Question 1

Srinivasan invests two equal amounts in two different banks. One bank offers simple interest at 8% per annum and the other offers simple interest at 12% per annum. At the end of one year, the total interest earned from both banks together is Rs 1500…

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Introduction / Context: This question deals with equal investments placed at different simple interest rates. Srinivasan invests the same principal in two banks, one at 8% and the other at 12%, and is told the total interest from both at the end of a year. The student must use the simple interest formula and the fact that the two principals are equal to form an equation in a single variable. Problems like this are common in aptitude tests and help students become comfortable with modeling financial situations using algebra. Given Data / Assumptions: Two investments with equal principal amounts. Rate in Bank 1 = 8% per annum simple interest. Rate in Bank 2 = 12% per annum simple interest. Time period T = 1 year for both investments. Total interest from both banks together after 1 year = Rs 1500. Interest is calculated using simple interest only. Concept / Approach: Let the amount invested in each bank be P rupees. For simple interest over 1 year, the interest from the first bank is (P * 8 * 1) / 100 and from the second bank is (P * 12 * 1) / 100. The sum of these two interests is given to be Rs 1500. Thus, we can write an equation involving P and solve it. This is essentially a linear equation in one variable where the total interest is the sum of the individual interests at different rates. Step-by-Step Solution: Let P be the amount invested in each bank. Bank 1: Rate = 8% per annum, time = 1 year. Simple interest from Bank 1: SI1 = (P * 8 * 1) / 100 = 0.08P. Bank 2: Rate = 12% per annum, time = 1 year. Simple interest from Bank 2: SI2 = (P * 12 * 1) / 100 = 0.12P. Total interest from both banks = SI1 + SI2 = 0.08P + 0.12P. So total interest = 0.20P. Given that total interest is Rs 1500, we have 0.20P = 1500. P = 1500 / 0.20. P = 7500. Therefore, the amount invested in each bank is Rs 7500. Verification / Alternative check: Check the interest values with P = 7500. From Bank 1 at 8% for 1 year, interest = (7500 * 8) / 100 = 600. From Bank 2 at 12% for 1 year, interest = (7500 * 12) / 100 = 900. Total interest = 600 + 900 = 1500, which matches the given total interest. Thus, the solution is verified as correct. Why Other Options Are Wrong: If P were Rs 5800, total interest at 8% and 12% would be 0.20 * 5800 = 1160, not 1500. If P were Rs 15000, total interest would be 3000, which is double the required value. If P were Rs 17000, or Rs 6000, similar calculations show total interest values different from 1500. Only P = Rs 7500 satisfies the equation 0.20P = 1500. Common Pitfalls: Common mistakes include assuming the total principal in both banks is 1500 or miscalculating the combined rate as an average rather than summing the interest. Some learners also forget that the time is 1 year and may mistakenly multiply by a different period. Writing the expressions for SI1 and SI2 clearly and then adding them helps avoid such confusion. Final Answer: The amount invested in each bank by Srinivasan is Rs 7,500.

Question 2

The simple interest accrued on a sum of money after 4 years is equal to one fifth of its principal. Assuming simple interest at a constant rate, what is the rate of interest per annum in percentage terms?

Accepted Answer

Introduction / Context: This question asks for the rate of simple interest when the simple interest over a fixed time is expressed as a fraction of the principal. The simple interest for 4 years is given to be one fifth of the principal. Under simple interest, interest is directly proportional to both rate and time. By equating the expression for simple interest to one fifth of the principal, we can solve for the rate. This type of question is common in conceptual tests of simple interest where fractional relationships are used instead of actual rupee values. Given Data / Assumptions: Simple interest for 4 years = one fifth of the principal. Let principal be P rupees. Time T = 4 years. Rate of interest per annum = R% (unknown). Interest is calculated using simple interest only. Concept / Approach: The simple interest formula is: SI = (P * R * T) / 100 The problem states: SI = P / 5 Substituting the simple interest formula for SI and equating to P / 5, we can cancel P from both sides and solve the resulting equation for R. Because the principal cancels out, the answer does not depend on the actual rupee amount invested, only on the ratio of interest to principal and the time period. Step-by-Step Solution: Let the principal be P rupees. Given that simple interest for 4 years is P / 5. Using SI formula: SI = (P * R * 4) / 100. Set this equal to P / 5: (P * R * 4) / 100 = P / 5. Cancel P from both sides, since P is nonzero. (R * 4) / 100 = 1 / 5. 4R / 100 = 1 / 5. Cross multiply: 4R * 5 = 100 * 1. 20R = 100. R = 100 / 20 = 5. Therefore, the rate of interest is 5% per annum. Verification / Alternative check: Assume any convenient principal, for example P = Rs 500. One fifth of P is 500 / 5 = Rs 100. At 5% per annum for 4 years, simple interest SI = (500 * 5 * 4) / 100 = 100, which matches one fifth of the principal. Trying any other principal will also show that 5% satisfies the given condition consistently, confirming the answer. Why Other Options Are Wrong: At 4% per annum, simple interest for 4 years would be (P * 4 * 4) / 100 = 16P / 100 = 4P / 25, which is less than P / 5. At 6% per annum, simple interest becomes 24P / 100 = 6P / 25, which is larger than P / 5. At 8% per annum, simple interest for 4 years is 32P / 100 = 8P / 25, again not equal to P / 5. Thus the data is adequate, and 5% is the unique correct rate, making the option “Inadequate data” incorrect. Common Pitfalls: Some students forget to cancel the principal and try to assume a numerical value without simplifying the equation, which can lead to arithmetic errors. Others misinterpret “one fifth of its principal” and incorrectly set up the equation. It is also possible to miscalculate cross multiplication if steps are rushed. Carefully writing the equation and canceling common factors simplifies the problem greatly. Final Answer: The rate of interest per annum is 5%.

