Question 1

Simple Interest – Check feasibility when interest equals half the sum: The simple interest on a sum at 9% per annum for 5 years is stated to be half the principal. Determine the sum or conclude if the data are not feasible.

Accepted Answer

Introduction / Context: Sometimes a simple-interest statement contradicts the formula, indicating that no real principal can satisfy the given relation. We must compare the proportional interest implied by the rate and time against the claimed fraction of the principal. Given Data / Assumptions: Rate r = 9% per annum Time t = 5 years Claim: simple interest equals half of the principal Concept / Approach: For simple interest, I = P * r * t / 100. Compute the actual fraction of P produced by the given r and t, then compare with the claim of 1/2 P. Step-by-Step Solution: I / P = (r * t) / 100 = (9 * 5) / 100 = 45 / 100 = 0.45The claim requires I / P = 0.50Since 0.45 ≠ 0.50, no principal P can satisfy both the formula and the claim simultaneously. Verification / Alternative check: Pick any P (e.g., ₹ 5,000): I = 5,000 * 9 * 5 / 100 = ₹ 2,250, which is 45% of P, not 50%. The mismatch is independent of P. Why Other Options Are Wrong: Specific rupee values (₹ 5,800, ₹ 5,000, ₹ 7,000) cannot repair a percentage inconsistency. The outcome does not depend on P. “Not possible” conveys infeasibility; “Data is inadequate” is the intended pick here since no sum can be determined from inconsistent data. Common Pitfalls: Mistaking amount for interest or assuming compound interest when the prompt specifies simple interest can mask such contradictions. Final Answer: Data is inadequate

Question 2

Simple Interest – Feasibility check repeated at 8% for 6 years: The simple interest on a sum at 8% per annum for 6 years is claimed to be half the principal. Determine the sum or conclude feasibility.

Accepted Answer

Introduction / Context: We test whether the given interest statement is compatible with simple-interest proportionality. If the computed interest fraction differs from the claim, no principal can satisfy the condition, and we cannot determine a unique sum. Given Data / Assumptions: Rate r = 8% per annum Time t = 6 years Claim: simple interest equals half of the principal Concept / Approach: Use I = P * r * t / 100 and compare I / P to 1/2. The fraction depends only on r and t for simple interest, not on P. Step-by-Step Solution: I / P = (r * t) / 100 = (8 * 6) / 100 = 48 / 100 = 0.48The claim requires 0.50. Since 0.48 ≠ 0.50, the condition cannot be met by any principal. Verification / Alternative check: Try P = ₹ 6,000: I = 6,000 * 8 * 6 / 100 = ₹ 2,880 (48% of P), not half. The contradiction persists for all P values. Why Other Options Are Wrong: Numerical principal choices cannot resolve a percentage contradiction. “Not possible” is a reasonable description; within the provided set, the intended answer is “Data is inadequate” (no sum can be uniquely determined). Common Pitfalls: Confusing “half the amount” with “half the principal,” or overlooking that simple interest scales linearly with P, r, and t, not with arbitrary claims. Final Answer: Data is inadequate

Question 3

Simple Interest – Find principal from difference due to rate increase: A sum is invested for 2 years at simple interest. If the rate is increased by 3% per annum, the total interest earned becomes ₹ 300 more. Find the principal.

Accepted Answer

Introduction / Context: When only the rate changes in simple interest, the change in interest is directly proportional to the principal and time. This allows us to solve for principal without knowing the original rate. Given Data / Assumptions: Time t = 2 years Increase in rate Δr = 3% per annum Increase in total interest ΔI = ₹ 300 Simple interest difference formula applies: ΔI = P * Δr * t / 100 Concept / Approach: Rearrange the difference formula to P = (ΔI * 100) / (Δr * t). This avoids computing the absolute interests at both rates. Step-by-Step Solution: P = (300 * 100) / (3 * 2)P = 30,000 / 6 = 5,000 Verification / Alternative check: At Δr = 3% for 2 years, extra interest on ₹ 5,000 is 5,000 * 3 * 2 / 100 = ₹ 300, which matches the given difference. Why Other Options Are Wrong: ₹ 6,000, ₹ 7,000, ₹ 4,000, and ₹ 8,000 yield differences of ₹ 360, ₹ 420, ₹ 240, and ₹ 480 respectively under the same Δr and t, not ₹ 300. Common Pitfalls: Forgetting to divide by 100, or misreading percentage points as decimal fractions, can cause scaling errors. Keep Δr in percent in the standard SI formula. Final Answer: ₹ 5,000

Question 4

Simple Interest – Feasibility at 10% for 6 years (claimed half the sum): The simple interest at 10% per annum for 6 years is said to be half the principal. Decide whether such a principal exists or report impossibility.

