Question 1

Successive discounts: Two successive discounts of 20% and 20% are equivalent to what single discount percentage on the list price?

Accepted Answer

Introduction / Context: Successive discounts multiply their remaining-price factors. A discount of d% keeps (1 − d/100) of the price. Two discounts combine by multiplying these factors, then the overall discount is 1 minus the product. Given Data / Assumptions: First discount = 20% ⇒ retention factor = 0.80 Second discount = 20% ⇒ retention factor = 0.80 Concept / Approach: Equivalent single discount D satisfies (1 − D) = 0.80 * 0.80. Compute the product and convert back to a percentage discount. Step-by-Step Solution: Retention after both = 0.80 * 0.80 = 0.64Equivalent single discount D = 1 − 0.64 = 0.36 = 36% Verification / Alternative check: On a ₹100 item: after 20% off → ₹80; second 20% off → ₹64. A single 36% off of ₹100 also gives ₹64. Why Other Options Are Wrong: 40% simply adds 20 + 20, which is incorrect for successive discounts. 42% and 34% do not match the multiplicative outcome. Common Pitfalls: Adding percentages directly for successive reductions. Always multiply retention factors. Final Answer: 36%

Question 2

Marked price and discount: On a 20% discount sale, an article costs ₹596. What was the original marked price?

Accepted Answer

Introduction / Context: This is a reverse percentage calculation. After a 20% discount, the selling price (SP) is known; we must recover the marked price (MP) before discount. A direct proportion or dividing by the retention factor solves it cleanly. Given Data / Assumptions: Discount = 20% ⇒ retention factor = 0.80 SP after discount = ₹596 Concept / Approach: SP = MP * 0.80. Therefore, MP = SP / 0.80. Compute and round only if needed (here it divides exactly to ₹745). Step-by-Step Solution: SP = 0.80 * MP = ₹596MP = ₹596 / 0.80 = ₹745 Verification / Alternative check: 20% of ₹745 = ₹149; subtracting gives ₹596, confirming the calculation. Why Other Options Are Wrong: Other values do not produce ₹596 after a 20% reduction; quick checks show mismatches in the final price. Common Pitfalls: Subtracting 20% of the final price instead of 20% of the marked price, or adding back 20% (which would overestimate). Final Answer: ₹ 745

Question 3

Early payment rebate: Paying an electricity bill before the due date gives a 4% reduction. A person saved ₹13 by early payment. What was the original bill amount?

Accepted Answer

Introduction / Context: Percentage reductions translate to a fixed saving when applied to a base amount. Here, a 4% rebate produced a known rupee saving; we back-calculate the original bill by dividing the saving by the rate as a decimal. Given Data / Assumptions: Rebate rate = 4% = 0.04 Saving amount = ₹13 Concept / Approach: Saving = Rate * Original Amount. Thus, Original Amount = Saving / Rate. No compounding is involved—this is a direct single reduction. Step-by-Step Solution: Let B be the bill amount. Then 0.04 * B = 13B = 13 / 0.04 = 325 Verification / Alternative check: 4% of ₹325 is ₹13; paying early reduces the bill by ₹13, consistent with the statement. Why Other Options Are Wrong: Other amounts do not yield ₹13 when 4% is computed; quick mental math shows the discrepancy. Common Pitfalls: Using 4 as the divisor instead of 0.04; always convert the percent to a decimal. Final Answer: ₹ 325

Question 4

Equivalent single discount: Successive discounts of 10%, 20%, and 30% are equivalent to what single discount percentage?

