Question 1

Simple interest on a sum for 6 months at 5% per annum is ₹65.50. What is the principal sum (in rupees)?

Accepted Answer

Introduction: This question tests calculating principal from simple interest when time is given in months but the rate is per annum. The main skill is converting 6 months into years (0.5 years) so the annual rate can be used correctly in SI = (P * r * t) / 100. Once time is converted, the principal is found by rearranging the formula to P = (SI * 100) / (r * t). Given Data / Assumptions: Simple interest SI = ₹65.50 Annual rate r = 5% per annum Time = 6 months = 6/12 years = 0.5 years Principal P = ? Formula: SI = (P * r * t) / 100 Concept / Approach: Convert time into years because r is per annum. Substitute SI, r, and t into the formula and solve for P. Carefully handle decimals: 65.50 is a rupee amount, and r is in percent, so keep r as 5 and use division by 100 exactly once. Step-by-Step Solution: t = 6/12 = 0.5 years SI = (P * r * t) / 100 65.50 = (P * 5 * 0.5) / 100 65.50 = (P * 2.5) / 100 P = 65.50 * 100 / 2.5 P = 6550 / 2.5 = 2620 Verification / Alternative check: If P = 2620, SI for 0.5 years at 5% is (2620*5*0.5)/100 = (2620*2.5)/100 = 65.50, matching exactly. Why Other Options Are Wrong: ₹2600 gives SI = 65.00, slightly short. ₹2880 gives SI = 72.00, too high. ₹1320 is far too low. Only ₹2620 produces SI = ₹65.50 under the given conditions. Common Pitfalls: Using t = 6 instead of 0.5, treating 5% as 0.05 while still dividing by 100, or rounding 65.50 to 65 and losing accuracy. Final Answer: The principal sum is ₹2,620.

Question 2

Simple interest on a sum for 5 years is equal to 20% of the principal. In how many years will the simple interest be equal to the principal itself at the same rate of simple interest?

Accepted Answer

Introduction: This question tests proportional reasoning in simple interest without needing any actual money values. Under simple interest, SI is directly proportional to time for a fixed principal and fixed rate. If you know that in 5 years the interest equals 20% of principal, you can scale the time to find when interest becomes 100% of principal (i.e., equal to principal). This is a classic time-scaling SI question. Given Data / Assumptions: Time t1 = 5 years SI after 5 years = 20% of principal = 0.20P Same principal and same rate are used for the new time Need t2 such that SI = P (i.e., 100% of principal) Simple interest proportionality: SI/P = (r * t) / 100 Concept / Approach: Since SI is proportional to time under fixed rate and principal, the fraction SI/P increases linearly with time. If SI/P is 0.20 at 5 years, then to reach SI/P = 1.00 (interest equals principal), time must be multiplied by 1.00/0.20 = 5. So t2 = 5 * 5 = 25 years. Step-by-Step Solution: Given SI in 5 years = 0.20P We want SI = 1.00P Time scales in the same ratio as interest under simple interest Required scaling factor = 1.00 / 0.20 = 5 t2 = 5 years * 5 = 25 years Verification / Alternative check: From SI/P = (r*t)/100: If at 5 years SI/P = 0.20, then (r*5)/100 = 0.20 => r = 4%. For SI=P, we need (4*t)/100 = 1 => t = 25 years. Same result, confirming correctness. Why Other Options Are Wrong: 20 years would give SI/P = 0.8 (80%), not 100%. 15 and 16 years are even smaller. 30 years would exceed the principal (120%). Only 25 years yields exactly SI = P. Common Pitfalls: Mixing up “20% in 5 years” with “20% per year,” or assuming compound growth. Another mistake is adding percentages instead of using proportional scaling. Final Answer: The simple interest equals the principal after 25 years.

Question 3

A bank offers 9% per annum simple interest on an investment. At the end of 4 years, the interest earned is $215. How much money (in dollars) was initially invested (principal)?

Accepted Answer

Introduction: This question tests finding principal when simple interest, rate, and time are known. Simple interest is SI = (P * r * t)/100. Rearranging gives P = (SI * 100) / (r * t). Because the rate is annual and time is in years, there are no unit conversions needed, making the computation direct. The only care needed is accurate division to get the decimal principal value in dollars. Given Data / Assumptions: Simple interest SI = $215 Annual rate r = 9% per annum Time t = 4 years Principal P = ? Formula: SI = (P * r * t) / 100 Concept / Approach: Rearrange the formula to isolate P. Substitute the given values. Since r is in percent, keep r as 9 and use the factor 100 from the formula. The result may be a decimal because interest values in dollars do not have to produce integer principals. Step-by-Step Solution: SI = (P * r * t) / 100 P = (SI * 100) / (r * t) P = (215 * 100) / (9 * 4) P = 21500 / 36 P = 597.2222... ≈ 597.22 Verification / Alternative check: Check: SI = (597.22 * 9 * 4)/100 ≈ 597.22 * 0.36 ≈ 215.0 (difference only due to rounding to 2 decimals). Using the full repeating decimal gives exactly 215. Why Other Options Are Wrong: $456 and $378 would yield much smaller interest at 9% over 4 years. $345 is even smaller. $620 would yield interest higher than $215. Only $597.22 matches the required principal based on the formula. Common Pitfalls: Forgetting to multiply SI by 100, using 0.09 and still dividing by 100 again, or mixing up amount and interest. Final Answer: The initial investment was $597.22 (approximately).