Accepted Answer

Introduction / Context: Under simple interest, the ratio I / P depends only on r and t via (r * t) / 100. If that ratio conflicts with a stated fraction of P, no principal can satisfy the condition. We check the claim that interest equals half the principal at 10% for 6 years. Given Data / Assumptions: Rate r = 10% per annum Time t = 6 years Claim: I = (1/2) P Concept / Approach: Compute I / P = (r * t) / 100 = (10 * 6) / 100 = 0.60. Compare with 0.50. If unequal, the claim is impossible for any P. Step-by-Step Solution: I / P = 0.60 ≠ 0.50Hence, the given requirement cannot be satisfied by any principal. Verification / Alternative check: Take P = ₹ 5,000: I = 5,000 * 10 * 6 / 100 = ₹ 3,000, which is 60% of P, not 50%. The mismatch is intrinsic to r and t, independent of P. Why Other Options Are Wrong: Any numeric principal contradicts the ratio. “Data is inadequate” is weaker than “Not possible,” because the data are sufficient to show infeasibility. Common Pitfalls: Confusing half the amount with half the principal, or applying compound interest ideas to a simple-interest prompt, can obscure this quick ratio check. Final Answer: Not possible

Question 5

Simple Interest – Symbolic rate/time: find the sum that yields interest Rs x: At x% simple interest for x years, the interest equals Rs x. On what principal will this occur?

Accepted Answer

Introduction / Context: This algebraic simple-interest question uses a symbolic percentage x% for a duration of x years and states that the resulting interest equals Rs x. We must infer the principal that makes the simple-interest formula produce that exact interest. Given Data / Assumptions: Rate r = x% per annum Time t = x years Interest I = Rs x Simple interest relation: I = P * r * t / 100 Concept / Approach: Substitute r and t into the formula and solve for P in terms of x. Keep x as a positive real to ensure meaningful financial interpretation. Step-by-Step Solution: I = P * x * x / 100 = P * x^2 / 100Given I = x ⇒ x = P * x^2 / 100Solve for P: P = 100 / x Verification / Alternative check: Plug P = 100 / x into I: I = (100 / x) * x^2 / 100 = x, which matches the given interest exactly. Why Other Options Are Wrong: Rs x and Rs 100x scale incorrectly with x; Rs (100/x^2) and Rs (x/100) produce wrong magnitudes when substituted back into I = P * x^2 / 100. Common Pitfalls: Dropping the 100 in the denominator or misinterpreting x% as x can produce quadratic or linear errors. Keep the percent handling consistent. Final Answer: Rs (100/x)

Question 6

Simple Interest – Find rate from two amounts at different times: A certain sum amounts to ₹ 575 in 3 years and ₹ 625 in 5 years under simple interest. Determine the annual rate of interest.

Accepted Answer

Introduction / Context: When amounts at two different times are known under simple interest, the yearly interest can be deduced from their difference because simple interest adds a fixed amount each year. This yields both the annual interest and then the rate relative to principal. Given Data / Assumptions: A(3 yr) = ₹ 575 A(5 yr) = ₹ 625 Simple interest adds a constant amount per year Concept / Approach: The difference in amounts over 2 years equals 2 times the annual interest. Use that to get the yearly interest, back-find principal from one amount, and compute the rate r = (annual interest / principal) * 100. Step-by-Step Solution: Difference over 2 years = 625 − 575 = 50Annual interest = 50 / 2 = 25Let P be principal; A(3 yr) = P + 3 * 25 = 575 ⇒ P = 575 − 75 = 500Rate r = (25 / 500) * 100 = 5% Verification / Alternative check: Check A(5 yr) = 500 + 5 * 25 = 625, consistent with data. Hence r = 5% is confirmed. Why Other Options Are Wrong: 3% and 4% yield too small an annual interest; 7% is too large relative to the observed differences. Common Pitfalls: Confusing amount differences with principal differences or assuming compound growth leads to incorrect inferences. Remember SI adds linearly per year. Final Answer: 5%

Question 7

Simple Interest – Rate equals time; interest is 1/9 of principal: The simple interest on a sum is one-ninth of the principal, and the number of years equals the rate percent per annum. Find the rate percent per annum.