Accepted Answer

Introduction / Context: Multiple successive discounts compound multiplicatively via retention factors. Compute the compounded retention, then convert back to a single overall discount percentage. Given Data / Assumptions: Discounts: 10%, 20%, 30% Retention factors: 0.90, 0.80, 0.70 respectively Concept / Approach: Overall retention = 0.90 * 0.80 * 0.70. Overall discount = 1 − overall retention. Convert to percent with one decimal place as appropriate. Step-by-Step Solution: Retention = 0.90 * 0.80 * 0.70 = 0.504Equivalent discount = 1 − 0.504 = 0.496 = 49.6% Verification / Alternative check: Test with ₹100: after successive cuts, price becomes ₹50.40, so the total reduction is ₹49.60, i.e., 49.6%. Why Other Options Are Wrong: 60% adds the percentages; 40.5% or 36% underestimates; 54% overestimates relative to the multiplicative rule. Common Pitfalls: Adding the percentages directly or rounding early; compute the product first, then subtract from 1. Final Answer: 49.6%

Question 5

Marked price from selling price with rebate: A shopkeeper offers a 14% rebate on the marked price. If the selling price is ₹645, what is the marked price?

Accepted Answer

Introduction / Context: This is an inverse percentage problem. The selling price equals the marked price multiplied by the retention factor after rebate. Recover the marked price by dividing by the retention factor. Given Data / Assumptions: Rebate = 14% ⇒ retention = 86% = 0.86 Selling Price = ₹645 Concept / Approach: SP = MP * 0.86 ⇒ MP = SP / 0.86. Ensure clean division and verify by reapplying 14% to check if SP returns to ₹645. Step-by-Step Solution: MP = 645 / 0.86 = 750 Verification / Alternative check: 14% of ₹750 is ₹105; subtracting from ₹750 yields ₹645, confirming the result. Why Other Options Are Wrong: All other values, when discounted by 14%, do not lead to ₹645. Common Pitfalls: Using 14% of SP to back out MP directly; always divide SP by the retention fraction. Final Answer: ₹ 750

Question 6

Rebate target: A merchant announces a 25% rebate on readymade garments. If a buyer wants a total rebate of ₹400, how many shirts priced at ₹320 each should he purchase?

Accepted Answer

Introduction / Context: Here, the discount per unit is fixed as a percentage of the marked price. Knowing the target total rebate, compute how many units are needed to accumulate that saving. Given Data / Assumptions: Unit price = ₹320 Rebate = 25% of unit price Desired total rebate = ₹400 Concept / Approach: Discount per shirt = 0.25 * 320. Number of shirts = total desired rebate / discount per shirt. Round only if the result is an integer requirement (it is exact here). Step-by-Step Solution: Discount per shirt = 0.25 * 320 = ₹80Number of shirts = 400 / 80 = 5 Verification / Alternative check: Buying 5 shirts: total marked price = ₹1600; 25% of this is ₹400, matching the target rebate. Why Other Options Are Wrong: Any other count gives a total rebate not equal to ₹400 (e.g., 4 shirts → ₹320; 6 shirts → ₹480). Common Pitfalls: Confusing 25% of the total with 25% of the unit price (they are consistent, since total is linear in the count). Final Answer: 5

Question 7

Compare a single 40% discount with successive discounts of 36% and 4% on ₹500. What is the difference (in rupees) between the two discount amounts?

Accepted Answer

Introduction / Context: Successive discounts do not add; they multiply. We are asked to compare the discount amounts (not final prices) for two schemes applied to ₹500: one discount of 40% versus successive 36% then 4% discounts. The answer is the absolute difference in rupee savings. Given Data / Assumptions: Base price = ₹500 Scheme A: single 40% discount Scheme B: successive 36% and 4% discounts Concept / Approach: Compute final prices for both and obtain discount amounts by subtracting from the base price. Then take the difference of the two discount amounts. Step-by-Step Solution: Scheme A discount = 0.40 * 500 = ₹200 ⇒ Final = ₹300Scheme B: after 36% off ⇒ 500 * 0.64 = ₹320; further 4% off ⇒ 320 * 0.96 = ₹307.20Scheme B discount = 500 − 307.20 = ₹192.80Difference in discounts = 200 − 192.80 = ₹7.20 Verification / Alternative check: Equivalently, 36% then 4% equals 1 − (0.64 * 0.96) = 1 − 0.6144 = 38.56% overall; 40% − 38.56% = 1.44% of 500 = ₹7.20. Why Other Options Are Wrong: ₹0 assumes additivity; ₹2 and ₹1.93 are numerical distractors not matching the exact multiplicative difference. Common Pitfalls: Adding 36% and 4% to get 40%; successive discounts never add linearly. Final Answer: ₹ 7.20

Question 8

Marked-up goods and discount: A merchant marks goods 20% above cost and then allows a 15% discount on the marked price. What is his overall gain percentage?

