the present worth (PW).

Accepted Answer

Introduction / Context:Banker’s gain (BG) equals BD − TD and also equals S * r^2 * t^2 / (1 + r t). From BG we can find the face value S and then the present worth PW = S / (1 + r t). Given Data / Assumptions: BG = Rs 36, r = 10% p.a., t = 3 years. Concept / Approach:Use BG = S * r^2 * t^2 / (1 + r t). Compute S, then PW = S / (1 + r t). Here r t = 0.3 and r^2 t^2 = 0.09. Step-by-Step Solution: 36 = S * 0.09 / 1.3 → S = 36 * 1.3 / 0.09 = 520.PW = S / (1 + r t) = 520 / 1.3 = Rs 400. Verification / Alternative check:BD = S * r * t = 520 * 0.3 = 156; TD = BD / (1 + r t) = 156 / 1.3 = 120; BG = 156 − 120 = 36 ✔️; PW = 520 / 1.3 = 400 ✔️. Why Other Options Are Wrong:300, 500, 350 do not make BD − TD equal to 36 at 10% for 3 years. Common Pitfalls:Using compound interest; forgetting to divide by (1 + r t) when moving from S to PW. Final Answer:Rs 400

Question 16

BG is 9/25 of BD over 2.5 years: find the annual rate: For a certain sum due 2.5 years hence, the banker’s gain equals 9/25 of the banker’s discount. Find the simple annual rate of interest.

Accepted Answer

Introduction / Context:For any bill, BG/BD = (r * t) / (1 + r * t). This comes from BD = S r t and TD = BD / (1 + r t), hence BG = BD − TD = BD * (r * t)/(1 + r * t). Given Data / Assumptions:BG/BD = 9/25; t = 2.5 years. Concept / Approach:Solve r * t / (1 + r * t) = 9/25. Let y = r * t. Then y/(1 + y) = 9/25 → 25y = 9 + 9y → 16y = 9 → y = 9/16 = 0.5625. Hence r = y / t. Step-by-Step Solution: r = 0.5625 / 2.5 = 0.225 = 22.5% p.a. Verification / Alternative check:Check: r t = 0.5625 → BG/BD = 0.5625 / 1.5625 = 9/25 ✔️. Why Other Options Are Wrong:18.12%, 24.13%, 22.22% do not satisfy the exact ratio for t = 2.5 years. Common Pitfalls:Solving for r t but forgetting to divide by t; confusing BG/BD with BD/TD. Final Answer:22.5% per annum

Question 17

Zero-loss investment rate against 10% banker’s discount: A bill is discounted at 10% per annum (banker’s discount) for its full 1-year term. At what simple-interest rate should the proceeds be invested to avoid any loss at maturity?

Accepted Answer

Introduction / Context:For term t under banker’s discount rate r, proceeds are P = S(1 − r t). To have no loss, invest P at rate i for t so that P(1 + i t) = S → (1 − r t)(1 + i t) = 1. Given Data / Assumptions:r = 10% p.a.; t = 1 year; simple interest on proceeds. Concept / Approach:i = r / (1 − r t). With t = 1 → i = r / (1 − r). Step-by-Step Solution: i = 0.10 / 0.90 = 1/9 ≈ 0.1111… = 11 1/9 %. Verification / Alternative check:Proceeds = 0.9 S. Invest at 11 1/9 % for 1 year: multiplier 1 + 1/9 = 10/9. Product = 0.9 * (10/9) = 1.00 → S ✔️. Why Other Options Are Wrong:10% or 11% do not return exactly S; 9 1/9 % is too small. Common Pitfalls:Setting i = r (incorrect); mixing simple and compound interest. Final Answer:11 1/9 % per annum

Question 18

Find discount date from proceeds paid: A banker paid Rs 5767.20 for a bill of Rs 5840, drawn on April 4 at 6 months, at a rate of 7% per annum. On what date was the bill discounted? (Assume 3 days grace.)

Accepted Answer

Introduction / Context:Given face value S, proceeds P, and rate r, we can find the banker’s discount BD = S − P and hence the time t between discount date and maturity. Counting back t from the maturity date yields the discount date. Given Data / Assumptions: S = 5840; P = 5767.20 → BD = 72.80. r = 7% p.a.; drawn April 4 at 6 months → nominal due Oct 4; +3 days grace → maturity Oct 7. Concept / Approach:t = BD / (S * r) (years). Convert to days and count back from Oct 7 to find the calendar date. Step-by-Step Solution: t = 72.8 / (5840 * 0.07) = 72.8 / 408.8 ≈ 0.1782 years ≈ 65 days.Counting back ~65 days from Oct 7 gives approximately Aug 3. Verification / Alternative check:Recompute BD using 65 days: t ≈ 65/365; BD ≈ 5840 * 0.07 * (65/365) ≈ 72.8 ✔️. Why Other Options Are Wrong:Other listed months/dates produce intervals inconsistent with the computed BD at 7%. Common Pitfalls:Omitting days of grace; mixing 360 and 365 day bases without checking against BD. Final Answer:3rd August

Question 19

Cash sale vs 1-year credit at 10% p.a.: Shankara buys a watch for Rs 1,950 in cash and sells it for Rs 2,200 on 1-year credit when the simple interest rate is 10% p.a. What is his gain or loss measured in present terms?

Accepted Answer

Introduction / Context:When selling on credit, compare present worth of the credited price against the cash cost using the market rate of simple interest. Profit or loss should be evaluated at the same time base (present time). Given Data / Assumptions: Cash cost = Rs 1,950. Credit selling price after 1 year = Rs 2,200. Rate r = 10% p.a. Concept / Approach:Present worth PW of Rs 2,200 due in 1 year at 10%: PW = 2200 / (1 + 0.10) = 2200/1.10. Step-by-Step Solution: PW = 2200 / 1.10 = Rs 2000.Profit (present basis) = PW − cost = 2000 − 1950 = Rs 50. Verification / Alternative check:Future value of cost after 1 year at 10% is 1950 * 1.10 = 2145. Comparing future values: 2200 − 2145 = 55. On a present basis, gain is Rs 50; the question asks for present-terms gain. Why Other Options Are Wrong:Rs 55 is the 1-year future-value gain (not present); losses do not apply since PW exceeds cost. Common Pitfalls:Comparing future and present amounts directly; forgetting to discount the credit price. Final Answer:gains Rs. 50

Question 20

Banker’s Discount for a dated bill: A bill for Rs 3000 is drawn on July 14 at 5 months. It is discounted on Oct 5 at 10% p.a. Find the banker’s discount (BD).

Accepted Answer

Introduction / Context:As in dated-bill problems, compute time from discount date to maturity and apply BD = S * r * t. Include 3 days of grace at maturity unless stated otherwise. Given Data / Assumptions: S = Rs 3000. Drawn July 14 at 5 months → due Dec 14; +3 days grace → Dec 17. Discount date Oct 5; r = 10% p.a. Concept / Approach:Time Oct 5 → Dec 17 is 73 days → t = 73/365 = 0.2 year. Then BD = S * r * t. Step-by-Step Solution: BD = 3000 * 0.10 * 0.2 = Rs 60. Verification / Alternative check:Using 360-day convention gives t ≈ 0.2028 and BD ≈ Rs 60 (rounded), matching the keyed value. Why Other Options Are Wrong:82, 90, 120 are inconsistent with the 73-day interval at 10%. Common Pitfalls:Forgetting grace days; miscounting days across months. Final Answer:Rs 60

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