Accepted Answer

Introduction / Context: Here the interest is a fixed fraction of principal (1/9), and the problem states an equality between two parameters: the number of years equals the rate percent. Such symmetry invites using the simple-interest formula with r = t to isolate the unknown rate. Given Data / Assumptions: I = P / 9 r = t (numerically equal) Simple interest I = P * r * t / 100 Concept / Approach: Substitute I and r = t into the formula to get P / 9 = P * r^2 / 100, cancel P, and solve for r. Keep r in percent units when interpreting the final numeric value. Step-by-Step Solution: P / 9 = P * r^2 / 100Cancel P (P > 0): 1 / 9 = r^2 / 100r^2 = 100 / 9 ⇒ r = 10 / 3 ≈ 3.333... percent Verification / Alternative check: Let r = t = 10 / 3. Then I / P = r * t / 100 = (10 / 3) * (10 / 3) / 100 = 100 / 9 / 100 = 1 / 9, matching the premise. Why Other Options Are Wrong: 3% and 4% yield different interest fractions; 3 1/10% (≈ 3.1%) is too small; 3.5% also does not satisfy r^2 = 100 / 9. Common Pitfalls: Confusing r (percent) with decimal rate, or failing to square r when r = t, results in incorrect values. Keep r in percent throughout. Final Answer: 10/3%

Question 8

Simple Interest – Income drop when rate falls from 13% to 12.5%: A moneylender’s yearly income decreases by ₹ 104 when his rate falls from 13% to 12.5% per annum. Find his capital.

Accepted Answer

Introduction / Context: Annual simple-interest income is proportional to both the rate and the capital. A small percentage drop producing a known rupee decrease allows direct computation of capital via proportional reasoning. Given Data / Assumptions: Old rate r1 = 13% per annum New rate r2 = 12.5% per annum Annual income drop ΔI = ₹ 104 Capital C is constant Concept / Approach: Income each year equals C * r / 100. Thus ΔI = C * (r1 − r2) / 100. Solve C = (ΔI * 100) / (r1 − r2). Step-by-Step Solution: Rate difference = 13% − 12.5% = 0.5% = 0.5C = (104 * 100) / 0.5 = 10,400 / 0.5 = 20,800 Verification / Alternative check: At 13%, income = 0.13C; at 12.5%, income = 0.125C; difference = 0.005C. With C = 20,800, 0.005C = 104, as given. Why Other Options Are Wrong: Other capitals produce income differences not equal to ₹ 104 under a 0.5% change, hence they violate the given condition. Common Pitfalls: Interpreting 0.5% as 0.5 (without dividing by 100) or mixing per-annum values with multi-year totals leads to errors. Here, the change is explicitly per year. Final Answer: ₹ 20,800

Question 9

Simple Interest – Mixed investments at 7%, 8%, and 10% yield ₹ 561 yearly: A man invests 1/3 of his capital at 7%, 1/4 at 8%, and the remainder at 10%. His total annual income is ₹ 561. Find the total capital.

Accepted Answer

Introduction / Context: This is a weighted-average simple-interest problem: parts of the capital earn different rates, and the total annual income is known. By summing the contributions, we can solve for the total capital. Given Data / Assumptions: Fractions: 1/3 at 7%, 1/4 at 8%, remainder at 10% Total annual income = ₹ 561 Let total capital be C Concept / Approach: Compute the effective rate on the whole capital as the weighted sum: (1/3)*7% + (1/4)*8% + (remainder)*10%. The remainder fraction is 1 − 1/3 − 1/4 = 5/12. Multiply the effective rate by C to match the given income. Step-by-Step Solution: Effective rate = (1/3)*7 + (1/4)*8 + (5/12)*10= 7/3 + 2 + 50/12 = 2.333... + 2 + 4.166... = 8.5%Thus 0.085 * C = 561 ⇒ C = 561 / 0.085 = 6,600 Verification / Alternative check: Income from parts: (C/3)*7% + (C/4)*8% + (5C/12)*10% = C*(0.085) = 561. Substituting C = 6,600 gives 561, confirming the result. Why Other Options Are Wrong: Other totals produce annual incomes not equal to ₹ 561 at the computed effective rate of 8.5%. Common Pitfalls: Forgetting to convert percentages to decimals, miscomputing the remainder fraction, or adding rates directly without weighting can cause mistakes. Final Answer: ₹ 6,600