Accepted Answer

Introduction / Context: This is a classic chain percentage problem linking cost price (CP), marked price (MP), discount, and selling price (SP). We compute SP in terms of CP and then convert the difference to a gain percentage. Given Data / Assumptions: MP = CP * (1 + 20%) = 1.20 * CP Discount on MP = 15% ⇒ SP = MP * 0.85 Concept / Approach: SP = CP * 1.20 * 0.85. Then gain% = [(SP − CP)/CP] * 100%. Step-by-Step Solution: SP = CP * 1.20 * 0.85 = CP * 1.02Gain = SP − CP = 0.02 * CPGain% = (0.02 * CP)/CP * 100% = 2% Verification / Alternative check: Take CP = ₹100. MP = ₹120. After 15% discount, SP = ₹102. Gain = ₹2 ⇒ 2%. Why Other Options Are Wrong: 1% or 5% and 10% do not match the multiplicative effect; 15% confuses the discount with profit. Common Pitfalls: Subtracting percentages (20% − 15% = 5%) to infer profit; the base of 15% is MP, not CP. Final Answer: 2%

Question 9

Television purchase and resale: Rita bought a TV at 20% discount on the labelled price and later sold it for ₹16,800, making a profit of ₹800. What was the labelled price?

Accepted Answer

Introduction / Context: We relate cost price (after discount) to selling price and profit to recover the labelled (marked) price. The chain is: Labelled Price → 20% off → Cost Price → add profit → Selling Price. Given Data / Assumptions: Buying discount = 20% on labelled price L ⇒ Cost Price (CP) = 0.80L Selling Price (SP) = ₹16,800 Profit = ₹800 ⇒ CP = SP − Profit = ₹16,000 Concept / Approach: Equate CP from both descriptions to solve for L: 0.80L = 16,000 ⇒ L = 20,000. Step-by-Step Solution: CP = SP − Profit = 16800 − 800 = 160000.80L = 16000 ⇒ L = 16000 / 0.80 = 20000 Verification / Alternative check: 20% of ₹20,000 is ₹4,000; CP = ₹16,000. Selling at ₹16,800 gives ₹800 profit—consistent. Why Other Options Are Wrong: They either understate or overstate the implied CP or profit when back-checked. Common Pitfalls: Applying 20% to SP or mixing up profit addition/subtraction direction. Final Answer: ₹ 20000

Question 10

Successive discounts on a marked price of ₹500: first 20% off and then 10% off. What is the final selling price?

Accepted Answer

Introduction / Context: Compute the selling price after two successive discounts on a known marked price. Each discount applies to the current price after the previous reduction, not to the original marked price again. Given Data / Assumptions: Marked Price = ₹500 First discount = 20% ⇒ multiply by 0.80 Second discount = 10% ⇒ multiply by 0.90 Concept / Approach: Final price = 500 * 0.80 * 0.90. This is equivalent to a single 28% discount, but computing stepwise avoids mistakes. Step-by-Step Solution: After 20% off: 500 * 0.80 = ₹400After 10% off: 400 * 0.90 = ₹360 Verification / Alternative check: Overall retention = 0.72; 500 * 0.72 = 360. Equivalent overall discount is 28%. Why Other Options Are Wrong: ₹400 stops after the first discount; ₹375 and ₹350 do not match the multiplicative process. Common Pitfalls: Adding discounts linearly (20% + 10% = 30%)—incorrect for successive reductions. Final Answer: ₹ 360

Question 11

Equivalent single discount: Two successive discounts of 20% and 5% equal what single discount percentage?

