Question 1

Simple Interest – Find rate percent from two amounts: A sum amounts to Rs 1,260 in 2 years and to Rs 1,350 in 5 years at simple interest. Find the annual rate of interest (percent per annum).

Accepted Answer

Introduction / Context:Two amounts at two times under SI directly reveal the uniform annual interest, enabling calculation of both principal and rate. Here, only the rate is asked. Given Data / Assumptions: A2 = Rs 1260 (t = 2 years) A5 = Rs 1350 (t = 5 years) Concept / Approach:Annual SI = (A5 - A2) / (5 - 2). Principal P = A2 - 2 * (annual SI). Rate r% = (annual SI / P) * 100. Step-by-Step Solution: Annual SI = (1350 - 1260) / 3 = 90 / 3 = Rs 30Principal P = 1260 - 2 * 30 = Rs 1200Rate r% = (30 / 1200) * 100 = 2.5% Verification / Alternative check: Check A5 = 1200 * (1 + 0.025 * 5) = 1200 * 1.125 = 1350 (matches) Why Other Options Are Wrong: 30% / 10% / 5% / 7.5%: do not fit the computed annual increase and principal. Common Pitfalls: Dividing by total time instead of the time gap between the two amounts. Using compound interest logic. Final Answer:2.5% per annum.

Question 2

Simple Interest – Infer principal from difference in interest rates: The difference between simple interest at 13% per annum and 12% per annum on the same sum for 1 year is Rs 110. Find the principal.

Accepted Answer

Introduction / Context:At simple interest, interest is P * r * t. For the same P and t, the difference between two interest rates over 1 year directly equals P multiplied by the rate gap. Given Data / Assumptions: Rate1 = 13% per annum Rate2 = 12% per annum Time = 1 year Difference in SI = Rs 110 Concept / Approach:Difference = P * (0.13 - 0.12) * 1 = 0.01 * P. Hence P = Difference / 0.01. Step-by-Step Solution: 0.01 * P = 110P = 110 / 0.01 = Rs 11000 Verification / Alternative check: At 12%: SI = 1320; at 13%: SI = 1430; difference = 110 (consistent) Why Other Options Are Wrong: Rs 12000 / Rs 13000 / Rs 16000 / Rs 10000: produce differences other than Rs 110 when multiplied by 1%. Common Pitfalls: Using percentage points incorrectly. Confusing difference in rate with ratio of rates. Final Answer:Rs 11000.

Question 3

Simple Interest – Rate to triple the principal: At what annual simple interest rate will a sum of money become three times the principal in 25 years?

Accepted Answer

Introduction / Context:Tripling under SI means the interest equals 2P over the period. The linear relation SI = P * r * t lets us directly solve for r. Given Data / Assumptions: Target amount = 3P Time t = 25 years Simple interest model Concept / Approach:If A = 3P, then SI = A - P = 2P. Therefore P * r * t = 2P → r = 2 / t. Step-by-Step Solution: r = 2 / 25 = 0.08 = 8% per annum Verification / Alternative check: Check: A = P * (1 + 0.08 * 25) = P * (1 + 2) = 3P Why Other Options Are Wrong: 5% / 6% / 7.5% / 12%: do not satisfy r = 2 / 25. Common Pitfalls: Interpreting tripling as interest = 3P (it is 2P). Final Answer:8% per annum.

Question 4

Simple Interest – Recover the principal from two amounts: A certain sum amounts to Rs 1,040 in 3 years and Rs 1,360 in 7 years at simple interest. Find the principal (original sum).

Accepted Answer

Introduction / Context:With SI, the difference in amounts over two times equals the uniform interest accrued during the gap. This reveals annual SI and then the principal. Given Data / Assumptions: A3 = Rs 1040 A7 = Rs 1360 Concept / Approach:Annual SI = (A7 - A3) / (7 - 3). Then P = A3 - 3 * (annual SI). Step-by-Step Solution: Annual SI = (1360 - 1040) / 4 = 320 / 4 = Rs 80Principal P = 1040 - 3 * 80 = 1040 - 240 = Rs 800 Verification / Alternative check: Check A7 = 800 + 7 * 80 = 1360 (matches) Why Other Options Are Wrong: Rs 750 / 900 / 1000 / 850: do not satisfy both given amounts under a single annual SI. Common Pitfalls: Miscalculating the time gap (7 - 3). Final Answer:Rs 800.