Question 10

Simple Interest – Determine rate from two amounts at 2 and 5 years: A sum amounts to ₹ 1,260 in 2 years and ₹ 1,350 in 5 years under simple interest. Find the rate per cent per annum.

Accepted Answer

Introduction / Context: The difference between amounts under simple interest over different times reveals the constant annual interest. From that, we can deduce both principal and rate. Here we only need the rate per annum. Given Data / Assumptions: A(2 yr) = ₹ 1,260 A(5 yr) = ₹ 1,350 Simple interest: linear increase per year Concept / Approach: Difference over 3 years is 1,350 − 1,260 = 90, so annual interest is 90 / 3 = 30. Then deduce principal from A(2 yr) and compute r = (annual interest / principal) * 100. Step-by-Step Solution: Annual interest = (1,350 − 1,260) / 3 = 30Let P be principal; A(2 yr) = P + 2*30 = 1,260 ⇒ P = 1,200Rate r = (30 / 1,200) * 100 = 2.5% Verification / Alternative check: Check A(5 yr) = 1,200 + 5*30 = 1,350, consistent with the given values. Therefore r = 2.5% is correct. Why Other Options Are Wrong: 3.75%, 5%, and 7.5% imply annual interest values inconsistent with the observed differences between 2 and 5 years. Common Pitfalls: Using compound growth or mixing up the units (months vs years) will produce incorrect rates in simple-interest settings. Final Answer: 2.5%

Question 11

Simple Interest – Two loans produce ₹ 90 total interest: A lends ₹ 600 to B for 2 years and ₹ 150 to C for 4 years, both at the same simple-interest rate. The total interest received is ₹ 90. Find the annual rate.

Accepted Answer

Introduction / Context: When multiple loans share the same rate, their simple interests add linearly. The total interest allows solving for the common rate by summing each interest expression and equating to the given total. Given Data / Assumptions: Loan 1: P1 = ₹ 600, t1 = 2 years Loan 2: P2 = ₹ 150, t2 = 4 years Total simple interest = ₹ 90 Common rate r% per annum for both loans Concept / Approach: Total I = (P1 * r * t1 / 100) + (P2 * r * t2 / 100). Factor r and solve for it from the known total ₹ 90. Step-by-Step Solution: I_total = 600*r*2/100 + 150*r*4/100 = (1,200r + 600r)/100 = 1,800r/100 = 18rSet 18r = 90 ⇒ r = 90 / 18 = 5% per annum Verification / Alternative check: Compute interests at 5%: Loan 1 earns 600 * 5 * 2 / 100 = 60; Loan 2 earns 150 * 5 * 4 / 100 = 30; total = 90, as required. Why Other Options Are Wrong: 4% yields only ₹ 72 total; 10% and 12% produce totals above ₹ 90; 6% gives ₹ 108, not ₹ 90. Common Pitfalls: Forgetting to apply the rate to each principal for its own time or omitting the /100 when converting percent to a fraction are typical mistakes. Final Answer: 5%

Question 12

Simple Interest – New amount if the rate rises by 3 percentage points: ₹ 800 amounts to ₹ 920 in 3 years at simple interest. If the annual rate increases by 3 percentage points, what would be the new amount after the same 3 years?