Accepted Answer

Introduction / Context: Successive percentage reductions require multiplication of retention factors. Compute the compounded factor, then translate back to a single discount value. Given Data / Assumptions: Discounts: 20% and 5% Retention factors: 0.80 and 0.95 Concept / Approach: Overall retention = 0.80 * 0.95 = 0.76. Hence overall discount = 1 − 0.76 = 0.24 = 24%. Step-by-Step Solution: Compute 0.80 * 0.95 = 0.76Single discount = 1 − 0.76 = 0.24 = 24% Verification / Alternative check: Apply to ₹100: After 20% off → ₹80; after 5% off → ₹76; single 24% off also gives ₹76. Why Other Options Are Wrong: 25% simply adds; 18% and 15% understate the reduction; 23% is a rounding distractor. Common Pitfalls: Adding discounts directly or rounding intermediate products before final conversion. Final Answer: 24%

Question 12

Present worth under simple interest: Find the present value of ₹920 due in 3 years at 5% simple interest per annum.

Accepted Answer

Introduction / Context: Present worth (under simple interest) is the amount today that will grow to the future value (amount due) when simple interest is applied for the given time and rate. The relation is A = P*(1 + r*t), so P = A / (1 + r*t). Given Data / Assumptions: Amount due A = ₹920 Time t = 3 years Rate r = 5% per annum (simple interest) Concept / Approach: Compute the simple interest factor 1 + r*t = 1 + 0.05*3 = 1.15. Divide the amount by this factor to get the present worth P. Step-by-Step Solution: Factor = 1 + 0.05*3 = 1.15P = 920 / 1.15 = 800 Verification / Alternative check: Grow ₹800 at 5% simple interest for 3 years: Interest = 800*0.05*3 = ₹120; Amount = ₹920, matching the due amount. Why Other Options Are Wrong: They do not grow to ₹920 under 5% simple interest over 3 years. Common Pitfalls: Using compound interest formula inadvertently; the problem explicitly uses simple interest. Final Answer: ₹800

Question 13

Simple interest and true discount combined: The simple interest on a certain sum at 6% per annum for t years is ₹180. The (true) discount at 5% on the same sum due for the same time is ₹140. Find the sum and the time.

Accepted Answer

Introduction / Context: This problem mixes simple interest (SI) with the concept of true discount (TD). SI is computed on the present principal, while TD is the rebate that makes the present worth grow to a future due amount at a given rate over time. We are told SI at 6% equals ₹180 and TD at 5% on the same sum for the same time equals ₹140. Given Data / Assumptions: Principal (sum) = S Time = t years SI: 0.06 * S * t = 180 True Discount on a sum S due for time t at 5%: TD = (S * 0.05 * t) / (1 + 0.05 * t) = 140 Concept / Approach: From SI we get S*t directly. Substitute into the TD expression (note TD uses the due amount S and adjusts by the time factor in the denominator). Solve for t, then compute S via S = (S*t)/t. Step-by-Step Solution: From SI: 0.06 S t = 180 ⇒ S t = 3000TD = (S * 0.05 * t)/(1 + 0.05 t) = 140Use S t = 3000 ⇒ numerator = 0.05 * (S t) = 0.05 * 3000 = 150So 150/(1 + 0.05 t) = 140 ⇒ 1 + 0.05 t = 150/140 = 15/140.05 t = 15/14 − 1 = 1/14 ⇒ t = (1/14)/0.05 = (1/14)/(1/20) = 20/14 = 10/7 = 1 3/7 yearsThen S = (S t)/t = 3000 / (10/7) = 2100 Verification / Alternative check: SI check: 0.06 * 2100 * (10/7) = 180. TD check: (2100 * 0.05 * 10/7)/(1 + 0.05 * 10/7) = (150)/(15/14) = 140. Both validate. Why Other Options Are Wrong: They correspond to incorrect algebra (e.g., treating discount as simple interest or omitting the denominator in TD). Common Pitfalls: Confusing true discount with simple interest on the principal; TD always includes the (1 + r t) factor in the denominator. Final Answer: ₹ 2100 and 1 3/7 Year

Question 14

Banker’s discount and gain application: A bill is due in 9 months at a simple rate of 4% per annum. The banker’s gain on discounting this bill is ₹2.25. Find the face value (sum due at maturity) of the bill.