Question 3

The difference between the compound interest and the simple interest on Rs 5000 for 2 years at 8% per annum, when interest is payable yearly, is to be found. Using both the simple interest and compound interest formulas, what is the value of this di…

Accepted Answer

Introduction / Context: This question compares compound interest and simple interest for the same principal, rate, and time, over a relatively short period of 2 years. Since compound interest allows interest to earn interest, it is slightly higher than simple interest for more than one year. The difference between these two is often asked in bank and finance related aptitude questions. Here, the principal is Rs 5000, the rate is 8% per annum, and the time is 2 years. The candidate must calculate both simple interest and compound interest accurately and then find their difference. Given Data / Assumptions: Principal P = Rs 5000. Rate of interest R = 8% per annum. Time period T = 2 years. Interest is compounded annually for the compound interest case. Interest is calculated using simple interest for the simple interest case. Concept / Approach: Simple interest is given by: SI = (P * R * T) / 100 For compound interest with annual compounding, the amount after T years is: A = P * (1 + R / 100) ^ T Compound interest is then: CI = A − P The required difference is: Difference = CI − SI By computing SI and CI separately using these formulas and then subtracting, we can obtain the exact numerical difference in rupees. Step-by-Step Solution: Principal P = Rs 5000, R = 8% per annum, T = 2 years. First compute simple interest: SI = (5000 * 8 * 2) / 100. 8 * 2 = 16, so SI = (5000 * 16) / 100. 5000 * 16 = 80000. SI = 80000 / 100 = Rs 800. Now compute compound interest. Amount A = 5000 * (1 + 8 / 100) ^ 2 = 5000 * (1.08) ^ 2. (1.08) ^ 2 = 1.1664. A = 5000 * 1.1664 = 5832. Compound interest CI = A − P = 5832 − 5000 = Rs 832. Difference between CI and SI = 832 − 800 = Rs 32. Therefore, the required difference is Rs 32. Verification / Alternative check: We can verify by computing the compound interest stepwise. In the first year, interest at 8% on Rs 5000 is 400, so amount becomes 5400. In the second year, interest is 8% of 5400, which is 432, so the amount after 2 years is 5400 + 432 = 5832. Compound interest CI = 5832 − 5000 = 832, which matches our earlier calculation. Simple interest for 2 years is 2 * 400 = 800. The difference remains 832 − 800 = 32, so the result is confirmed. Why Other Options Are Wrong: Differences of Rs 30, Rs 31, Rs 33, or Rs 35 would require slightly different interest amounts or would arise from incorrect rounding of the compound amount. Since 8% and 2 years are exact and the calculations yield an exact difference of Rs 32, none of those other values is correct. Common Pitfalls: Some students approximate (1.08) ^ 2 incorrectly or forget to subtract the principal when finding compound interest. Others might mistakenly compute simple interest for only 1 year instead of 2 years. Confusing compound interest with simple interest and using the same formula for both is another common error. Following the formulas carefully and checking each step ensures a correct and accurate difference. Final Answer: The difference between the compound interest and the simple interest on Rs 5000 for 2 years at 8% per annum is Rs 32.

Question 4

The simple interest on a sum of money for 10 years is Rs 3130 at a certain rate per annum. If, after 5 years, the principal is increased so that it becomes 5 times the original principal for the remaining 5 years at the same rate of simple interest,…