Accepted Answer

Introduction / Context: We first deduce the original rate from the given amount progression under simple interest, then apply an increased rate for the same time period to compute the new amount. Given Data / Assumptions: Original: P = ₹ 800, A = ₹ 920 after 3 years Rate increase Δr = 3 percentage points per annum Simple interest applies in both scenarios Concept / Approach: Find original interest I = A − P; deduce annual interest and rate. New rate r_new = r_old + 3. Compute new SI and new amount. Step-by-Step Solution: Original I = 920 − 800 = 120 over 3 years ⇒ 40 per yearOriginal rate r_old = (40 / 800) * 100 = 5%New rate r_new = 5% + 3% = 8%New SI in 3 years = 800 * 8 * 3 / 100 = 192New amount = 800 + 192 = 992 Verification / Alternative check: At 8% per annum, one-year interest is 64; over 3 years, 64 * 3 = 192; adding to principal gives ₹ 992, consistent with the calculation. Why Other Options Are Wrong: ₹ 1,056, ₹ 1,112, and ₹ 1,182 correspond to higher rates or compounding (not applicable). ₹ 980 is less than principal, impossible with positive rates. Common Pitfalls: Confusing an increase of 3 percentage points with multiplying the original rate by 1.03. In simple interest, a “+3%” change means add 3 points to the rate, not 3% of the rate. Final Answer: ₹ 992

Question 13

Simple Interest – Repeat feasibility check (8% for 6 years equals half the sum): The simple interest on a sum at 8% per annum for 6 years is claimed to be half the principal. Determine whether a unique sum exists or report inadequacy.

Accepted Answer

Introduction / Context: This is the same structural check as earlier feasibility problems. Under simple interest, the fraction I / P depends solely on r and t. If it does not equal the claimed fraction, no specific principal can satisfy the condition, and a unique sum cannot be determined. Given Data / Assumptions: r = 8% per annum t = 6 years Claim: I = (1/2) P Concept / Approach: Compute I / P = (r * t) / 100. Compare with 1/2. If unequal, the data do not yield a unique principal compatible with the claim. Step-by-Step Solution: I / P = (8 * 6) / 100 = 0.48Claim requires 0.50 → inconsistent. Therefore no unique P exists under this claim. Verification / Alternative check: Testing any P shows the same 48% outcome, not 50%. Thus the contradiction is independent of P. Why Other Options Are Wrong: Specific rupee values cannot fix a percentage inconsistency. “Not possible” is acceptable wording; the intended key is that the data do not allow a unique principal to be found. Common Pitfalls: Misreading the claim as “half the amount” would lead to different equations. The problem clearly mentions the principal. Final Answer: Data inadequate

Question 14

Simple Interest – Rate from interest difference on ₹ 1,200 vs ₹ 1,000 over 3 years: The interest on ₹ 1,200 exceeds the interest on ₹ 1,000 by ₹ 50 in 3 years at the same rate. Find the annual rate percent.

Accepted Answer

Introduction / Context: With simple interest at the same rate, the extra interest earned by a higher principal over a fixed time equals the interest on the principal difference. This allows direct computation of the rate from the stated rupee difference. Given Data / Assumptions: P1 = ₹ 1,200, P2 = ₹ 1,000 Time t = 3 years Interest difference ΔI = ₹ 50 Common rate r% per annum Concept / Approach: The difference in interest equals (P1 − P2) * r * t / 100. Solve r from ΔI and the known difference in principal and time. Step-by-Step Solution: ΔP = 1,200 − 1,000 = 200ΔI = 200 * r * 3 / 100 = 6rSet 6r = 50 ⇒ r = 50 / 6 = 8 1/3% Verification / Alternative check: Compute interests at r = 8 1/3%: I1 − I2 = (200 * 8 1/3 * 3) / 100 = 50, validating the result. Why Other Options Are Wrong: 10 1/3%, 6 2/3%, and 9 2/3% produce differences not equal to ₹ 50 over 3 years for a ₹ 200 principal gap; 7 1/2% also does not match. Common Pitfalls: Ignoring that both loans share the same rate leads to unnecessary system solving. Use the principal difference directly. Final Answer: 8 1/3%

Question 15

Simple Interest – Time to double at 12% per annum: In how many years will a sum of money become twice its principal at 12% per annum under simple interest?