Accepted Answer

Introduction / Context: This question tests core ideas in bill discounting: banker’s discount (BD), true discount (TD), present worth (PW), and banker’s gain (BG). BG is the excess of BD over TD, and it equals the simple interest on the true discount for the unexpired time. Using these relationships, we can back out both TD and the face value of the bill due at maturity. Given Data / Assumptions: Time to maturity t = 9 months = 0.75 year. Rate r = 4% per annum (simple). Banker’s gain BG = ₹2.25. Standard banking convention for simple discounting and no grace days unless stated. Concept / Approach: Use the identity BG = (TD * r * t) / 100, i.e., banker’s gain equals simple interest on the true discount. Once TD is obtained, present worth PW follows from TD = (PW * r * t) / 100. Face value (sum due) = PW + TD. Step-by-Step Solution: BG = 2.25, r = 4, t = 0.75 ⇒ TD = BG * 100 / (r * t) = 2.25 * 100 / (4 * 0.75) = 225 / 3 = ₹75.TD = (PW * r * t)/100 ⇒ PW = TD * 100 / (r * t) = 75 * 100 / (4 * 0.75) = 7500 / 3 = ₹2500.Face value (sum due) = PW + TD = 2500 + 75 = ₹2575. Verification / Alternative check: Compute BD and TD explicitly for a face value of ₹2575 at 4% for 0.75 year. Their difference equals ₹2.25, confirming the calculation. Why Other Options Are Wrong: ₹2500 is the present worth, not the face value; ₹2250, ₹2525, ₹3250 do not satisfy BG = ₹2.25 at the stated r and t. Common Pitfalls: Confusing face value with present worth; forgetting that BG is simple interest on TD, not on PW or face directly. Final Answer: ₹2575

Question 15

Present worth under compound interest: A bill of ₹1764 is due in 2 years. If money is worth 5% compounded annually, what is the present worth today?

Accepted Answer

Introduction / Context: Present worth (PW) under compound interest discounts a future amount back to today using the compound factor. This is a standard time value of money computation in finance and aptitude tests. Given Data / Assumptions: Future amount (face value) A = ₹1764. Rate r = 5% per annum, compounded annually. Time n = 2 years. Concept / Approach: For compound interest, PW = A / (1 + r)^n. Substitute r = 0.05 and n = 2 to compute the exact present worth. Since 1.05^2 = 1.1025, division is straightforward here and yields an integer result. Step-by-Step Solution: Compute the discount factor: (1 + 0.05)^2 = 1.1025.PW = 1764 / 1.1025 = ₹1600 (because 1600 * 1.1025 = 1764). Verification / Alternative check: Forward check: Invest ₹1600 at 5% for 2 years → 1600 * 1.1025 = ₹1764, matching the due amount. Why Other Options Are Wrong: ₹1650, ₹1700, ₹1714, ₹1620 do not compound exactly to ₹1764 in 2 years at 5%. Common Pitfalls: Using simple interest instead of compound, or rounding prematurely when the values here are exact. Final Answer: ₹1600

Question 16

True discount and present worth: A sum due in 146 days at 5% simple interest has a present worth of ₹400. What is the sum due at maturity?