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Introduction / Context: This problem involves a change in principal during the investment period under simple interest. Initially, a sum is kept for 10 years at a certain rate, and the simple interest for the full 10 years is known to be Rs 3130. In a modified scenario, after 5 years the principal is increased so that it becomes 5 times the original principal for the remaining 5 years. The rate remains the same throughout. The question asks for the total interest that will be obtained in this modified arrangement. Such questions test a deeper understanding of simple interest, especially how changes in principal affect total interest over different segments of time. Given Data / Assumptions: Original principal = P rupees. Rate of simple interest per annum = R% (unknown). Simple interest for 10 years at rate R on principal P is Rs 3130. In the modified case, principal is P for the first 5 years and 5P for the next 5 years. The rate of interest R remains the same throughout. We must find the total interest in the modified case. Concept / Approach: Under simple interest, interest depends linearly on principal and time. From the original information, we can express Rs 3130 in terms of P, R, and 10 years: 3130 = (P * R * 10) / 100 This allows us to find the product P * R as a single combined constant. In the modified scenario, interest accumulates in two segments: Segment 1: P at rate R for 5 years. Segment 2: 5P at rate R for 5 years. We compute the interest in each segment using the simple interest formula and then add them. By expressing both in terms of P * R, we can relate the new total interest to the original 10 year interest. Step-by-Step Solution: From the original 10 year scenario: 3130 = (P * R * 10) / 100. So (P * R) / 100 = 3130 / 10 = 313. Thus, P * R = 313 * 100 = 31300. Now consider the modified scenario. Segment 1 (first 5 years): principal = P, time = 5 years. Interest I1 = (P * R * 5) / 100. But (P * R) / 100 = 313, so I1 = 313 * 5 = 1565. Segment 2 (next 5 years): principal = 5P, time = 5 years. Interest I2 = (5P * R * 5) / 100 = 25 * (P * R) / 100. Using (P * R) / 100 = 313, I2 = 25 * 313 = 7825. Total interest in the modified scenario = I1 + I2. Total interest = 1565 + 7825 = 9390. Therefore, the total interest obtained after 10 years in the changed arrangement is Rs 9390. Verification / Alternative check: We can verify the proportional reasoning. In the original case, interest for 10 years on P is 3130. This implies interest for 5 years on P is half of 3130, that is 1565. In the modified case, we still have 5 years on P (giving 1565), plus 5 years on 5P. Interest for 5 years on P is 1565, so on 5P it is 5 times that, which is 7825. Total = 1565 + 7825 = 9390. This checks out and matches the previous calculation exactly. Why Other Options Are Wrong: Rs 6260 would correspond to only doubling the principal for the second half rather than multiplying it by 5. Rs 7825 is just the interest on 5P for 5 years and ignores the first 5 years on P. Rs 15650 or Rs 5000 do not match the structure of the two segment calculation and would require different relationships between principal, rate, and time that are not consistent with the given data. Only Rs 9390 matches the correct segment wise interest computation. Common Pitfalls: A common mistake is to treat the principal as 5P for the entire 10 years, which vastly overestimates the interest. Another error is to forget that the first 5 years still earn interest on the original P and to count that part incorrectly. Some students also try to find the numeric values of P and R separately, which is unnecessary because the combinations P * R and (P * R) / 100 are sufficient. Working with these combined terms keeps the algebra simple and helps avoid arithmetic overload. Final Answer: The total simple interest obtained after 10 years in the changed arrangement is Rs 9390.

Question 5

A sum of money is invested at simple interest. The difference between compound interest (compounded half-yearly) for 1 year and simple interest for the same 1 year at 8% per annum is ₹64. What is the principal amount (in rupees)?

Accepted Answer

Introduction: This is the same concept as the earlier CI vs SI difference problem: half-yearly compounding makes CI slightly higher than SI for the same 1-year period. The difference becomes a small fraction of principal. Once you compute that fraction at 8% with two half-year periods, the principal is found by dividing ₹64 by that fraction. This checks compounding frequency handling and precise subtraction between CI and SI. Given Data / Assumptions: CI is compounded half-yearly for 1 year SI is for 1 year Annual rate = 8% CI - SI = ₹64 Principal = P Concept / Approach: Half-yearly rate = 8%/2 = 4%. Number of half-years in 1 year = 2. CI = P * [(1.04)^2 - 1] = 0.0816P. SI for 1 year at 8% = 0.08P. Difference = 0.0016P. Set 0.0016P = 64 and solve for P. Step-by-Step Solution: SI = 0.08P CI factor = (1.04)^2 = 1.0816 CI = 0.0816P CI - SI = 0.0816P - 0.08P = 0.0016P 0.0016P = 64 P = 64 / 0.0016 = 40000 Verification / Alternative check: For P=40000: CI=3264 and SI=3200, difference=64. Matches exactly. Why Other Options Are Wrong: All other values produce a difference not equal to ₹64 since the difference scales directly with P. Common Pitfalls: Using 8% per half-year, using only one period, or using amount instead of interest when computing CI. Final Answer: The principal amount is ₹40,000.

Question 6

On a principal of ₹9,500, the simple interest earned over 10 years is equal to 130% of the principal amount. What is the annual rate of simple interest (in % per annum)?

Accepted Answer

Introduction: This question tests a clean proportional use of the simple interest formula when interest is expressed as a percentage of the principal. Under simple interest, SI grows linearly with time, so if you know SI as a multiple of principal and the time duration, the rate is obtained directly without needing any complicated calculations. Given Data / Assumptions: Principal P = ₹9,500 Time t = 10 years Simple interest earned SI = 130% of P = 1.30P Formula: SI = (P * r * t) / 100 Concept / Approach: Substitute SI = 1.30P into the simple interest formula. Since P appears on both sides, it cancels out. This is the main shortcut: when SI is given as a percentage (or multiple) of principal, you can solve for r using only that percentage and time. Step-by-Step Solution: SI = (P * r * t) / 100 Given SI = 1.30P and t = 10 1.30P = (P * r * 10) / 100 Cancel P: 1.30 = (10r) / 100 1.30 = r / 10 r = 13 Verification / Alternative check: At 13% for 10 years: SI = (9500 * 13 * 10)/100 = 9500 * 1.30 = 12350, which is exactly 130% of 9500. This confirms the rate is correct. Why Other Options Are Wrong: 12% gives SI = 120% of P in 10 years, too low. 15% gives 150%, too high. 19% is far too high. 10% gives only 100% in 10 years. Common Pitfalls: Interpreting 130% as 0.13 instead of 1.30, or forgetting that “130% of principal” refers to interest (not amount). Final Answer: The annual simple interest rate is 13% per annum.