Question 5

Simple Interest – Find principal from annual interest requirement: At a simple interest rate of 12% per annum, what principal will earn Rs 6,000 interest per year?

Accepted Answer

Introduction / Context:Under SI, yearly interest equals P * r. If the required yearly interest is known, we can directly solve for P. Given Data / Assumptions: Annual SI desired = Rs 6000 r = 12% = 0.12 per annum Concept / Approach:P = (Annual SI) / r. Step-by-Step Solution: P = 6000 / 0.12 = Rs 50000 Verification / Alternative check: Annual SI on Rs 50000 at 12% = 50000 * 0.12 = Rs 6000 Why Other Options Are Wrong: Rs 7200 / 48543.69: numerically inconsistent. Rs 72000 / Rs 60000: give different annual interests than Rs 6000 at 12%. Common Pitfalls: Treating the figure as total interest over multiple years instead of annual. Final Answer:Rs 50000.

Question 6

Simple Interest – Find the principal from total interest: The simple interest on a certain sum for 3 years at 14% per annum is Rs 235.20. Find the principal.

Accepted Answer

Introduction / Context:Given SI, rate, and time, the principal is obtained using SI = P * r * t. This is a direct inversion problem under simple interest. Given Data / Assumptions: SI = Rs 235.20 r = 14% = 0.14 per annum t = 3 years Concept / Approach:P = SI / (r * t). Step-by-Step Solution: r * t = 0.14 * 3 = 0.42P = 235.20 / 0.42 = Rs 560 Verification / Alternative check: Check SI = 560 * 0.14 * 3 = 560 * 0.42 = Rs 235.20 (matches) Why Other Options Are Wrong: Rs 480 / 650 / 720 / 520: do not reproduce SI = Rs 235.20 under the given rate and time. Common Pitfalls: Miscalculating decimal multiplication 0.14 * 3. Final Answer:Rs 560.

Question 7

Simple Interest – Determine rate percent from two amounts: A sum of money amounts to Rs 702 in 2 years and Rs 783 in 3 years at simple interest. Find the annual rate of interest (percent per annum).

Accepted Answer

Introduction / Context:The difference between consecutive-year amounts under SI equals the constant annual interest. Dividing by the principal yields the rate. Given Data / Assumptions: A2 = Rs 702 A3 = Rs 783 Concept / Approach:Annual SI = A3 - A2. Then find P from A2 = P + 2 * (annual SI). Compute r% = (annual SI / P) * 100. Step-by-Step Solution: Annual SI = 783 - 702 = Rs 81P = 702 - 2 * 81 = 702 - 162 = Rs 540r% = (81 / 540) * 100 = 15% per annum Verification / Alternative check: A3 check: 540 + 3 * 81 = 540 + 243 = 783 (matches) Why Other Options Are Wrong: 12% / 13% / 14% / 11%: not equal to (81 / 540) * 100. Common Pitfalls: Forgetting that annual SI is the difference between adjacent yearly amounts. Final Answer:15% per annum.

Question 8

Simple Interest – Scale an amount at the same rate: If Rs 64 amounts to Rs 83.20 in 2 years at simple interest, then at the same rate what will Rs 86 amount to in 4 years?

Accepted Answer

Introduction / Context:We first extract the rate from the first scenario, then apply the same simple interest rate to the new principal and time to get the new amount. Given Data / Assumptions: 64 amounts to 83.20 in 2 years → SI over 2 years = 19.20 Need amount for 86 in 4 years at same rate Concept / Approach:From the first case, find yearly SI and rate. Then use A = P * (1 + r * t) for the second case. Step-by-Step Solution: Yearly SI on Rs 64 = 19.20 / 2 = 9.60Rate r% = (9.60 / 64) * 100 = 15%For P = 86, t = 4: A = 86 * (1 + 0.15 * 4) = 86 * 1.60 = Rs 137.60 Verification / Alternative check: Direct proportionality under SI confirms linear scaling with P and t. Why Other Options Are Wrong: Other values do not match A = 86 * 1.60. Common Pitfalls: Applying compound growth instead of simple interest. Final Answer:Rs 137.60.

Question 9

Simple Interest – Find the principal from two amounts: A sum amounts to Rs 850 in 3 years and Rs 925 in 4 years at simple interest. Find the principal (original sum).