Accepted Answer

Introduction / Context: Under simple interest, doubling time is computed from the fact that the interest must equal the principal. This yields a direct formula for the time required given the annual rate. Given Data / Assumptions: Target amount A = 2P Rate r = 12% per annum Simple interest relation I = P * r * t / 100 Concept / Approach: For doubling, I = P. So P = P * r * t / 100 ⇒ t = 100 / r years. Substitute r = 12 to get the exact time in years and months. Step-by-Step Solution: t = 100 / 12 years = 25 / 3 years25 / 3 years = 8 + 1/3 years = 8 years 4 months Verification / Alternative check: At 12% per annum, annual interest is 12% of P. Over 8 1/3 years, interest totals (12% * 8 1/3) = 100% of P, so A = 2P, confirming the result. Why Other Options Are Wrong: 6 years 9 months, 7 years 6 months, and 8 years 6 months correspond to different rates or targets; only 8 years 4 months precisely equals 100/12 years. Common Pitfalls: Using compound interest rules (e.g., 72-rule) leads to approximations that are not required here. Simple interest gives an exact linear relation. Final Answer: 8 years 4 months

Question 16

Simple Interest – Find principal from ₹ 24 extra due to 1% higher rate over 2 years: A sum is invested for 2 years at simple interest. If raising the rate by 1% per annum increases the total interest by ₹ 24, find the principal.

Accepted Answer

Introduction / Context: This is a direct application of the simple-interest difference formula: the extra interest generated by a change in rate over a fixed time is proportional to the principal. We can solve for the principal without knowing the original rate. Given Data / Assumptions: Time t = 2 years Rate increase Δr = 1% per annum Extra interest ΔI = ₹ 24 Concept / Approach: Use ΔI = P * Δr * t / 100 ⇒ P = (ΔI * 100) / (Δr * t). Substitute the given values directly. Step-by-Step Solution: P = (24 * 100) / (1 * 2) = 2,400 / 2 = 1,200 Verification / Alternative check: At Δr = 1% for 2 years, extra interest on ₹ 1,200 is 1,200 * 1 * 2 / 100 = ₹ 24, matching the statement. Why Other Options Are Wrong: ₹ 600, ₹ 800, ₹ 480, and ₹ 1,000 produce extra interests of ₹ 12, ₹ 16, ₹ 9.6, and ₹ 20 respectively under the same Δr and t, not ₹ 24. Common Pitfalls: Confusing “1% higher” with multiplying the rate by 1.01, or forgetting that percent must be divided by 100 in SI computations. Final Answer: ₹ 1,200

Question 17

Simple Interest – Rate when amount becomes 8/5 of principal in 5 years: A sum becomes (8/5) times itself in 5 years under simple interest. Find the annual rate percent.

Accepted Answer

Introduction / Context: If a final amount is expressed as a multiple of principal under simple interest, the interest portion is the excess over 1 times principal. This gives a direct fraction for I / P and leads to the annual rate via the standard formula. Given Data / Assumptions: A = (8/5) P Time t = 5 years Simple interest I = A − P Concept / Approach: Compute the fraction I / P = (8/5 − 1) = 3/5. Then use r = (I / (P * t)) * 100 = ((3/5) / 5) * 100. Step-by-Step Solution: I / P = 3 / 5r = (I / (P * t)) * 100 = ((3/5) / 5) * 100 = (3/25) * 100 = 12% Verification / Alternative check: At 12% per annum for 5 years, total interest is 60% of P; amount is 160% of P = (8/5) P, confirming the statement. Why Other Options Are Wrong: 5%, 8%, and 10% produce smaller multiples than 8/5 over 5 years; 15% gives too large a multiple under simple interest. Common Pitfalls: Confusing simple interest with compound interest may lead to solving (1 + r)^t = 8/5, which is not applicable here. Use linear SI relations. Final Answer: 12%

Question 18

Simple Interest — Two banks and a small rate gap: On a principal of ₹ 500 kept for a period of 2 years, the difference between the simple interest earned from two different banks is ₹ 2.50. What is the difference between their annual rates of intere…