Question 7

A person invests a total of ₹7,900 in three different simple interest schemes offering 3%, 5%, and 8% per annum. After 1 year, the interest earned from each scheme is the same. What amount (in rupees) is invested at 3% per annum?

Accepted Answer

Introduction: This problem tests the idea that under simple interest, for the same time (1 year here), interest depends only on principal and rate. If the interest amounts are equal across different rates, the principal amounts must be inversely proportional to the rates. That proportionality is the shortcut that makes multi-scheme split problems solvable cleanly. Given Data / Assumptions: Total investment = ₹7,900 Three rates: 3% p.a., 5% p.a., 8% p.a. Time = 1 year for all schemes Interest earned from each scheme is the same (say I rupees) Formula: SI = (P * r * t) / 100 Concept / Approach: Let the equal interest from each scheme be I. For 1 year, SI = (P * r)/100, so P = (100 * I)/r. Compute the three principals in terms of I and add them to match the total ₹7,900. Solve for I, then compute the principal at 3%. Step-by-Step Solution: For 3%: P3 = (100I)/3 For 5%: P5 = (100I)/5 For 8%: P8 = (100I)/8 Total: (100I)(1/3 + 1/5 + 1/8) = 7900 1/3 + 1/5 + 1/8 = (40 + 24 + 15)/120 = 79/120 (100I)*(79/120) = 7900 (7900I)/120 = 7900 => I = 120 P3 = (100*120)/3 = 4000 Verification / Alternative check: If P3=4000, interest at 3% in 1 year is 120. Then P5 must be 2400 (5% of 2400 is 120) and P8 must be 1500 (8% of 1500 is 120). Sum = 4000+2400+1500 = 7900, correct. Why Other Options Are Wrong: Other values do not allow a consistent split where 3%, 5%, and 8% each yield the same interest while totaling ₹7,900. Common Pitfalls: Assuming equal principal instead of equal interest, forgetting to use inverse proportionality, or treating the rates as decimals while still dividing by 100. Final Answer: The amount invested at 3% per annum is ₹4,000.

Question 8

A person lends a certain sum of money at 10% per annum simple interest. After 20 years, the total simple interest earned is ₹500 more than the original principal lent. What was the principal amount (in rupees) that was lent?

Accepted Answer

Introduction: This question tests forming an equation using simple interest when a relationship between interest and principal is described in words. The key phrase is “interest is ₹500 more than the principal,” which means SI = P + 500. Under simple interest, SI depends linearly on P, r, and t, so we can compute SI in terms of P and equate it to P + 500 to find the principal directly. Given Data / Assumptions: Rate r = 10% per annum Time t = 20 years Simple interest SI is ₹500 more than principal P Formula: SI = (P * r * t) / 100 Concept / Approach: Compute SI using the formula in terms of P. Then use the word condition SI = P + 500 and solve for P. Because r and t are fixed, SI becomes a constant multiple of P, making the algebra simple. Step-by-Step Solution: SI = (P * 10 * 20) / 100 SI = (200P) / 100 = 2P Given SI = P + 500 So 2P = P + 500 P = 500 Verification / Alternative check: If P = 500, then SI at 10% for 20 years is (500*10*20)/100 = 1000. Interest (1000) is indeed 500 more than principal (500), satisfying the condition exactly. Why Other Options Are Wrong: ₹250 would give SI=₹500, which is not ₹500 more than ₹250. ₹1,000 would give SI=₹2,000, which is ₹1,000 more than principal, not ₹500. The other values similarly fail the equation 2P = P + 500. Common Pitfalls: Misreading “₹500 more than principal” as “₹500 in total,” or accidentally using amount instead of interest in the word condition. Final Answer: The principal lent was ₹500.

Question 9

A person divides ₹17,200 into three parts and invests them at simple interest rates of 5%, 6%, and 9% per annum respectively. At the end of 2 years, the simple interest earned on each part is the same. What is the amount (in rupees) invested at 9% p…

Accepted Answer

Introduction: This question tests proportional allocation of principal across multiple simple interest rates when the interest earned is the same for each part. Because all investments run for the same time (2 years), equal interest implies the principals are inversely proportional to the rates. This is a common aptitude pattern: equal SI at different rates means higher rate gets smaller principal. Given Data / Assumptions: Total sum = ₹17,200 Rates: 5%, 6%, 9% per annum Time = 2 years for each part Simple interest on each part after 2 years is equal (say I rupees) Formula: SI = (P * r * t) / 100 Concept / Approach: Let the common interest (for 2 years) be I for each part. Then for each rate r, principal P = (I * 100) / (r * t). With t = 2, this becomes P = (50I)/r. Express each principal in terms of I, add them to equal ₹17,200, solve for I, then compute the 9% principal. Step-by-Step Solution: P5 = (50I)/5 = 10I P6 = (50I)/6 = 25I/3 P9 = (50I)/9 Total: 10I + 25I/3 + 50I/9 = 17200 Convert to denominator 9: (90I/9) + (75I/9) + (50I/9) = 17200 (215I/9) = 17200 => I = 17200*9/215 = 720 P9 = (50*720)/9 = 4000 Verification / Alternative check: If P9=4000, SI in 2 years at 9% is (4000*9*2)/100 = 720. Then P5 must be 8000 (SI=720) and P6 must be 5200 (SI=720). Total = 8000+5200+4000 = 17200, correct. Why Other Options Are Wrong: Other values do not allow the 5% and 6% parts to adjust to the same 2-year interest while still summing to ₹17,200. Common Pitfalls: Forgetting to include the 2-year time factor, using direct proportionality instead of inverse proportionality, or assuming equal principal instead of equal interest. Final Answer: The amount invested at 9% per annum is ₹4,000.