Accepted Answer

Introduction / Context:The per-year increase under SI equals the difference between consecutive-year amounts. Subtracting the appropriate multiple from an earlier amount reveals the principal. Given Data / Assumptions: A3 = Rs 850 A4 = Rs 925 Concept / Approach:Annual SI = A4 - A3. Then P = A3 - 3 * (annual SI). Step-by-Step Solution: Annual SI = 925 - 850 = Rs 75P = 850 - 3 * 75 = 850 - 225 = Rs 625 Verification / Alternative check: A4 check: 625 + 4 * 75 = 625 + 300 = 925 Why Other Options Are Wrong: Rs 600 / 575 / 650: not consistent with both amounts. Data inadequate: data is sufficient in SI. Common Pitfalls: Mistaking SI for compound interest. Final Answer:Rs 625.

Question 10

Simple Interest – Rate percent when a sum trebles: A sum of money placed at simple interest becomes three times the principal in 15 years. Find the annual rate of interest (percent per annum).

Accepted Answer

Introduction / Context:Trebles means the amount equals 3P, so the interest earned is 2P. With SI, SI = P * r * t; solve for r using t = 15 years. Given Data / Assumptions: A = 3P t = 15 years Concept / Approach:Since SI = A - P = 2P, we have P * r * 15 = 2P ⇒ r = 2 / 15 per year = 0.1333... = 13 1/3%. Step-by-Step Solution: r = 2 / 15 = 0.1333... = 13 1/3% Verification / Alternative check: A = P * (1 + r * t) = P * (1 + 2) = 3P (consistent) Why Other Options Are Wrong: 16 2/3% / 12 2/3% / 20% / 10%: do not equal 2 / 15 as a percent. Common Pitfalls: Confusing treble (3P) with double (2P). Final Answer:13 1/3% per annum.

Question 11

Simple Interest – Time to treble when doubling time is known: At a certain simple interest rate, a sum doubles itself in 10 years. In how many years will it become three times the principal?

Accepted Answer

Introduction / Context:From the doubling time under SI, we can derive the rate and then compute the time to reach any other multiple of P, such as 3P (treble). Given Data / Assumptions: Doubling time = 10 years Simple interest model Concept / Approach:Doubling means P * r * 10 = P ⇒ r = 1 / 10 = 10%. For trebling (A = 3P), interest must be 2P, so t = 2P / (P * r) = 2 / 0.10 = 20 years. Step-by-Step Solution: r = 1 / 10 = 10% per annumt for 3P = 2 / 0.10 = 20 years Verification / Alternative check: A = P * (1 + 0.10 * 20) = 3P (matches) Why Other Options Are Wrong: 15 / 12 / 25 years: inconsistent with r = 10%. 30 years: overestimates time. Common Pitfalls: Treating SI as compound interest. Final Answer:20 years.

Question 12

Simple Interest – Find the principal from two amounts: A sum amounts to Rs 2,240 in 2 years and Rs 2,600 in 5 years at simple interest. Find the principal (original sum).

Accepted Answer

Introduction / Context:Two amounts at different times let us compute the uniform annual SI and hence the principal in a linear SI model. Given Data / Assumptions: A2 = Rs 2240 A5 = Rs 2600 Concept / Approach:Annual SI = (A5 - A2) / (5 - 2). Then P = A2 - 2 * (annual SI). Step-by-Step Solution: Annual SI = (2600 - 2240) / 3 = 360 / 3 = Rs 120P = 2240 - 2 * 120 = 2240 - 240 = Rs 2000 Verification / Alternative check: A5 check: 2000 + 5 * 120 = 2600 (matches) Why Other Options Are Wrong: Rs 1880 / 2120 / 1960: do not fit both given amounts. Data inadequate: sufficient for SI. Common Pitfalls: Mistaking the time gap. Final Answer:Rs 2000.

Question 13

Simple Interest – Parameterized symbol problem: The simple interest at R percent per annum for R years is Rs R. On what principal will this occur?

Accepted Answer

Introduction / Context:This symbolic question checks formula manipulation in simple interest: SI = P * r * t, with r expressed in percent per annum and t in years. Given Data / Assumptions: SI = R rupees Rate = R% per annum = R / 100 per annum Time = R years Concept / Approach:Using SI = P * (R / 100) * R, solve for P such that SI equals R rupees. Step-by-Step Solution: SI = P * (R / 100) * R = P * (R^2 / 100)Set SI = R → P * (R^2 / 100) = RP = R * 100 / R^2 = 100 / RHence P = Rs (100 / R) Verification / Alternative check: Substitute back: SI = (100 / R) * (R / 100) * R = R Why Other Options Are Wrong: Rs R / Rs 100R / Rs (R/100): dimensionally incorrect. Rs (100/R2): miswritten as R squared in denominator without proper notation; intended value is 100 / R. Common Pitfalls: Mishandling the percent-to-decimal conversion. Final Answer:Rs (100/R).

