Question 1

Simple Interest — In how many years will a sum become four times itself at 12% per annum simple interest?

Accepted Answer

Introduction / Context: Becoming four times under simple interest means the interest earned equals three times the principal over a certain time at a given rate. Given Data / Assumptions: Target: Amount A = 4P. Rate r = 12% per annum. Simple interest formula applies. Concept / Approach: For simple interest: SI = P * r * t and A = P + SI. If A = 4P, then SI = 3P. Hence solve P * r * t = 3P. Step-by-Step Solution: SI = 3P.P * r * t = 3P ⇒ r * t = 3.Given r = 12% = 0.12, so 0.12 * t = 3.t = 3 / 0.12 = 25 years. Verification / Alternative check: At 12% for 25 years: SI = P * 0.12 * 25 = 3P; Amount = P + 3P = 4P. Why Other Options Are Wrong: 22, 27, or 28 years do not satisfy r * t = 3 with r = 0.12. Common Pitfalls: Using compound interest logic; here growth is linear. Final Answer: 25 yr

Question 2

Simple Interest — The interest earned at 5%, 6%, and 8% in three consecutive years totals ₹ 760. Find the principal.

Accepted Answer

Introduction / Context: Here the rate changes each year but simple interest is computed independently each year on the same principal, then summed. Given Data / Assumptions: Year 1 rate = 5%. Year 2 rate = 6%. Year 3 rate = 8%. Total simple interest over 3 years = ₹ 760. Let principal be P. Concept / Approach: Total SI = P * (0.05 + 0.06 + 0.08) = P * 0.19. Step-by-Step Solution: P * 0.19 = 760.P = 760 / 0.19.P = ₹ 4000. Verification / Alternative check: Check per year interest: 5% of 4000 = 200; 6% = 240; 8% = 320; sum = 760. Why Other Options Are Wrong: ₹ 4600, ₹ 3600, ₹ 3200, ₹ 5000 do not satisfy 0.19 * P = 760. Common Pitfalls: Adding percentages incorrectly or treating it as compound interest across years. Final Answer: ₹ 4000

Question 3

Simple Interest — What is the simple interest accrued in 4 years on a principal of ₹ 18,440 at 15% per annum?

Accepted Answer

Introduction / Context: This is a direct application of the simple interest formula with clear principal, rate, and time. Given Data / Assumptions: P = ₹ 18,440. r = 15% per annum. t = 4 years. Concept / Approach: Simple interest SI = P * r * t, with r as decimal (15% = 0.15). Step-by-Step Solution: SI = 18,440 * 0.15 * 4.0.15 * 4 = 0.60.SI = 18,440 * 0.60 = ₹ 11,064. Verification / Alternative check: Compute 10% of 18,440 = 1,844; 5% = 922; hence 15% per year = 2,766; in 4 years: 2,766 * 4 = 11,064. Why Other Options Are Wrong: Other values deviate from precise multiplication; they are plausible approximations but not exact. Common Pitfalls: Rounding mid-steps; here exact arithmetic yields a clean result. Final Answer: ₹ 11,064

Question 4

Simple Interest — What is the simple interest on ₹ 4000 at 12.5% per annum from 4 February 2005 to 18 April 2005?

Accepted Answer

Introduction / Context: Date-based simple interest questions require converting the exact period into a fraction of a year and then applying SI = P * r * t. Given Data / Assumptions: P = ₹ 4000. r = 12.5% per annum = 0.125. From 4 Feb 2005 to 18 Apr 2005. Use a 365-day year for t. Concept / Approach: Compute number of days between dates, convert to years t = days / 365, then SI = P * r * t. Step-by-Step Solution: Days from 2005-02-04 to 2005-04-18 = 73 days.t = 73 / 365 = 0.2 years exactly.SI = 4000 * 0.125 * 0.2 = 4000 * 0.025 = ₹ 100. Verification / Alternative check: 12.5% per year implies 1/8 of principal each year. For 0.2 years, take 1/5 of 1/8 of P: (P / 8) / 5 = P / 40 = 4000 / 40 = 100. Why Other Options Are Wrong: ₹ 120, ₹ 150, ₹ 200, ₹ 215 correspond to incorrect day counts or wrong fractions of a year. Common Pitfalls: Using 360-day convention without being told; miscounting inclusive/exclusive dates. The 73-day difference gives an exact 0.2 year. Final Answer: ₹ 100

Question 5

Simple Interest — Rakesh lends ₹ 8750 at 7% per annum. Find the simple interest in 3 years.