Question 10

A certain sum of money fetches a total simple interest of ₹5,400 at the rate of 12.5% per annum in 4 years. What is the principal sum (in rupees)?

Accepted Answer

Introduction: This is a direct simple interest calculation where interest, rate, and time are given and you must find the principal. The simple interest formula can be rearranged to compute principal as P = (SI * 100) / (r * t). Because it is straightforward substitution with one rearrangement, it is an easy problem. Given Data / Assumptions: Simple interest SI = ₹5,400 Rate r = 12.5% per annum Time t = 4 years Formula: SI = (P * r * t) / 100 Concept / Approach: Rearrange the simple interest formula to isolate P: P = (SI * 100) / (r * t). Substitute the values and compute carefully. Since the rate is given in percent, the factor 100 in the formula is already accounted for by dividing by 100 (or multiplying SI by 100 when solving for P). Step-by-Step Solution: SI = (P * r * t) / 100 P = (SI * 100) / (r * t) P = (5400 * 100) / (12.5 * 4) Denominator: 12.5 * 4 = 50 P = 540000 / 50 = 10800 Verification / Alternative check: If P = 10800, then SI = (10800 * 12.5 * 4)/100. Since 12.5*4 = 50, SI = (10800 * 50)/100 = 5400, matching the given interest exactly. Why Other Options Are Wrong: Any other principal value would produce an SI different from ₹5,400 because SI is directly proportional to P for fixed r and t. Common Pitfalls: Using 0.125 in place of 12.5 while still dividing by 100 again, or forgetting to multiply SI by 100 when rearranging for P. Final Answer: The principal sum is ₹10,800.

Question 11

A person borrows money for 4 years at a simple interest rate. If the ratio of the principal to the total interest earned in 4 years is 5 : 1, what is the annual simple interest rate (in % per annum)?

Accepted Answer

Introduction: This question tests interpreting a ratio between principal and total interest and converting that ratio into a simple interest rate. Since simple interest is linear, the total interest over a period is a fixed fraction of principal: SI/P = (r*t)/100. Once you identify SI as a fraction of P from the given ratio, the rate follows immediately. Given Data / Assumptions: Principal : total interest in 4 years = 5 : 1 Time t = 4 years Simple interest formula: SI = (P * r * t) / 100 Therefore SI/P = (r * t) / 100 Concept / Approach: From the ratio P:SI = 5:1, we get SI = P/5. Substitute into SI = (P*r*4)/100 and cancel P to solve for r. This avoids needing any actual numeric principal value because the ratio already gives the proportional relationship. Step-by-Step Solution: Given P : SI = 5 : 1 So SI = P/5 SI = (P * r * 4) / 100 P/5 = (P * r * 4) / 100 Cancel P: 1/5 = (4r) / 100 4r = 20 r = 5 Verification / Alternative check: At 5% per year for 4 years, SI/P = (5*4)/100 = 20/100 = 1/5, which matches SI = P/5 derived from the ratio. So the rate is consistent. Why Other Options Are Wrong: 10% would make SI/P = 0.4 in 4 years (ratio 5:2). 20% would make SI/P = 0.8 (ratio 5:4). Higher rates move the ratio away from 5:1. Common Pitfalls: Using interest per year instead of total interest for 4 years, or inverting the ratio as SI:P instead of P:SI. Final Answer: The annual simple interest rate is 5% per annum.

Question 12

A person borrows money for 8 years at a simple interest rate. If the ratio of the principal to the total interest earned in 8 years is 5 : 8, what is the annual simple interest rate (in % per annum)?

Accepted Answer

Introduction: This question tests converting a principal-to-interest ratio into a simple interest rate. Under simple interest, total interest over t years is SI = (P * r * t)/100, so the fraction SI/P equals (r*t)/100. A given ratio between P and SI immediately fixes SI/P, and therefore fixes r when time is known. Given Data / Assumptions: Principal : total interest in 8 years = 5 : 8 Time t = 8 years Simple interest formula: SI = (P * r * t) / 100 Thus SI/P = (r * t) / 100 Concept / Approach: From P:SI = 5:8, compute SI/P = 8/5. Then set (r*8)/100 = 8/5 and solve for r. Since 8 appears on both sides, it cancels neatly, making the computation quick and reliable. Step-by-Step Solution: Given P : SI = 5 : 8 So SI/P = 8/5 But SI/P = (r * t) / 100 = (r * 8) / 100 (r * 8) / 100 = 8/5 Cancel 8: r / 100 = 1/5 r = 100/5 = 20 Verification / Alternative check: If r = 20% for 8 years, then SI/P = (20*8)/100 = 160/100 = 1.6 = 8/5, which matches the ratio exactly. So the annual rate is consistent. Why Other Options Are Wrong: 10% gives SI/P = 0.8 (ratio 5:4). 25% gives SI/P = 2 (ratio 5:10). 30% gives 2.4 (ratio 5:12). Only 20% gives SI/P = 1.6 (ratio 5:8). Common Pitfalls: Inverting the ratio, using yearly interest instead of total 8-year interest, or forgetting the division by 100 when converting percent to a fraction. Final Answer: The annual simple interest rate is 20% per annum.