Question 14

Simple Interest – Rate when a sum doubles: At simple interest, a sum doubles itself in 20 years. Find the annual rate of interest (percent per annum).

Accepted Answer

Introduction / Context:Doubling under SI means the interest over the period equals the principal. This gives a direct relation between rate and time. Given Data / Assumptions: Doubling time t = 20 years Concept / Approach:If A = 2P, SI = P. With SI = P * r * t, we get P = P * r * 20 → r = 1 / 20 = 5% per annum. Step-by-Step Solution: r = 1 / 20 = 0.05 = 5% per annum Verification / Alternative check: A = P * (1 + 0.05 * 20) = 2P Why Other Options Are Wrong: 10% / 12% / 7.5%: inconsistent with doubling in 20 years under SI. Data inadequate: not true; data is sufficient. Common Pitfalls: Treating as compound interest. Final Answer:5% per annum.

Question 15

Simple Interest – Equal annual payments to discharge a debt: What equal annual payment will exactly discharge a debt of Rs 580 due in 5 years at 8% per annum simple interest, assuming payments are made at the end of each year?

Accepted Answer

Introduction / Context:When equal annual payments are made under simple interest and the target is to clear a debt at the end of a fixed period, earlier payments accrue simple interest up to the final date. The sum of accumulated values of all payments equals the debt due at maturity. Given Data / Assumptions: Debt due at end of year 5: Rs 580 Rate r = 8% per annum Five equal payments X at ends of years 1, 2, 3, 4, 5 Concept / Approach:Accumulate each payment to the end of year 5 using SI factors: (1 + r * n), where n is the number of years remaining to year 5. Sum of accumulated payments = 580. Step-by-Step Solution: Accumulation factors to end of year 5: 1.32 (4 yrs), 1.24 (3 yrs), 1.16 (2 yrs), 1.08 (1 yr), 1.00 (0 yr)Sum of factors = 1.32 + 1.24 + 1.16 + 1.08 + 1.00 = 5.80Let annual payment = X. Then X * 5.80 = 580 ⇒ X = Rs 100 Verification / Alternative check: Backward check confirms total accumulated value equals Rs 580 at year 5. Why Other Options Are Wrong: Rs 166.40 / 120 / 90 / 65.60: do not satisfy X * 5.80 = 580. Common Pitfalls: Compounding instead of using simple accumulation factors. Using discounting to present instead of accumulation to year 5. Final Answer:Rs 100 per year.

Question 16

Simple Interest – Find the rate from total interest paid: Ashok borrowed Rs 15,000 for 3 years at simple interest. If the total interest paid is Rs 2,700, find the annual rate of interest (percent per annum).

Accepted Answer

Introduction / Context:Total interest over a period with known principal and time under SI directly yields the annual rate by rearranging SI = P * r * t. Given Data / Assumptions: P = Rs 15000 t = 3 years SI total = Rs 2700 Concept / Approach:r = SI / (P * t), expressed in percent by multiplying by 100 if needed. Here options are numeric rate values already in percent units. Step-by-Step Solution: r = 2700 / (15000 * 3) = 2700 / 45000 = 0.06 = 6 Verification / Alternative check: Annual interest = 15000 * 6% = 900; for 3 years = 2700 (consistent) Why Other Options Are Wrong: 18 / 9 / 7.2 / 5.4: do not match computed r. Common Pitfalls: Forgetting to divide by both P and t. Final Answer:6.

Question 17

Simple Interest – Find the rate given total interest: Yogesh borrowed Rs 12,000 at simple interest for 5 years. If he paid Rs 3,600 as simple interest, find the annual rate of interest (percent per annum).

Accepted Answer

Introduction / Context:With principal, time, and total SI known, the SI rate is r = SI / (P * t). This is a standard direct-calculation problem under simple interest assumptions. Given Data / Assumptions: P = Rs 12000 t = 5 years SI = Rs 3600 Concept / Approach:Compute r as a pure number (fraction), then read as percentage consistent with the options provided. Step-by-Step Solution: r = 3600 / (12000 * 5) = 3600 / 60000 = 0.06 = 6 Verification / Alternative check: Annual SI = 12000 * 6% = 720; total over 5 years = 3600 (matches) Why Other Options Are Wrong: 5 / 8 / 10 / 7.5: do not equal the computed rate. Common Pitfalls: Mistaking the units, e.g., writing 0.06% instead of 6%. Final Answer:6.