Question 4

An amount of $255 is invested at 8.5% per annum simple interest. To the nearest year, how long will it take to earn $86.70 in interest under simple interest?

Accepted Answer

Introduction: This question tests solving for time in simple interest when the interest amount is given. The formula SI = (P * r * t)/100 can be rearranged to t = (SI * 100)/(P * r). Since the rate is per annum and the answer is requested in years, we can compute t directly in years. Finally, because the question asks “to the nearest year,” we confirm whether the computed value is essentially 4 years or needs rounding up/down. Given Data / Assumptions: Principal P = $255 Rate r = 8.5% per annum Simple interest SI = $86.70 Time t = ? years Formula: SI = (P * r * t) / 100 Concept / Approach: Rearrange to solve for time: t = (SI * 100) / (P * r). Substitute the values. Keep r as 8.5 (percent form) because the formula divides by 100. Compute the quotient accurately and then round to the nearest whole year as requested. Step-by-Step Solution: t = (SI * 100) / (P * r) t = (86.70 * 100) / (255 * 8.5) Numerator = 8670 Denominator = 255 * 8.5 = 2167.5 t = 8670 / 2167.5 = 4.0 Nearest year = 4 years Verification / Alternative check: Interest per year at 8.5% on $255 is (255*8.5)/100 = 21.675. Over 4 years, SI = 21.675 * 4 = 86.70 exactly, confirming t = 4 years without any rounding ambiguity. Why Other Options Are Wrong: 2 years gives only $43.35, 3 years gives $65.025, and 5 years gives $108.375. Only 4 years yields exactly $86.70. Common Pitfalls: Using 0.085 while still dividing by 100, mixing up interest with final amount, or rounding too early in intermediate multiplication/division steps. Final Answer: It will take 4 years.

Question 5

Jaclyn buys company debentures worth $50,000 and earns 9.5% simple interest per annum, paid every quarter (every 3 months). If the agreed term of the debentures is 18 months, what amount of simple interest will she receive at the end of each quarter?

Accepted Answer

Introduction / Context: This question tests the basic application of the simple interest formula when interest is quoted per annum but actually paid at regular sub annual intervals, in this case quarterly. Many savings products and debentures pay investors their interest every month, quarter, or half year rather than only once at maturity. The key skill is to compute the total simple interest over the full term in years and then divide it correctly across the number of payment periods to find the interest amount per period. Given Data / Assumptions: Principal invested in debentures = $50,000 Annual simple interest rate = 9.5 percent per annum Total investment term = 18 months Interest is paid every quarter, that is once every 3 months Assume simple interest with no reinvestment of interest payments Concept / Approach: Under simple interest, the interest depends only on the original principal, the annual rate, and the total time in years. The standard formula is: Simple interest I = P * R * T Here P is the principal, R is the rate per year written as a decimal, and T is the time in years. Once the total simple interest over the full 18 months is known, it can be shared equally between the number of quarters in 18 months, because each quarter earns the same simple interest amount. Step-by-Step Solution: Step 1: Convert the total time of 18 months to years. T = 18 months / 12 = 1.5 years. Step 2: Convert the annual rate of 9.5 percent to decimal. R = 9.5 percent = 9.5 / 100 = 0.095. Step 3: Apply the simple interest formula for the entire 1.5 years. I = P * R * T = 50,000 * 0.095 * 1.5. I = 50,000 * 0.1425 = 7,125 dollars. Step 4: Find the number of quarters in 18 months. 18 months / 3 months per quarter = 6 quarters. Step 5: Interest per quarter = total interest / number of quarters. Interest each quarter = 7,125 / 6 = 1,187.50 dollars. Verification / Alternative check: Another way is to think directly in quarterly terms. Each year has 4 quarters. Since the annual simple interest is 50,000 * 0.095 = 4,750 dollars per year, the simple interest for one quarter is 4,750 / 4 = 1,187.50 dollars. There are 6 quarters in 18 months, so 1,187.50 * 6 = 7,125 dollars total, which matches the earlier calculation. This confirms the quarterly interest figure is correct. Why Other Options Are Wrong: Option $1,234.00 is larger than the correct quarterly interest and does not correspond to dividing the total simple interest evenly over six quarters. Option $1,289.00 gives an even higher quarterly amount and would imply a much greater annual interest than 9.5 percent. Option $1,345.00 is even more unrealistic and would imply more than the total simple interest that should be earned over the 18 month period when multiplied by six. Common Pitfalls: A frequent error is to treat 18 months as 18 years or as 2 years, which leads to large mistakes in the time factor. Another common mistake is to forget that the given 9.5 percent applies per annum and does not change simply because interest is paid quarterly. Some learners also divide the annual interest by 3 instead of 4 when trying to find the quarterly interest. Always convert time to years, compute the total simple interest correctly, and then divide by the exact number of periods for which payments are made. Final Answer: The fixed simple interest amount that Jaclyn receives at the end of each quarter is $1,187.50.