Question 13

A sum of ₹3,000 yields a simple interest of ₹1,080 at 12% per annum. For how many years was the money invested to earn this interest under simple interest?

Accepted Answer

Introduction: This question tests solving for time in a simple interest situation. When principal, rate, and interest are known, time can be found by rearranging the standard formula SI = (P * r * t) / 100. Because it is a direct substitution with one rearrangement and no tricky unit conversion (rate is annual and time is asked in years), it is an easy problem. Given Data / Assumptions: Principal P = ₹3,000 Simple interest SI = ₹1,080 Rate r = 12% per annum Time = t years (unknown) Formula: SI = (P * r * t) / 100 Concept / Approach: Rearrange the formula to isolate t: t = (SI * 100) / (P * r). Substitute the given values and compute carefully. Since r is already a percentage, keep it as 12 (not 0.12) because the formula includes division by 100. Step-by-Step Solution: SI = (P * r * t) / 100 t = (SI * 100) / (P * r) t = (1080 * 100) / (3000 * 12) t = 108000 / 36000 t = 3 Verification / Alternative check: At 12% per year on ₹3000, yearly interest is (3000*12)/100 = 360. Over 3 years, total interest is 360*3 = 1080, matching the given interest exactly. Why Other Options Are Wrong: 2.5 years would give 360*2.5 = 900. 4 years would give 1440. 5 years would give 1800. Only 3 years produces exactly ₹1080 at 12% on ₹3000. Common Pitfalls: Forgetting to multiply SI by 100, using 0.12 and also dividing by 100 again, or confusing amount with interest. Final Answer: The money was invested for 3 years.

Question 14

Simple interest on a principal sum for 3 years at 18% per annum is equal to half of the compound interest on ₹9,000 for 2 years at 10% per annum (compounded annually). What is the principal sum (in rupees) invested at simple interest?

Accepted Answer

Introduction: This question combines simple interest (SI) and compound interest (CI) in a single equation. The main skill tested is computing CI for a given principal, rate, and time, then relating it to SI on an unknown principal. Because you must compute CI first, take half of it, and then solve for the SI principal using an SI expression, it involves multiple steps and is therefore hard. Given Data / Assumptions: Unknown principal for SI = P SI rate = 18% per annum SI time = 3 years CI principal = ₹9,000 CI rate = 10% per annum CI time = 2 years, compounded annually Given: SI(P) = (1/2) * CI(9000) Concept / Approach: Compute CI on ₹9,000 for 2 years at 10% compounded annually. CI = 9000 * [(1 + 10/100)^2 - 1]. Then take half of that value. Set SI on P, which is (P*18*3)/100, equal to that half-CI value and solve for P. Step-by-Step Solution: CI factor for 2 years at 10%: (1.10)^2 = 1.21 CI on 9000 = 9000 * (1.21 - 1) = 9000 * 0.21 = 1890 Half of CI = 1890 / 2 = 945 SI on P for 3 years at 18%: SI = (P * 18 * 3) / 100 = 0.54P Given 0.54P = 945 P = 945 / 0.54 = 1750 Verification / Alternative check: If P = 1750, SI = (1750*18*3)/100 = 945. CI on 9000 is 1890, and half is 945, so the equality holds exactly. Why Other Options Are Wrong: Each incorrect principal would change SI proportionally (since SI is linear in P), so it would no longer equal 945, which is fixed by the CI part. Common Pitfalls: Computing amount instead of compound interest, using simple interest on ₹9000 instead of CI, or compounding incorrectly (not squaring 1.10). Final Answer: The principal invested at simple interest is ₹1,750.

Question 15

The simple interest on a sum at 5% per annum for 8 years is ₹840. For what annual rate of simple interest (in %) would the same sum earn the same interest of ₹840 in 5 years?