Accepted Answer

Introduction / Context: A straightforward application of SI = P * r * t with clearly given values. Given Data / Assumptions: P = ₹ 8750. r = 7% per annum = 0.07. t = 3 years. Concept / Approach: Compute simple interest using the standard formula. Step-by-Step Solution: SI = 8750 * 0.07 * 3.0.07 * 3 = 0.21.SI = 8750 * 0.21 = ₹ 1837.50. Verification / Alternative check: 10% of 8750 = 875; 7% = 612.5; in 3 years: 612.5 * 3 = 1837.5. Why Other Options Are Wrong: ₹ 1870 and others are near but do not match the exact computation. Common Pitfalls: Rounding prematurely or misplacing the decimal when multiplying percentages. Final Answer: ₹ 1837.50

Question 6

Simple Interest — What is the simple interest for 1 year 4 months on ₹ 25,800 at 14% per annum?

Accepted Answer

Introduction / Context: Convert mixed time (years and months) into years, then apply SI = P * r * t. Given Data / Assumptions: P = ₹ 25,800. r = 14% per annum. t = 1 year 4 months = 1 + 4/12 = 4/3 years. Concept / Approach: Use t in years as a fraction for simple interest computations. Step-by-Step Solution: t = 16/12 = 4/3 years.SI = 25,800 * 0.14 * (4/3).0.14 * (4/3) = 0.186666...SI = 25,800 * 0.186666... = ₹ 4816 exactly. Verification / Alternative check: Per year SI = 25,800 * 0.14 = 3612; one third of that = 1204; sum = 3612 + 1204 = 4816. Why Other Options Are Wrong: ₹ 4815 and ₹ 4816.75 are rounding errors; ₹ 2580 is only 10%; ₹ 4700 is an approximation. Common Pitfalls: Using 1.4 (140%) instead of 0.14; not converting months to fraction of year correctly. Final Answer: ₹ 4816

Question 7

Simple Interest — A sum at 13.5% per annum amounts to ₹ 3080 in 4 years. Find the principal (original sum).

Accepted Answer

Introduction / Context: Given amount after a period under simple interest, find the original principal using A = P * (1 + r * t). Given Data / Assumptions: A = ₹ 3080. r = 13.5% = 0.135 per annum. t = 4 years. Concept / Approach: A = P * (1 + r * t) ⇒ P = A / (1 + r * t). Step-by-Step Solution: 1 + r * t = 1 + 0.135 * 4 = 1 + 0.54 = 1.54.P = 3080 / 1.54 = ₹ 2000. Verification / Alternative check: Compute SI = P * r * t = 2000 * 0.135 * 4 = 1080. Amount = 2000 + 1080 = 3080. Why Other Options Are Wrong: Other values do not reproduce amount 3080 when used in A = P * (1 + r * t). Common Pitfalls: Using compound formula mistakenly; here interest is simple. Final Answer: ₹ 2000

Question 8

Simple Interest — The sum of money that amounts to ₹ 364.80 in 8 years at 3.5% simple interest per annum is:

Accepted Answer

Introduction / Context: Reverse-calculating principal from amount under simple interest is a standard manipulation of A = P * (1 + r * t). Given Data / Assumptions: A = ₹ 364.80. r = 3.5% = 0.035 per annum. t = 8 years. Concept / Approach: P = A / (1 + r * t) with linear growth under simple interest. Step-by-Step Solution: 1 + r * t = 1 + 0.035 * 8 = 1 + 0.28 = 1.28.P = 364.80 / 1.28 = ₹ 285. Verification / Alternative check: SI = P * r * t = 285 * 0.035 * 8 = 79.80; Amount = 285 + 79.80 = 364.80. Why Other Options Are Wrong: ₹ 280, ₹ 275, ₹ 270, ₹ 300 do not yield the given amount when forward checked. Common Pitfalls: Mixing up 3.5% with 0.35; remember to divide by 100. Final Answer: ₹ 285

Question 9

Simple Interest — A sum of ₹ 2668 amounts to ₹ 4669 in 5 years at simple interest. Find the annual rate of interest (percent per annum).

Accepted Answer

Introduction / Context: Here amount and principal are known over a time period, so the total simple interest and the annual rate can be computed directly. Given Data / Assumptions: P = ₹ 2668. A = ₹ 4669. t = 5 years. Concept / Approach: SI = A − P; then r = SI / (P * t). Step-by-Step Solution: SI = 4669 − 2668 = ₹ 2001.r = 2001 / (2668 * 5) = 2001 / 13340 = 0.15.Convert to percent: r = 15% per annum. Verification / Alternative check: Per year SI = P * r = 2668 * 0.15 = 400.2; in 5 years: 400.2 * 5 = 2001; A = 2668 + 2001 = 4669. Why Other Options Are Wrong: They are near-misses to distract; only 15% exactly reproduces the given amount. Common Pitfalls: Arithmetic slips when subtracting or multiplying decimals. Final Answer: 15%

Question 10

Simple Interest — Find the difference between amount and principal for ₹ 4000 at 5% per annum in 4 years (i.e., the simple interest).