Accepted Answer

Introduction / Context: When a sum is due in the future, its present worth (today’s value) is less by the true discount under simple interest. The sum due equals present worth plus the simple interest for the remaining time to maturity. Short-date questions commonly use day-count fractions like 146/365 year. Given Data / Assumptions: Present worth PW = ₹400. Rate r = 5% per annum (simple). Time t = 146/365 = 0.4 year. Concept / Approach: Sum due (face value) A = PW * (1 + r * t). Because interest is simple and time is a fraction of a year, multiply PW by 1 plus the percentage for the fraction 0.4. Step-by-Step Solution: Compute r * t = 0.05 * 0.4 = 0.02 (i.e., 2%).Amount due A = 400 * (1 + 0.02) = 400 * 1.02 = ₹408. Verification / Alternative check: True discount TD = A − PW = 408 − 400 = ₹8 equals simple interest on PW for 0.4 year at 5%, which is 400 * 0.05 * 0.4 = ₹8. Why Other Options Are Wrong: ₹410, ₹415, ₹450, ₹404 arise from using wrong day fraction or compounding instead of simple interest. Common Pitfalls: Mixing up present worth with face value, or using 360-day convention without instruction, which shifts the result slightly. Final Answer: ₹408

Question 17

No-loss investment after discounting: A banker discounts a 4-month bill at a simple discount rate of 3% per annum. To ensure nothing is lost overall, at what simple annual rate should the banker invest the proceeds for those 4 months so that the mat…

Accepted Answer

Introduction / Context: When a bill is discounted at a simple discount rate, the banker receives the proceeds (face less discount). If those proceeds are invested until maturity, the investment rate must be high enough to recover exactly the face value so that there is “no loss.” This links simple discounting and simple interest growth over the same period. Given Data / Assumptions: Discount rate d = 3% per annum (simple). Time t = 4 months = 1/3 year. Face value F (symbolic); proceeds P = F * (1 − d * t). Concept / Approach: Require P * (1 + i * t) = F, where i is the simple annual investment rate. Solve for i using the proceeds from discounting and the condition that the invested proceeds grow back to F at maturity. Step-by-Step Solution: Proceeds P = F * (1 − 0.03 * 1/3) = F * (1 − 0.01) = 0.99F.No-loss condition: 0.99F * (1 + i/3) = F ⇒ 1 + i/3 = 1 / 0.99.i/3 = (1/0.99) − 1 = 0.010101… ⇒ i ≈ 0.030303… = 3 1/3% per annum. Verification / Alternative check: Using fractions: 1/0.99 = 100/99; so i/3 = 1/99 ⇒ i = 3/99 = 1/33 ≈ 3.0303%, i.e., 3 1/3%. Why Other Options Are Wrong: 3% under-recovers the face; 4% over-recovers; 3 1/36% and 2 2/3% do not satisfy 0.99(1 + i/3) = 1. Common Pitfalls: Treating the discount as simple interest on proceeds or compounding over 4 months; the setup requires simple-rate equivalence over the same period. Final Answer: 3 1/3%

Question 18

Credit sale and real gain: A motor-cycle costs ₹32500. It is sold for ₹35000 on 6-month credit. If money is worth 4% per annum (simple), what is the seller’s actual gain percentage based on the true present value of the credit sale?

Accepted Answer

Introduction / Context: When goods are sold on credit, the cash-equivalent present value is lower than the listed credit price. To find the true gain, discount the credit price back to today at the money value (opportunity cost) and compare this present value to the cost price. This avoids overstating profit by ignoring the time value of money. Given Data / Assumptions: Cost price C = ₹32500. Credit selling price after 6 months S = ₹35000. Money worth r = 4% per annum (simple), time t = 0.5 year. Use simple true discount to find present value. Concept / Approach: Present value PV = S / (1 + r * t). Real gain = PV − C. Gain% = (Real gain / C) * 100. This compares like with like in today’s rupees. Step-by-Step Solution: PV = 35000 / (1 + 0.04 * 0.5) = 35000 / 1.02 ≈ ₹34313.73.Real gain = 34313.73 − 32500 ≈ ₹1813.73.Gain% ≈ 1813.73 / 32500 * 100 ≈ 5.58% ≈ 5.5% (rounded). Verification / Alternative check: Using simple interest deduction: PV = 35000 − (35000 * 0.04 * 0.5) = 35000 − 700 = ₹34300. Then gain% = (34300 − 32500)/32500 = 1800/32500 ≈ 5.54%, consistent with ≈ 5.5%. Why Other Options Are Wrong: The higher mixed-fraction percentages (e.g., 7 5/13%, 8 1/7%, 8 2/5%, 7 9/13%) ignore the required discounting and overstate profit. Common Pitfalls: Computing gain on the nominal ₹35000 without discounting; mixing up base (cost versus present value) when expressing the percentage. Final Answer: 5.5%