Accepted Answer

Introduction: This question tests how simple interest scales with time and rate for the same principal. In simple interest, SI = (P * r * t)/100. If the principal and interest are fixed and only the time changes, the rate must adjust inversely with time. A clean way is to compute the principal from the first condition, then compute the new required rate for the new time. An even faster method uses proportionality (r1*t1 = r2*t2 when P and SI are fixed). Given Data / Assumptions: SI = ₹840 Case 1: r1 = 5% per annum, t1 = 8 years Case 2: t2 = 5 years, rate r2 = ? Same principal in both cases Formula: SI = (P * r * t) / 100 Concept / Approach: Method 1: Find P from case 1, then solve for r2 from case 2. Method 2 (shortcut): Since SI and P are constant, (r1*t1) must equal (r2*t2). Use r2 = (r1*t1)/t2. Step-by-Step Solution: From case 1: 840 = (P * 5 * 8) / 100 840 = (P * 40) / 100 = 0.4P P = 840 / 0.4 = 2100 Now case 2: 840 = (2100 * r2 * 5) / 100 840 = (10500 * r2) / 100 r2 = (840 * 100) / 10500 = 8 Verification / Alternative check: Shortcut: r2 = (r1*t1)/t2 = (5*8)/5 = 8%. Same result, confirming correctness. Why Other Options Are Wrong: 7% would produce less interest in 5 years, while 9% and 10% would produce more. 6% is far too low. Only 8% keeps SI at ₹840 for the same principal when time is 5 years. Common Pitfalls: Assuming SI is proportional to time only, forgetting the inverse relation between rate and time when SI is fixed, or mixing up years between the two cases. Final Answer: The required annual rate is 8%.

Question 16

A sum becomes ₹1,392 in 2 years and ₹1,488 in 3 years at simple interest. What is the annual rate of simple interest (in % per annum)?

Accepted Answer

Introduction: This question tests the defining property of simple interest: the amount increases by the same interest each year. When you are given amounts at two different times, the difference between those amounts represents interest earned during the extra time period. From that, you can find the yearly interest, the principal, and then the rate. This is a standard “two amounts at two times” simple interest pattern. Given Data / Assumptions: Amount after 2 years: A2 = ₹1,392 Amount after 3 years: A3 = ₹1,488 Under simple interest, yearly interest is constant Formula: A = P + SI and SI = (P * r * t) / 100 Concept / Approach: Compute the difference A3 - A2 to get interest earned in 1 extra year. That difference equals the yearly interest. Then subtract 2 years of yearly interest from A2 to get the principal P. Finally compute r using yearly interest = (P * r) / 100. Step-by-Step Solution: Interest for the 3rd year = A3 - A2 = 1488 - 1392 = 96 So yearly interest = 96 Interest in 2 years = 2 * 96 = 192 Principal P = A2 - 192 = 1392 - 192 = 1200 Yearly interest = (P * r) / 100 96 = (1200 * r) / 100 r = (96 * 100) / 1200 = 8 Verification / Alternative check: At 8% on ₹1200, yearly interest is ₹96. Amount after 2 years = 1200 + 192 = 1392, and after 3 years = 1200 + 288 = 1488, both matching the given values. Why Other Options Are Wrong: 10% would make yearly interest 120 on a principal near 1200, causing a larger yearly increase than 96. 12% is even larger. 8.5% gives a non-matching yearly difference. 6% is too low to reach the given amounts. Common Pitfalls: Treating the amounts as compound growth, or forgetting that the difference between A3 and A2 is exactly one year of interest under simple interest. Final Answer: The annual simple interest rate is 8% per annum.

Question 17

At what annual rate of simple interest (in % per annum) will a sum of money double itself in 16 2/3 years?

Accepted Answer

Introduction: This question tests the relationship between time and rate for doubling under simple interest. Unlike compound interest, doubling under simple interest is not exponential; it happens when the interest earned equals the principal (SI = P). Using the amount formula A = P * (1 + r*t/100), doubling means A = 2P, which directly gives r*t/100 = 1. The only careful part is converting the mixed fraction time 16 2/3 years into an improper fraction. Given Data / Assumptions: Time t = 16 2/3 years Final amount is double the principal: A = 2P Simple interest amount relation: A = P * (1 + r*t/100) Concept / Approach: Set 2P = P * (1 + r*t/100) and cancel P. This yields r*t/100 = 1, so r = 100/t. Convert t = 16 2/3 into an improper fraction to compute r exactly. Step-by-Step Solution: t = 16 2/3 = (16*3 + 2)/3 = 50/3 years Doubling condition: 2P = P * (1 + r*t/100) Cancel P: 2 = 1 + r*t/100 r*t/100 = 1 r = 100 / t = 100 / (50/3) r = 100 * 3 / 50 = 6 Verification / Alternative check: If r = 6% and t = 50/3, then r*t/100 = (6 * 50/3)/100 = (100)/100 = 1. So A = P(1+1)=2P, confirming doubling exactly. Why Other Options Are Wrong: 5% would require 20 years to double under simple interest. 4% would require 25 years. 6 2/3% would double sooner than 16 2/3 years. Only 6% fits the exact time given. Common Pitfalls: Using compound interest doubling rules (like the rule of 72), mis-converting 16 2/3 years, or forgetting that doubling means SI equals principal (not “amount equals interest”). Final Answer: The required annual simple interest rate is 6% per annum.

Question 18

A sum of ₹4,000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest (both per annum). If the total interest earned in 1 year from both parts together is ₹352, what is the amount (in rupees) lent at 8% per annum?