Accepted Answer

Introduction / Context: The difference between amount and principal under simple interest over a time period is exactly the simple interest accrued. Given Data / Assumptions: P = ₹ 4000. r = 5% = 0.05 per annum. t = 4 years. Concept / Approach: SI = P * r * t; Amount A = P + SI. The requested difference is SI itself. Step-by-Step Solution: SI = 4000 * 0.05 * 4 = 4000 * 0.20 = ₹ 800. Verification / Alternative check: A = 4000 + 800 = 4800; difference A − P = 800, as expected. Why Other Options Are Wrong: ₹ 865, ₹ 865.50, ₹ 780, ₹ 400 are not equal to SI computed at 5% for 4 years. Common Pitfalls: Confusing rate per year with total rate over multiple years; always multiply by time. Final Answer: ₹ 800

Question 11

Simple Interest — A sum becomes double in 10 years. Find the annual rate of simple interest.

Accepted Answer

Introduction / Context: Doubling under simple interest implies the interest earned equals the principal over the given time. Given Data / Assumptions: A = 2P in t = 10 years. Simple interest applies. Concept / Approach: If A = 2P then SI = P. With SI = P * r * t, solve for r. Step-by-Step Solution: P = P * r * 10 ⇒ r = 1 / 10 = 0.10 = 10%. Verification / Alternative check: At 10% for 10 years, SI = P; amount = 2P. Why Other Options Are Wrong: 1% and 5% are too small; 20% is too large. Common Pitfalls: Applying compound interest ideas; stay with SI linearity. Final Answer: 10%

Question 12

Simple Interest — How long will a sum invested at 5% per annum simple interest take to increase by 50% of its value?

Accepted Answer

Introduction / Context: An increase by 50% means SI = 0.5P. With rate and time known or unknown, use SI = P * r * t to solve for the missing variable. Given Data / Assumptions: r = 5% per annum = 0.05. Target increase = 50% of P, i.e., SI = 0.5P. Concept / Approach: Use SI = P * r * t ⇒ 0.5P = P * 0.05 * t. Step-by-Step Solution: 0.5P = 0.05P * t ⇒ 0.5 = 0.05 * t.t = 0.5 / 0.05 = 10 years. Verification / Alternative check: At 5% for 10 years: total interest = 50% of P, so amount = 1.5P. Why Other Options Are Wrong: 7, 12, 15 years do not satisfy 0.05 * t = 0.5. Common Pitfalls: Interpreting “increase by 50%” as “becomes 50% of the amount.” It means amount becomes 1.5P. Final Answer: 10 yr

Question 13

Simple Interest — A sum becomes 8 times in 15 years at simple interest. What is the annual rate of interest?

Accepted Answer

Introduction / Context: When an amount becomes a multiple of the principal under simple interest, we relate the multiple to the total simple interest accumulated over time. Given Data / Assumptions: A = 8P. t = 15 years. Simple interest applies. Concept / Approach: For simple interest: A = P + SI. If A = 8P, then SI = 7P over 15 years. Since SI = P * r * t, solve for r. Step-by-Step Solution: P * r * 15 = 7P.Cancel P: r * 15 = 7.r = 7 / 15 = 0.466666... = 46 2/3% per annum. Verification / Alternative check: Annual SI = 46 2/3% of P; in 15 years: (46 2/3%)*15 = 700% of P; A = P + 7P = 8P. Why Other Options Are Wrong: 45%, 44%, 42 2/3%, 40% do not yield A = 8P in 15 years under simple interest. Common Pitfalls: Confusing 46 2/3% with 46.2% or 46.7% rounded. Final Answer: 46 2/3%

Question 14

Simple Interest — A sum amounts to ₹ 1012 in 2.5 years and to ₹ 1067.20 in 4 years at simple interest. Find the annual rate.