Question 19

Linking simple interest and true discount: On the same sum and time, the simple interest is ₹24 while the true discount is ₹22. Find the sum due (face value) on which these were computed.

Accepted Answer

Introduction / Context: This classic TD–SI linkage uses the time-rate factor R = r * t (in decimal). For the same “sum due” S and same time, the simple interest on S is S * R, while the true discount is S * R / (1 + R). Their ratio eliminates S and gives R directly; then recover S from the given SI value. Given Data / Assumptions: SI on S for time t at rate r: SI = ₹24. True discount on the same S, time, rate: TD = ₹22. Let R = r * t (in decimal units). Concept / Approach: For the same S and R: SI = S * R and TD = S * R / (1 + R). Hence TD/SI = 1/(1 + R). Use the numerical values to find R. Then S = SI / R. Step-by-Step Solution: TD / SI = 22 / 24 = 11 / 12 = 1 / (1 + R).⇒ 1 + R = 12 / 11 ⇒ R = 1 / 11.SI = S * R ⇒ 24 = S * (1/11) ⇒ S = 24 * 11 = ₹264. Verification / Alternative check: TD predicted = S * R / (1 + R) = 264 * (1/11) / (12/11) = 24 / 12 = ₹22, matching the given TD. Why Other Options Are Wrong: ₹220, ₹288, ₹295, ₹242 do not satisfy both SI = 24 and TD = 22 under a single R. Common Pitfalls: Assuming SI equals TD (that holds when SI is on present worth, not on the sum due S). Here SI is on S. Final Answer: ₹264

Question 20

Dating a discounted bill with grace: A bill for ₹17850 is nominally due on May 21, 1991. The holder received ₹357 less than the bill amount by discounting it at 5% simple interest. On which date was it discounted? (Assume the usual 3 days of grace o…

Accepted Answer

Introduction / Context: To find the discounting date, first compute the time interval t for which the bill was discounted using banker’s discount BD = Face * r * t. Many bill problems include 3 days of grace, meaning the legal due date is 3 days after the nominal date; this affects the backward count when converting time to a calendar date. Given Data / Assumptions: Face value F = ₹17850. Discount rate r = 5% p.a. (simple). Banker’s discount BD = ₹357. Assume standard 3 grace days beyond the nominal due date. Concept / Approach: Compute t from BD = F * r * t. Convert t years to days. Add grace (for due date) and count back to the discounting date from the legal due date. Step-by-Step Solution: BD = 357 = 17850 * 0.05 * t ⇒ t = 357 / 892.5 = 0.4 year.0.4 year = 146 days (using a 365-day year).Legal due date = May 21, 1991 + 3 days grace = May 24, 1991.Discount date = Legal due date − 146 days = Dec 29, 1990. Verification / Alternative check: Counting back 146 days from May 24, 1991 to Dec 29, 1990 matches standard solutions; without grace, you would get Dec 26, 1990. Why Other Options Are Wrong: Dates in 1989 or 1995 are inconsistent; Dec 19, 1990/Dec 26, 1990 correspond to different grace assumptions. Common Pitfalls: Forgetting the 3 days of grace or mixing 360-day and 365-day conventions without instruction. Final Answer: Dec 29, 1990

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