Question 6

Townbank offers a term deposit account that pays investors 12.5% simple interest per annum on investments over $100,000 for periods of 2 years or more. Peta invests $150,000 in this simple interest account for exactly 2 years. How much simple intere…

Accepted Answer

Introduction / Context: This aptitude question checks understanding of basic simple interest on a term deposit. When a bank advertises a rate like 12.5 percent per annum, the investor needs to be able to calculate the interest earned over a given number of years on a known principal. This is a direct and very common real life application in banking and personal finance, such as fixed deposits and term investment accounts. Given Data / Assumptions: Principal deposited by Peta = $150,000 Annual simple interest rate = 12.5 percent per annum Investment term = 2 years Interest is calculated using simple interest, not compound interest Assume there are no additional deposits or withdrawals during the term Concept / Approach: Under simple interest, interest is calculated only on the original principal throughout the entire term. The formula is: Simple interest I = P * R * T where P is the principal, R is the annual rate expressed as a decimal, and T is the time in years. Once interest is found, that is Peta's earnings in dollars, and the maturity amount would be principal plus interest. Here the question only asks for the interest amount, not the final balance. Step-by-Step Solution: Step 1: Identify the principal P = 150,000 dollars. Step 2: Convert the annual rate R from percent to decimal. R = 12.5 percent = 12.5 / 100 = 0.125. Step 3: Identify the time T in years. Here T = 2 years. Step 4: Substitute into the simple interest formula. I = P * R * T = 150,000 * 0.125 * 2. Step 5: Calculate the product. 150,000 * 0.125 = 18,750. Step 6: Multiply by 2 years: I = 18,750 * 2 = 37,500 dollars. Verification / Alternative check: An alternative way is to note that 12.5 percent is equal to one eighth. One eighth of 150,000 is 150,000 / 8 = 18,750. That is the interest for one year. For two years of simple interest, simply double 18,750 to get 37,500 dollars. This mental check matches the earlier calculation and confirms the answer is consistent and reasonable for the given rate and principal. Why Other Options Are Wrong: Option $57,500 would correspond to a much higher effective rate or a longer term than 2 years. Option $47,500 also overstates the interest compared with 12.5 percent per year on 150,000. Option $67,500 is even larger and clearly incompatible with a 2 year term at 12.5 percent. Only 37,500 dollars matches the simple interest formula applied to the given figures. Common Pitfalls: A common mistake is to treat the 12.5 percent rate as if it were applied for each of the two years separately and then compounded, which would be a different problem. Another frequent error is misreading the principal as 100,000 instead of 150,000 or miscalculating the decimal form of 12.5 percent. Candidates should always convert the rate to decimal carefully and verify that the time is measured in years when using the standard simple interest formula. Final Answer: Peta earns a total simple interest of $37,500 at the end of the 2 year deposit period.

Question 7

An investment bond is offered to the public at 9% per annum simple interest. Louise buys a bond with a face value of $2,000 that will mature in 2 years. At maturity, how much money in total, including both principal and simple interest, will Louise …

Accepted Answer

Introduction / Context: Investment bonds and fixed deposits often pay a fixed simple interest rate on a known face value or principal for a specified term. This problem focuses on calculating both the simple interest and the total maturity amount that the investor receives at the end of the period. Understanding this calculation is essential for comparing different fixed income products and for basic personal finance planning. Given Data / Assumptions: Face value or principal of the bond = $2,000 Annual simple interest rate = 9 percent per annum Term to maturity = 2 years Interest is calculated using simple interest, not compound interest No intermediate repayments or reinvestment of interest occur Concept / Approach: The main steps are to calculate the simple interest using the formula I = P * R * T and then add this interest to the original principal to obtain the total maturity value. Simple interest means that the interest each year is based only on the original principal, not on accumulated interest. This is different from compound interest where interest is periodically added to principal. Step-by-Step Solution: Step 1: Identify the principal P = 2,000 dollars. Step 2: Convert the annual rate R from percent to decimal: 9 percent = 0.09. Step 3: Identify the time T in years, which is 2 years. Step 4: Compute simple interest with I = P * R * T. I = 2,000 * 0.09 * 2. Step 5: Calculate the product: 2,000 * 0.09 = 180 dollars per year. Step 6: Multiply by 2 years: I = 180 * 2 = 360 dollars. Step 7: Add interest to principal to get maturity amount. Maturity amount A = P + I = 2,000 + 360 = 2,360 dollars. Verification / Alternative check: A quick check is to compute 9 percent of 2,000 as 0.09 * 2,000 = 180 and then reason that over 2 years of simple interest the investor earns 180 dollars each year. Doubling 180 gives 360 total interest. Adding this to 2,000 again produces 2,360 dollars. This alternative mental method confirms that the calculations are consistent and free from arithmetic errors. Why Other Options Are Wrong: Option $3,360 would require an interest of 1,360 dollars on 2,000, which is far more than 9 percent per year for 2 years. Option $4,360 and option $5,360 are even larger and are not compatible with the given rate and term. Only $2,360 is consistent with 9 percent simple interest for 2 years on a principal of 2,000 dollars. Common Pitfalls: Learners sometimes confuse simple interest with compound interest and incorrectly apply exponential growth formulas. Others may forget to add the interest back to the principal and instead report only the interest as the final answer. It is also easy to misplace the decimal when converting a percentage to a decimal rate. Always ensure that the rate is written correctly as R over 100, that the time is in years, and that principal plus interest is used for the final maturity value. Final Answer: At maturity, Louise receives a total of $2,360 from the bond.