Accepted Answer

Introduction / Context: Two amounts at different times under simple interest allow us to extract the annual interest directly from their difference and then back out the rate. Given Data / Assumptions: A1 = ₹ 1012 at t1 = 2.5 years. A2 = ₹ 1067.20 at t2 = 4 years. Simple interest applies. Concept / Approach: The increase in amount from t1 to t2 equals the extra interest accrued in (t2 − t1) years. That extra interest per year equals P * r. Step-by-Step Solution: A2 − A1 = 1067.20 − 1012 = ₹ 55.20 over 1.5 years.Hence annual interest = 55.20 / 1.5 = ₹ 36.80 = P * r.At t1 = 2.5 years, interest = 36.80 * 2.5 = ₹ 92.00, so P = 1012 − 92 = ₹ 920.Therefore r = 36.80 / 920 = 0.04 = 4% per annum. Verification / Alternative check: Check A2: Interest in 4 years = 920 * 0.04 * 4 = 147.20; Amount = 920 + 147.20 = 1067.20 (matches). Why Other Options Are Wrong: 2.5%, 3%, 5%, 6% do not satisfy both amounts simultaneously. Common Pitfalls: Assuming the difference depends on changing principal; under SI, principal remains the same. Final Answer: 4%

Question 15

Simple Interest — A sum becomes three times in 20 years at simple interest. In how many years will it become double at the same rate?

Accepted Answer

Introduction / Context: First use the tripling information to deduce the rate under simple interest, then reuse that rate to find the doubling time. Given Data / Assumptions: A = 3P in 20 years (simple interest). Same rate is used to find time to double. Concept / Approach: If A = 3P, then SI = 2P over 20 years. Hence P * r * 20 = 2P ⇒ r = 2/20 = 0.10 = 10% p.a. Step-by-Step Solution: Rate r = 10% per annum.To double: need SI = P.P = P * r * t ⇒ P = P * 0.10 * t ⇒ t = 10 years. Verification / Alternative check: At 10% for 10 years: SI = P; amount = 2P. Why Other Options Are Wrong: 8, 12, 14, 16 years do not match r = 10% derived from the tripling data. Common Pitfalls: Carrying compound interest ideas into a simple interest setting. Final Answer: 10 yr

Question 16

Simple Interest — For a principal of ₹ 1500, the simple interest is ₹ 30 in 4 years and ₹ 60 in 8 years. Find the annual rate of simple interest.

Accepted Answer

Introduction / Context: The proportionality of simple interest to time lets us infer the rate from any correct time-interest pair. Given Data / Assumptions: P = ₹ 1500. SI in 4 years = ₹ 30. SI in 8 years = ₹ 60 (consistent with linearity). Concept / Approach: SI = P * r * t ⇒ r = SI / (P * t). Step-by-Step Solution: Using the 4-year data: r = 30 / (1500 * 4) = 30 / 6000 = 0.005.Convert to percent: 0.5% per annum. Verification / Alternative check: Using 8-year data: r = 60 / (1500 * 8) = 60 / 12000 = 0.005 = 0.5%. Why Other Options Are Wrong: 2.5%, 1.5%, 1%, 0.25% do not produce the given SI pairs. Common Pitfalls: Forgetting to divide the percent by 100 when converting to decimal for formulas. Final Answer: 0.5%

Question 17

Simple Interest — At what annual rate will the simple interest in 10 years be one-fifth of the amount?

Accepted Answer

Introduction / Context: The phrase “simple interest is one-fifth of the amount” relates SI to A (not to P). Convert that relation to P and SI to find the rate over the given time. Given Data / Assumptions: In 10 years, SI = (1/5) * A. A = P + SI (simple interest). Concept / Approach: Let SI = A / 5. Since A = P + SI, substitute to relate SI to P alone and then use SI = P * r * t. Step-by-Step Solution: Given SI = A / 5 and A = P + SI.So SI = (P + SI) / 5 ⇒ 5SI = P + SI ⇒ 4SI = P.Hence SI = P / 4 over 10 years.But SI = P * r * t ⇒ P / 4 = P * r * 10.Cancel P: 1 / 4 = 10r ⇒ r = 1 / 40 = 0.025 = 2.5% per annum. Verification / Alternative check: At 2.5% for 10 years, SI = 25% of P; A = 125% of P; SI / A = 0.25 / 1.25 = 1/5, which matches. Why Other Options Are Wrong: 2%, 1%, 4%, 5% do not satisfy SI = A / 5 at 10 years. Common Pitfalls: Misreading “one-fifth of the amount” as “one-fifth of the principal.” They are different statements. Final Answer: 2.5%

Question 18

Simple Interest – Find the annual rate from final amount: Mr. Deepak invests ₹ 21,250 for 6 years at simple interest. The total amount received at the end of 6 years is ₹ 26,350. At what annual simple-interest rate (per annum) did his money grow?