Accepted Answer

Introduction / Context: When two banks offer slightly different simple interest (SI) rates on the same principal for the same time, the difference in interest directly reveals the difference in their annual percentage rates. This question tests the SI formula and unit handling for small percentage gaps. Given Data / Assumptions: Principal P = ₹ 500 Time t = 2 years Difference in simple interest ΔI = ₹ 2.50 Let rate difference = Δr (in % per annum) Concept / Approach: Simple interest is I = (P * r * t) / 100. For the same P and t, the interest difference equals (P * Δr * t)/100. Solve for Δr. Step-by-Step Solution: ΔI = (P * Δr * t) / 1002.50 = (500 * Δr * 2) / 1002.50 = (1000 * Δr) / 1002.50 = 10 * ΔrΔr = 2.50 / 10 = 0.25% Verification / Alternative check: If Bank A is r% and Bank B is (r + 0.25)%, the annual gap on ₹ 500 is 500 * 0.25 / 100 = ₹ 1.25. Over 2 years the gap is ₹ 2.50, matching the data. Why Other Options Are Wrong: 1% and 2.50% would produce much larger gaps; 0.50% doubles the required difference; 0.75% is also too large relative to ₹ 2.50 over 2 years. Common Pitfalls: Confusing the percentage gap with rupees, forgetting to divide by 100, or using 2.50 as a percent rather than rupees can lead to mistakes. Final Answer: 0.25%

Question 19

Simple Interest — Inferring the annual rate from two amounts: A certain principal at simple interest amounts to ₹ 1012 in 2.5 years and to ₹ 1067.20 in 4 years. Find the annual rate of interest (percent per annum).

Accepted Answer

Introduction / Context: With simple interest (SI), the amount grows linearly with time. If we know the amounts at two different times for the same principal, we can isolate the interest added between those times to find the rate. Given Data / Assumptions: Amount after 2.5 years, A1 = ₹ 1012 Amount after 4 years, A2 = ₹ 1067.20 Time gap Δt = 1.5 years Principal = P, annual rate = r% (unknowns) Concept / Approach: Amount A = P * (1 + r * t / 100). The extra interest from 2.5 to 4 years equals P * r * Δt / 100 = A2 - A1. Use this with one of the amount equations to solve r. Step-by-Step Solution: A2 - A1 = 1067.20 - 1012 = 55.20P * r * (1.5) / 100 = 55.20P * r = (55.20 * 100) / 1.5 = 3680A1 = P * (1 + 2.5r / 100) = 10121012 = P + (P * r * 2.5 / 100) = P + (3680 * 2.5) / 100 = P + 92P = 1012 - 92 = 920r = 3680 / 920 = 4% Verification / Alternative check: With P = ₹ 920 and r = 4%, A2 at 4 years: 920 * (1 + 0.04 * 4) = 920 * 1.16 = ₹ 1067.20, matching the data. Why Other Options Are Wrong: 2.5%, 3%, and 3.5% undercount growth; 5% overshoots the observed difference between A1 and A2. Common Pitfalls: Mixing amount with interest, or treating the 1.5 years gap as 15 months without scaling the rate correctly can cause errors. Final Answer: 4%

Question 20

Simple Interest — Equal principals, different durations: Two equal sums are deposited at 15% per annum, one for 3.5 years and the other for 5 years. If the difference between the interests earned is ₹ 144, find each principal amount.

Accepted Answer

Introduction / Context: This problem uses the linearity of simple interest with respect to both time and principal. The same rate applies to the same principal, but for different durations—so the interest difference isolates the time difference effect. Given Data / Assumptions: Rate r = 15% per annum Times t1 = 3.5 years, t2 = 5 years Difference in interest ΔI = ₹ 144 Equal principals = P (each) Concept / Approach: Simple interest I = (P * r * t) / 100. Hence ΔI = P * r * (t2 - t1) / 100. Solve for P using the known gap in time and rate. Step-by-Step Solution: Δt = 5 - 3.5 = 1.5 yearsΔI = P * 15 * 1.5 / 100 = 0.225 * P144 = 0.225 * PP = 144 / 0.225 = ₹ 640 Verification / Alternative check: Interest for 5 years: 640 * 15 * 5 / 100 = 640 * 0.75 = ₹ 480. For 3.5 years: 640 * 15 * 3.5 / 100 = 640 * 0.525 = ₹ 336. Difference = ₹ 144 (correct). Why Other Options Are Wrong: ₹ 460, ₹ 500, ₹ 560, and ₹ 720 do not produce the required 144 difference when substituted into the SI expression with the given times. Common Pitfalls: Using the amount difference instead of interest difference, or forgetting to divide by 100 when applying the SI formula. Final Answer: ₹ 640

Simple Interest Questions