Question 8

A sapphire ring has a marked cash price of $1,800. It is offered on hire purchase terms with a $200 deposit and the remaining balance to be paid over 24 equal monthly instalments. Interest is charged at a flat rate of 11.5% per annum on the outstand…

Accepted Answer

Introduction / Context: This problem is based on a common consumer finance arrangement called hire purchase. The buyer pays a deposit and then repays the remaining balance with interest through equal monthly instalments. The key concept is the calculation of flat rate simple interest on the financed balance, not on the full cash price. Understanding such calculations helps in comparing the true cost of credit when buying goods like jewellery, appliances, or vehicles on instalment plans. Given Data / Assumptions: Cash price of the sapphire ring = $1,800 Deposit paid immediately = $200 Balance financed on hire purchase = cash price minus deposit Flat rate simple interest = 11.5 percent per annum on the financed balance Repayment term = 24 months = 2 years Monthly instalments are equal throughout the term Concept / Approach: First, compute the financed balance by subtracting the deposit from the cash price. Next, calculate simple interest on this balance using the formula I = P * R * T, where P is the financed amount, R is the annual rate in decimal, and T is the time in years. Then add the interest to the financed balance to obtain the total amount to be repaid in instalments. Finally, divide the total payable by the number of monthly payments to obtain the monthly instalment amount. Step-by-Step Solution: Step 1: Compute the financed balance. Financed balance P = 1,800 - 200 = 1,600 dollars. Step 2: Convert the annual flat rate from percent to decimal. R = 11.5 percent = 11.5 / 100 = 0.115. Step 3: Express the term T in years: 24 months = 2 years. Step 4: Compute simple interest on the financed balance. I = P * R * T = 1,600 * 0.115 * 2. Step 5: Calculate the interest: 1,600 * 0.115 = 184 per year. Step 6: For 2 years, I = 184 * 2 = 368 dollars. Step 7: Compute total amount to be repaid in instalments. Total instalment amount = financed balance + interest = 1,600 + 368 = 1,968 dollars. Step 8: Number of monthly instalments = 24. Step 9: Monthly instalment = 1,968 / 24 = 82 dollars. Verification / Alternative check: To verify, multiply the monthly instalment back by the number of months. That is 82 * 24 = 1,968 dollars. Subtract the financed balance of 1,600 dollars from this total to obtain the interest component: 1,968 - 1,600 = 368 dollars. Now check whether this interest equals simple interest at 11.5 percent per annum over 2 years on 1,600 dollars. Indeed, 1,600 * 0.115 * 2 = 368. This confirms that the monthly instalment of 82 dollars is correct. Why Other Options Are Wrong: Option $53 and option $42 produce far too little total repayment over 24 months and would not cover both principal and the flat rate interest. Option $62 is closer but still results in a total repayment of only 62 * 24 = 1,488 dollars, which is even less than the financed balance of 1,600 dollars. Only 82 dollars per month correctly repays both the financed balance and the charged interest. Common Pitfalls: One common mistake is to apply the interest to the entire cash price instead of the balance after the deposit, which inflates the interest excessively. Another error is to treat 24 months as 24 years in the formula, or to treat 11.5 percent as a monthly rate instead of an annual rate. Always convert the term into years for the simple interest formula and ensure that the deposit is subtracted before calculating the financed amount. Final Answer: Each monthly repayment on the hire purchase plan is $82.

Question 9

Determine the ordinary simple interest, using a 360 day year convention, on a 90 day loan of $8,000 at a simple interest rate of 8.5% per annum.

Accepted Answer

Introduction / Context: Banks and finance companies sometimes use the ordinary simple interest method, where a 360 day year is assumed for convenience instead of the actual 365 day year. This question checks whether you can correctly convert days to a fraction of a year, apply the simple interest formula, and interpret the meaning of an annual percentage rate when the borrowing period is less than one full year. Given Data / Assumptions: Loan principal P = $8,000 Annual simple interest rate R = 8.5 percent per annum Loan term = 90 days A 360 day year is used for time conversion (ordinary simple interest) No part repayments are made during the 90 day term Concept / Approach: For ordinary simple interest, time in years is calculated by dividing the number of days by 360. Then the simple interest formula I = P * R * T is applied. Here, R must be expressed as a decimal, and T is the time in years. Since the borrowing period is less than one year, the interest earned will be a fraction of the annual interest that the principal would generate in a full year. Step-by-Step Solution: Step 1: Convert the annual rate to decimal form. R = 8.5 percent = 8.5 / 100 = 0.085. Step 2: Convert the 90 day term to years using a 360 day year. T = 90 / 360 = 0.25 years. Step 3: Use the simple interest formula I = P * R * T. I = 8,000 * 0.085 * 0.25. Step 4: Compute intermediate product: 8,000 * 0.085 = 680 dollars per year. Step 5: Apply the time fraction: I = 680 * 0.25 = 170 dollars. Verification / Alternative check: An alternative check is to note that 0.25 of a year is exactly three months. Annual interest on 8,000 at 8.5 percent is 680 dollars. One quarter of that amount corresponds to three months: 680 / 4 = 170 dollars. This is consistent with the time calculation based on 90 days out of 360 and confirms the accuracy of the interest computed. Why Other Options Are Wrong: Option $150 and option $160 are both less than the correct value and would correspond to either a lower rate or a shorter time than 90 days. Option $180 is higher than the correct interest and would imply either a slightly higher annual rate or a longer loan term. Only 170 dollars fits exactly with 8.5 percent per annum simple interest for a quarter of a year on 8,000 dollars. Common Pitfalls: Students sometimes divide by 365 instead of 360 when the question explicitly instructs them to use a 360 day year, which would give a slightly different result. Others mistakenly treat 90 days as 9 months or as 0.9 years. Always read carefully whether the problem specifies ordinary simple interest with 360 days and ensure that days are correctly converted to a fraction of a year before applying the formula. Final Answer: The ordinary simple interest on the 90 day loan is $170.