Question 18

Simple Interest — A sum of money doubles itself in 20 years under simple interest. What is the annual rate of simple interest (per cent per year)?

Accepted Answer

Introduction / Context:Many aptitude questions ask for the rate of simple interest when the final amount is a given multiple of the original principal. Under simple interest, growth is linear with time, so doubling or tripling leads to direct proportional relations between time, rate, and principal. Given Data / Assumptions: The amount becomes double of the principal in 20 years. Interest is simple, applied per annum. Let principal be P (any positive amount). Concept / Approach:For simple interest: Amount A = P + SI, and SI = P * r * t, where r is rate per year (in decimal) and t is time in years. Step-by-Step Solution:Given A = 2P in 20 years.So SI = A - P = 2P - P = P.But SI = P * r * t.Hence P = P * r * 20.Cancel P (P > 0): 1 = r * 20.Therefore r = 1 / 20 = 0.05 = 5% per annum. Verification / Alternative check:If r = 5%, then SI in 20 years = P * 0.05 * 20 = P, so A = P + P = 2P, which matches the condition. Why Other Options Are Wrong:4% or 8% or 10% would produce amounts not exactly equal to 2P in 20 years under simple interest. Common Pitfalls:Confusing simple interest with compound interest; for simple interest, use linear SI = P * r * t. Final Answer:5%

Question 19

Simple Interest — Mr. Patel borrows ₹ 8000 at simple interest. After 2 years he repays ₹ 8800 (₹ 800 more than he borrowed) and clears the loan. What is the annual rate of interest?

Accepted Answer

Introduction / Context:This is a direct simple-interest rate computation from the difference between amount repaid and principal. Given Data / Assumptions: Principal P = ₹ 8000. Time t = 2 years. Amount repaid A = ₹ 8800, so total simple interest SI = ₹ 8800 − ₹ 8000 = ₹ 800. Concept / Approach:Under simple interest: SI = P * r * t, where r is the annual rate in decimal. Step-by-Step Solution:SI = 800.P * r * t = 8000 * r * 2 = 800.So r = 800 / (8000 * 2) = 800 / 16000 = 0.05.Convert to percent: r = 5% per annum. Verification / Alternative check:At 5% per annum for 2 years: SI = 8000 * 0.05 * 2 = 800. Amount = 8000 + 800 = 8800, which matches the repayment. Why Other Options Are Wrong:6% or 8% produce higher interest than ₹ 800 over 2 years; 4% produces less. Common Pitfalls:Forgetting to convert the rate to decimal (divide by 100) when using the formula. Final Answer:5%

Question 20

Simple Interest — ₹ 4200 amounts to ₹ 5712 in 4 years. If the rate is then increased by 3 percentage points, what will be the new amount after the same 4 years on ₹ 4200?

Accepted Answer

Introduction / Context:This problem first determines the original rate using a known amount after 4 years, then increases the rate by 3 percentage points to compute a new amount for the same principal and time. Given Data / Assumptions: Original principal P = ₹ 4200. Original amount A = ₹ 5712 after t = 4 years. Rate is increased by 3 percentage points (e.g., 9% to 12%). Concept / Approach:Simple interest: A = P * (1 + r * t). First solve for the original rate r from the first scenario, then compute the new amount with r_new = r + 0.03. Step-by-Step Solution:Original: 5712 = 4200 * (1 + r * 4).Divide: 5712 / 4200 = 1 + 4r.5712 / 4200 = 1.36; hence 4r = 0.36 ⇒ r = 0.09 = 9%.Increase rate by 3 points ⇒ r_new = 12% = 0.12.New amount = 4200 * (1 + 0.12 * 4) = 4200 * 1.48 = ₹ 6216. Verification / Alternative check:Compute SI directly: new SI = 4200 * 0.12 * 4 = 4200 * 0.48 = 2016; Amount = 4200 + 2016 = 6216. Why Other Options Are Wrong:₹ 6372 is too high; ₹ 6120 too low; ₹ 4000 or ₹ 3000 ignore interest. Common Pitfalls:Confusing “+3%” (relative increase) with “+3 percentage points.” Here it is absolute points, so 9% becomes 12%. Final Answer:₹ 6216

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