Accepted Answer

Introduction / Context: Simple interest problems often ask for one missing variable among principal, rate, time, or amount. Here, the principal (₹ 21,250), time (6 years), and final amount (₹ 26,350) are given; we must determine the annual simple-interest rate. Simple interest grows linearly with time, making back-calculations straightforward when any three of the four quantities are known. Given Data / Assumptions: Principal P = ₹ 21,250 Time t = 6 years Amount A = ₹ 26,350 Simple interest I = A − P Rate r is the annual rate in percent per annum Concept / Approach: For simple interest, I = P * r * t / 100 and A = P + I. When P, t, and A are known, compute I and solve for r using r = (I * 100) / (P * t). Step-by-Step Solution: I = A − P = 26,350 − 21,250 = 5,100r = (I * 100) / (P * t)r = (5,100 * 100) / (21,250 * 6)r = 510,000 / 127,500 = 4Therefore r = 4% per annum Verification / Alternative check: Check I using r = 4%: I = 21,250 * 4 * 6 / 100 = 21,250 * 0.24 = 5,100A = P + I = 21,250 + 5,100 = 26,350 (matches the given amount) Why Other Options Are Wrong: 5%, 6%, 8%, and 12% would produce higher interest than ₹ 5,100 over 6 years for the same principal, so they do not match the stated final amount. Common Pitfalls: Confusing amount with interest, or using compound interest formulas when the question clearly states simple interest, often leads to incorrect rates. Always compute interest first, then substitute into the simple interest formula. Final Answer: 4% per annum

Question 19

Simple Interest – Equate two interest expressions to find the unknown rate: The simple interest on ₹ 4,000 for 3 years at R% per annum equals the simple interest on ₹ 5,000 at 12% per annum for 2 years. Find the value of R.

Accepted Answer

Introduction / Context: When two simple-interest amounts are stated as equal, we can equate their formulas and solve for the unknown rate. This is a standard algebraic setup involving I = P * r * t / 100 for each case. Given Data / Assumptions: Case 1: P1 = ₹ 4,000, time t1 = 3 years, rate = R% per annum Case 2: P2 = ₹ 5,000, time t2 = 2 years, rate = 12% per annum Simple interest: I = P * r * t / 100 Concept / Approach: Set I1 = I2 and solve for R. This avoids computing the principal or amount; we only manipulate proportional quantities. Step-by-Step Solution: I1 = 4,000 * R * 3 / 100 = 120RI2 = 5,000 * 12 * 2 / 100 = 1,200Equate: 120R = 1,200 ⇒ R = 10 Verification / Alternative check: Compute I1 with R = 10%: I1 = 4,000 * 10 * 3 / 100 = 1,200, which equals I2. Hence R = 10% is consistent. Why Other Options Are Wrong: 6%, 8%, and 9% give less than ₹ 1,200 for Case 1; 12% gives more than required when substituted back, so they do not satisfy equality. Common Pitfalls: Using amounts instead of interests, or forgetting to divide by 100, leads to scale errors. Keep units and percent handling consistent. Final Answer: 10%

Question 20

Simple Interest – Compute 6-month interest after back-finding principal: A sum amounts to ₹ 2,240 at 4% per annum simple interest in 3 years. Find the interest on the same principal for 6 months at 3.5% per annum.

Accepted Answer

Introduction / Context: This problem requires back-calculating the principal from a given amount under simple interest and then using that principal to find interest for a different time and rate. The linear nature of simple interest keeps calculations direct and proportional. Given Data / Assumptions: A = ₹ 2,240 after 3 years at 4% per annum Simple interest relation: A = P + I and I = P * r * t / 100 We need 6-month interest (t = 0.5 year) at 3.5% per annum on the same P Concept / Approach: First find P from A = P(1 + r * t / 100). Then compute I for the new t and r with I = P * r * t / 100. Step-by-Step Solution: A = P(1 + 4 * 3 / 100) = P(1 + 0.12) = 1.12PSo P = 2,240 / 1.12 = 2,000For 6 months at 3.5%: I = 2,000 * 3.5 * 0.5 / 100 = 35 Verification / Alternative check: Compute the original 3-year interest at 4%: I = 2,000 * 4 * 3 / 100 = 240, amount = 2,240 as given. The interim calculation of P = ₹ 2,000 is confirmed. Why Other Options Are Wrong: ₹ 30 and ₹ 25 understate the half-year interest; ₹ 50 and ₹ 150 overstate it for the specified rate and principal. Common Pitfalls: Misreading 6 months as 6 years or as 1 month, and mixing compound interest with simple interest, can distort results. Ensure time is in years for the formula. Final Answer: ₹ 35

Simple Interest Questions