Question 10

You deposit $600 into a 6 month certificate of deposit (CD). After 6 months, the balance in the CD is $618. Assuming simple interest over this 6 month period, what is the annual simple interest rate on this investment?

Accepted Answer

Introduction / Context: Short term deposits such as certificates of deposit often quote an annual interest rate, even when the money is invested for only part of a year. This question works in reverse. Instead of giving the rate and asking for the interest, it gives the principal, the final amount after 6 months, and asks you to infer the annual simple interest rate that must have applied. This is a practical skill when comparing different investment products with different terms. Given Data / Assumptions: Principal deposited P = $600 Term of the CD = 6 months = 0.5 years Final balance after 6 months = $618 Interest is assumed to be simple interest over the term No additional deposits or withdrawals are made Concept / Approach: First, determine the interest actually earned over the 6 month period by subtracting the principal from the final amount. Then use the simple interest formula I = P * R * T and solve for R, the annual rate. Here, T must be expressed in years. Rearranging the formula gives R = I / (P * T). Once R is found as a decimal, convert it to a percentage by multiplying by 100 and matching it with the closest option. Step-by-Step Solution: Step 1: Calculate the interest earned in 6 months. I = final amount - principal = 618 - 600 = 18 dollars. Step 2: Express the time T in years. 6 months corresponds to T = 6 / 12 = 0.5 years. Step 3: Start from the simple interest formula I = P * R * T. Step 4: Rearrange to find R: R = I / (P * T). Step 5: Substitute the known values: R = 18 / (600 * 0.5). Step 6: Evaluate the denominator: 600 * 0.5 = 300. Step 7: Compute R = 18 / 300 = 0.06. Step 8: Convert R to percent: 0.06 * 100 = 6 percent per annum. Verification / Alternative check: To verify, assume a 6 percent annual rate and calculate the interest for 6 months on 600 dollars. Annual interest would be 600 * 0.06 = 36 dollars per year. For half a year, the interest would be 36 / 2 = 18 dollars. Adding this to the principal yields 600 + 18 = 618 dollars, which matches the given final balance. This confirms that the correct annual simple interest rate is 6 percent. Why Other Options Are Wrong: If the rate were 5 percent, the annual interest would be 600 * 0.05 = 30 dollars, so for 6 months the interest would be only 15 dollars, not 18 dollars. A 4 percent rate would give even less. A 7 percent rate would produce 600 * 0.07 = 42 dollars per year, or 21 dollars in half a year, which is larger than the observed interest. Thus only 6 percent fits the data. Common Pitfalls: Some learners forget to convert the time period into years and mistakenly treat 6 months as T = 6, which leads to an incorrect and extremely small rate. Others divide by 12 twice or confuse simple and compound interest. Always ensure that T is in years when using the simple interest formula and remember that the rate calculated is per annum, even if the actual investment period is shorter. Final Answer: The annual simple interest rate on the CD investment is 6% per annum.

Question 11

Rondell's parents borrow $6,300 from a bank to buy a new car. The bank charges 6% simple interest per year on this car loan. If they take 2 years to repay the loan in full, how much simple interest will they pay in total over the 2 year period?

Accepted Answer

Introduction / Context: This question models a basic car loan with simple interest. Many entry level aptitude tests and banking exams include similar items to check whether candidates can compute the total interest on a loan when given the principal, the annual simple interest rate, and the term in years. The calculation is straightforward but must be carried out with care, especially when interpreting the interest as a separate cost on top of the original loan amount. Given Data / Assumptions: Loan principal P = $6,300 Annual simple interest rate R = 6 percent per annum Loan term T = 2 years Interest is calculated using simple interest, not compound interest No part repayments that affect the interest calculation are considered Concept / Approach: Simple interest on a loan can be computed using the standard formula: I = P * R * T Here I is the interest, P is the principal, R is the annual rate in decimal, and T is the time in years. Once I is obtained, it represents the total extra amount that Rondell's parents must pay to the bank over and above the principal. The question asks only for the interest, not the overall repayment amount that includes principal plus interest. Step-by-Step Solution: Step 1: Convert the annual rate into decimal form. R = 6 percent = 6 / 100 = 0.06. Step 2: Identify the principal and time. P = 6,300 dollars and T = 2 years. Step 3: Apply the simple interest formula. I = P * R * T = 6,300 * 0.06 * 2. Step 4: Compute 6,300 * 0.06 = 378 dollars per year. Step 5: Multiply by 2 years to obtain total interest. I = 378 * 2 = 756 dollars. Verification / Alternative check: A simple mental check is to note that 6 percent of 6,300 is slightly more than 5 percent of 6,300. Five percent of 6,300 is 315 dollars, and 1 percent is 63 dollars, so 6 percent is 315 + 63 = 378 dollars per year. Over two years, the interest doubles to 756 dollars. This reasoning matches the formal calculation and confirms that the answer is consistent. Why Other Options Are Wrong: Option $556 is too low and would correspond to a rate lower than 6 percent or a shorter term than 2 years. Option $665 is closer but still underestimates the interest compared to 378 dollars per year. Option $856 is higher than the correct value and would require a higher rate or a longer loan duration. Only 756 dollars matches the product of 6 percent per year for 2 years on 6,300 dollars. Common Pitfalls: A common error is to miscalculate 6 percent of 6,300, for example by incorrectly shifting the decimal point. Another mistake is to forget that the time is 2 years and to multiply only once by the annual interest. Some test takers mistakenly add the interest to the principal and choose that sum as the answer, even though the question asks only for the interest amount. Carefully reading what is asked and properly applying the formula avoids these issues. Final Answer: The total simple interest paid over the 2 year car loan is $756.