Accepted Answer

Introduction: This question tests splitting a total principal into two parts with different simple interest rates such that the combined yearly interest is known. Because the time is 1 year, interest from each part is simply rate% of that part. This becomes a simple linear equation in the unknown split amount. The numbers are designed so the equation solves cleanly. Given Data / Assumptions: Total principal = ₹4,000 Part 1 at 8% per annum for 1 year Part 2 at 10% per annum for 1 year Total interest in 1 year = ₹352 Formula for 1 year: SI = (P * r) / 100 Concept / Approach: Let x be the amount lent at 8%. Then (4000 - x) is lent at 10%. Compute interest from each part for 1 year, add them, and set equal to 352. Solve for x. Step-by-Step Solution: Let x = amount at 8% Amount at 10% = 4000 - x Interest from 8% part (1 year) = (x * 8) / 100 = 0.08x Interest from 10% part (1 year) = ((4000 - x) * 10) / 100 = 0.10(4000 - x) Total interest: 0.08x + 0.10(4000 - x) = 352 0.08x + 400 - 0.10x = 352 -0.02x = -48 x = 2400 Verification / Alternative check: If x=2400, interest at 8% is 192. Remaining 1600 at 10% gives 160. Total interest = 192+160 = 352, matching exactly. Why Other Options Are Wrong: Each incorrect split changes the weighted interest mix. For example, higher x reduces the 10% portion too much and total interest falls below 352, while lower x increases 10% portion too much and total interest exceeds 352. Common Pitfalls: Forgetting time is 1 year (so no need for t), mixing up which part is at 8% vs 10%, or adding rates directly instead of using a weighted sum. Final Answer: The amount lent at 8% per annum is ₹2,400.

Question 19

A bank offers a fixed deposit scheme with 8% interest in the first year and 9% interest in the second year (compounded annually). If ₹17,658 is received at the end of 2 years, what was the initial amount (principal, in rupees) invested?

Accepted Answer

Introduction: This problem tests reverse calculation of principal when the final amount is given under year-wise compounding with different rates each year. The essential idea is that compounding multiplies the principal by (1 + rate/100) each year. With two different annual rates, the final amount equals P * (1 + 8/100) * (1 + 9/100). So the principal is found by dividing the final amount by this combined growth factor. Given Data / Assumptions: Amount received after 2 years = ₹17,658 Year 1 rate = 8% (annual compounding) Year 2 rate = 9% (annual compounding) Principal = P (unknown) Compounding rule: Amount after year = previous amount * (1 + r/100) Concept / Approach: Compute the two-year multiplication factor: (1.08) for the first year and (1.09) for the second year. Multiply them to get the net factor. Then P = final amount / net factor. This is the cleanest method because rates vary by year. Step-by-Step Solution: After year 1: amount = P * 1.08 After year 2: amount = (P * 1.08) * 1.09 Final amount = P * (1.08 * 1.09) 1.08 * 1.09 = 1.1772 17658 = P * 1.1772 P = 17658 / 1.1772 = 15000 Verification / Alternative check: If P = 15000, after year 1 amount = 15000*1.08 = 16200. After year 2 amount = 16200*1.09 = 17658, matching the given amount exactly. Why Other Options Are Wrong: Any principal other than ₹15,000 would produce a final amount different from ₹17,658 because the growth factor 1.1772 is fixed by the rates and compounding pattern. Common Pitfalls: Adding rates (8%+9%) and treating it like simple interest, or forgetting that the second year’s interest is earned on the first year’s grown amount (compounding effect). Final Answer: The initial investment (principal) was ₹15,000.

Question 20

What is the difference (in rupees) between: (1) the compound interest earned in 1 year on ₹10,000 at 40% per annum when interest is compounded quarterly, and (2) the compound interest earned in 1 year when it is compounded annually at the same 40% p…

Accepted Answer

Introduction: This question tests comparing compound interest under different compounding frequencies for the same annual rate and time. More frequent compounding produces a higher amount because interest is added sooner and then earns interest again within the year. Here we compare quarterly compounding versus annual compounding for 1 year at a high rate of 40%, which makes the difference noticeable. Given Data / Assumptions: Principal P = ₹10,000 Annual rate r = 40% per annum Time = 1 year Case 1: Compounded quarterly (4 times/year) Case 2: Compounded annually (1 time/year) Concept / Approach: Compute CI in each case and subtract. For annual compounding over 1 year: amount = P * (1 + 40/100). CI = amount - P. For quarterly compounding: quarterly rate = 40%/4 = 10%, number of quarters = 4, amount = P * (1 + 10/100)^4 = P * (1.1)^4. CI is again amount minus principal. Difference is CI_quarterly - CI_annual. Step-by-Step Solution: Annual compounding amount = 10000 * 1.40 = 14000 CI (annual) = 14000 - 10000 = 4000 Quarterly rate = 10% Quarterly compounding factor = (1.1)^4 (1.1)^2 = 1.21, so (1.1)^4 = 1.21^2 = 1.4641 Quarterly amount = 10000 * 1.4641 = 14641 CI (quarterly) = 14641 - 10000 = 4641 Difference = 4641 - 4000 = 641 Verification / Alternative check: Since quarterly compounding is more frequent, the difference must be positive. The computed difference ₹641 is consistent and matches the gap between 1.4641P and 1.40P for P=10000. Why Other Options Are Wrong: 461, 463, and 346 are too small compared to the correct compounding gap at 40% annual. 400 matches neither CI difference nor any correct intermediate step. Common Pitfalls: Using 40% as quarterly rate, using only one quarter instead of four, or subtracting annual amount from quarterly interest without consistently converting to CI first. Final Answer: The required difference is ₹641.

Simple Interest Questions