Question 12

Derrick's dad buys new tires for $900 using a credit card that charges simple interest at an annual rate of 19%. He has no other charges on the card and does not pay off the balance at the end of the month. Assuming simple interest, how much interes…

Accepted Answer

Introduction / Context: This question illustrates how an annual percentage rate on a credit card translates into a charge for a shorter period such as one month. Understanding this helps consumers see how expensive high credit card rates can be, even over short intervals. The calculation is based on simple interest, which is a reasonable approximation over a single month when there are no additional purchases or payments. Given Data / Assumptions: Purchase amount and outstanding balance P = $900 Annual simple interest rate R = 19 percent per annum Time outstanding T = 1 month Assume simple interest with no compounding during the month Assume a standard year of 12 months Concept / Approach: First, convert the annual rate into a decimal. Then convert one month into a fraction of a year, which is 1 / 12. Apply the simple interest formula I = P * R * T. The result gives the interest owed for one month. This method assumes that the balance remains unchanged during the month and that interest is not compounded over such a short period, which is typical in introductory quantitative problems. Step-by-Step Solution: Step 1: Convert annual rate to decimal. R = 19 percent = 19 / 100 = 0.19. Step 2: Express one month as a fraction of a year. T = 1 month = 1 / 12 years. Step 3: Use the simple interest formula I = P * R * T. I = 900 * 0.19 * (1 / 12). Step 4: Compute product: 900 * 0.19 = 171 dollars per year. Step 5: Divide by 12 for one month: I = 171 / 12 = 14.25 dollars. Verification / Alternative check: To verify, approximate 20 percent of 900, which is 180 dollars per year. Nineteen percent is slightly less, at 171 dollars per year. Since one month is roughly one twelfth of a year, the interest should be about 171 / 12, which is just over 14 dollars. The exact calculation gives 14.25 dollars, confirming the accuracy and indicating that the answer is in a reasonable range for the given rate and principal. Why Other Options Are Wrong: Option $11.25 would correspond to a lower annual rate, closer to 15 percent, not 19 percent. Option $13.25 underestimates the fraction of 171 dollars for one month. Option $15.25 overestimates the interest and would correspond to a slightly higher effective annual rate than 19 percent. Only $14.25 exactly matches the simple interest computation for one month at 19 percent on a 900 dollar balance. Common Pitfalls: Some learners mistakenly use T = 1 instead of 1 / 12, effectively charging a full year of interest for a single month. Others incorrectly divide by 10 or by 100 instead of 12 when converting the annual figure into a monthly one. There can also be confusion between simple and compound interest, but for one month on a fixed balance, both will be very similar. Carefully converting time and rate units is essential for correct answers. Final Answer: The interest owed after one month on the credit card purchase is $14.25.

Question 13

An amount of Rs 5,000 is invested at a fixed nominal rate of 8% per annum, with interest compounded every six months (semi annually). What will be the value of this investment after 5 years under compound interest with half yearly compounding?

Accepted Answer

Introduction / Context: This question tests understanding of compound interest with semi annual compounding. In many bank deposits and financial products, interest is not added just once per year but more frequently, such as twice a year. When the interest is compounded, each period's interest is added to the principal, and future interest is calculated on this increased amount. This produces exponential growth rather than the linear growth seen with simple interest. Given Data / Assumptions: Principal P = Rs 5,000 Nominal annual interest rate = 8 percent per annum Compounding frequency = semi annually (twice per year) Number of years = 5 years Interest is compounded at each half year interval Concept / Approach: For compound interest with m compounding periods per year, the amount A after T years is: A = P * (1 + r / m)^(m * T) Here r is the nominal annual rate as a decimal, m is the number of compounding periods per year, and T is the number of years. In this problem, r = 0.08 and m = 2 because the interest is compounded every six months. Over 5 years, there will be 2 * 5 = 10 compounding periods. After calculating A, we choose the option that matches the obtained value. Step-by-Step Solution: Step 1: Convert annual rate to decimal. r = 8 percent = 8 / 100 = 0.08. Step 2: Identify the number of compounding periods per year. m = 2 (semi annual compounding). Step 3: Compute the periodic rate per half year. Periodic rate = r / m = 0.08 / 2 = 0.04. Step 4: Determine the total number of compounding periods. Total periods = m * T = 2 * 5 = 10. Step 5: Apply the compound interest formula. A = 5,000 * (1 + 0.04)^10. Step 6: Evaluate the factor (1.04)^10, which is approximately 1.480244. Step 7: Multiply: A ≈ 5,000 * 1.480244 = 7,401.22 rupees (approximately). Verification / Alternative check: To verify, we can approximate by noting that a simple interest approximation at 8 percent for 5 years would give 5,000 * 0.08 * 5 = 2,000 rupees of interest, for a total of 7,000 rupees. Compound interest should give a slightly higher figure than simple interest because each half year's interest is added to the principal. The calculated amount of about 7,401.22 rupees is somewhat above 7,000 and therefore fits this expectation. It is also very close to the given option Rs 7,401.22. Why Other Options Are Wrong: Option Rs 3,456.00 is far below the original principal and clearly impossible after earning positive interest. Option Rs 4,567.00 is less than the starting amount and therefore cannot be correct. Option Rs 7,890.00 is higher than the computed compound amount for 8 percent with semi annual compounding over 5 years and corresponds to a higher effective rate or longer duration. Only Rs 7,401.22 matches the correct compound interest calculation. Common Pitfalls: Learners sometimes confuse simple and compound interest and wrongly use I = P * r * T, which would underestimate the final amount. Another common mistake is to treat the rate per compounding period as 8 percent instead of 4 percent, which leads to a large overestimate. Some also miscount the number of compounding periods, forgetting that 5 years with semi annual compounding gives 10 periods. Careful attention to periodic rate and total number of periods is essential in compound interest questions. Final Answer: The value of the investment after 5 years with semi annual compounding is approximately Rs 7,401.22.

Question 14

A sum of Rs 1,200 amounts to Rs 1,740 in 3 years at simple interest. If the annual rate of interest is increased by 3 percentage points, what will be the new amount, in rupees, after 3 years on the same principal?

Accepted Answer

Introduction / Context: This question focuses on determining an unknown simple interest rate from one scenario and then applying an increased rate to find a new maturity amount. It reflects real life situations where a bank or financial institution changes its interest rates, and an investor wants to know how this affects the amount accumulated over the same period on the same principal. Given Data / Assumptions: Original principal P = Rs 1,200 Original amount after 3 years = Rs 1,740 Original time T = 3 years Interest is simple interest in both scenarios New rate is 3 percentage points higher than the original rate Concept / Approach: First, deduce the original annual simple interest rate from the initial information. The interest earned is the difference between the amount and the principal. Then use I = P * r * T to solve for r. Once r is known, increase it by 3 percentage points to get the new rate r_new. Finally, compute the new simple interest for 3 years at this new rate and add it to the principal to get the new maturity amount. Step-by-Step Solution: Step 1: Find the original simple interest over 3 years. I_original = amount - principal = 1,740 - 1,200 = 540 rupees. Step 2: Use the simple interest formula I = P * r * T to get r. 540 = 1,200 * r * 3. Step 3: Solve for r: r = 540 / (1,200 * 3). Denominator = 1,200 * 3 = 3,600. r = 540 / 3,600 = 0.15 = 15 percent per annum. Step 4: Increase the rate by 3 percentage points. New rate r_new = 15 percent + 3 percent = 18 percent per annum. Step 5: Compute new interest with r_new for 3 years. I_new = 1,200 * 0.18 * 3. Step 6: Evaluate: 1,200 * 0.18 = 216 per year; over 3 years I_new = 216 * 3 = 648. Step 7: Find the new amount after 3 years. New amount = principal + I_new = 1,200 + 648 = 1,848 rupees. Verification / Alternative check: An alternative reasoning is to observe that the original rate 15 percent gives 180 rupees interest per year (since 1,200 * 0.15 = 180). When the rate increases to 18 percent, the annual interest becomes 1,200 * 0.18 = 216 rupees, which is 36 rupees more per year. Over 3 years, the extra interest due to the rate increase is 36 * 3 = 108 rupees. The original interest was 540 rupees, so the new interest is 540 + 108 = 648 rupees. Adding this to the principal again gives 1,848 rupees, confirming the result. Why Other Options Are Wrong: Option Rs 1,946 would require a higher rate than 18 percent per year over 3 years. Option Rs 1,812 and option Rs 1,924 correspond to different combinations of rate and time and do not match the specified 3 percent increase from 15 percent. Only Rs 1,848 is consistent with 18 percent simple interest on 1,200 rupees over 3 years. Common Pitfalls: A common mistake is to add 3 percent of the original amount instead of increasing the rate itself by 3 percentage points. Another error is miscalculating the original rate or using 3 years twice. Candidates may also confuse percentage points with relative percentage change. It is crucial to first compute the original rate accurately using I = P * r * T, then add 3 percentage points directly to that rate before recomputing the future amount. Final Answer: The new amount after 3 years at the higher rate is Rs 1,848.

Question 15

Simple interest (S.I.) and compound interest (C.I.) are both calculated at the same rate of 10% per annum on the same principal. If compound interest is calculated yearly for 2 years, then for how many years must simple interest be calculated so tha…

Accepted Answer

Introduction / Context: This question compares simple interest and compound interest for the same principal and annual rate. It asks for the time period under simple interest that will generate the same total interest as compound interest generates in 2 years. This highlights the difference between linear growth (simple interest) and exponential growth (compound interest), and it is a common conceptual test in quantitative aptitude and banking exams. Given Data / Assumptions: Principal P is the same for both cases (exact amount is not required) Annual interest rate r = 10 percent per annum Compound interest is calculated yearly for 2 years Simple interest is to be calculated at the same rate for an unknown number of years n We want simple interest over n years to equal compound interest over 2 years Concept / Approach: First, compute compound interest on principal P for 2 years at 10 percent per year compounded annually using A = P * (1 + r)^2. The compound interest C.I. is A minus P. Then express simple interest S.I. for n years as S.I. = P * r * n (with r in decimal). Equate S.I. to C.I. and solve for n. Note that because P and r are common factors, we can cancel them and solve directly for n without needing the actual principal. Step-by-Step Solution: Step 1: Convert rate to decimal: r = 10 percent = 0.10. Step 2: Compute the compound amount for 2 years. A = P * (1 + r)^2 = P * (1 + 0.10)^2 = P * (1.10)^2. Step 3: Evaluate (1.10)^2 = 1.21. So A = P * 1.21. Step 4: Compound interest C.I. for 2 years is A - P. C.I. = P * 1.21 - P = P * (1.21 - 1) = P * 0.21. Step 5: Express simple interest S.I. for n years. S.I. = P * r * n = P * 0.10 * n = 0.10 * P * n. Step 6: Set simple interest equal to compound interest. 0.10 * P * n = 0.21 * P. Step 7: Cancel P from both sides (P is non zero). 0.10 * n = 0.21. Step 8: Solve for n: n = 0.21 / 0.10 = 2.1 years. Verification / Alternative check: As a check, assume a convenient principal such as P = 1,000 rupees. Compound interest at 10 percent for 2 years is P * 0.21 = 210 rupees. Simple interest at 10 percent per year for 2.1 years would be S.I. = 1,000 * 0.10 * 2.1 = 210 rupees, which matches the compound interest exactly. This confirms that 2.1 years of simple interest at 10 percent per annum produces the same interest as 2 years of compound interest at the same rate. Why Other Options Are Wrong: Option 4.2 years would produce simple interest S.I. = P * 0.10 * 4.2 = 0.42 * P, which is double the required interest of 0.21 * P. Option 1.1 years would yield S.I. = 0.11 * P, which is too small. Option 1.4 years gives S.I. = 0.14 * P, also less than 0.21 * P. Only 2.1 years results in simple interest that matches the 2 year compound interest. Common Pitfalls: Some students mistakenly equate the amounts instead of the interest components or forget to subtract principal when computing compound interest. Others treat 10 percent for 2 years under compound interest as the same as 20 percent under simple interest, ignoring the extra interest on interest that arises in the compound case. Careful attention to the definitions of simple and compound interest and a clear distinction between amount and interest help avoid these errors. Final Answer: The simple interest must be calculated for 2.1 years in order to equal the 2 year compound interest at 10 percent per annum.

Question 16

Ankita borrows Rs 7,000 at simple interest from a lender. At the end of 3 years, she borrows an additional Rs 3,000 from the same lender at the same annual rate of interest. She settles all her borrowings by paying a total of Rs 4,615 as interest af…

Accepted Answer

Introduction / Context: This problem involves two separate simple interest loans taken at different times but at the same annual rate. It is a common type of question in aptitude tests that checks whether you can track interest over different time periods for different principal amounts, then combine those interest amounts to find an unknown rate. Real world analogues include top up loans and staged borrowing from the same lender. Given Data / Assumptions: First loan principal P1 = Rs 7,000 Second loan principal P2 = Rs 3,000 Second loan is taken 3 years after the first loan Total interest paid on both loans together = Rs 4,615 Total time for first loan = 8 years Time for second loan = 8 - 3 = 5 years Same annual simple interest rate r for both loans Concept / Approach: Simple interest for each loan is calculated using I = P * r * T, with r as a fraction (r over 100). Since the rate is the same, the total interest is the sum of the interests for both principals over their respective time periods. Set this total equal to 4,615 rupees and solve for r. Because the principal and time for each loan are known, this results in a simple linear equation in r. Step-by-Step Solution: Step 1: Express interest on the first loan. I1 = P1 * r * T1 / 100 = 7,000 * r * 8 / 100. Step 2: Express interest on the second loan. I2 = P2 * r * T2 / 100 = 3,000 * r * 5 / 100. Step 3: Express total interest as sum of I1 and I2. Total interest = I1 + I2 = 4,615. Step 4: Substitute and simplify. I1 = 7,000 * 8 * r / 100 = 56,000 * r / 100 = 560 * r. I2 = 3,000 * 5 * r / 100 = 15,000 * r / 100 = 150 * r. Total interest = 560 * r + 150 * r = 710 * r. Step 5: Set 710 * r = 4,615. r = 4,615 / 710. Step 6: Compute r: 4,615 / 710 = 6.5 percent per annum. Verification / Alternative check: To verify, use r = 6.5 percent explicitly and recalculate the interests. First loan interest: 7,000 * 6.5 * 8 / 100 = 7,000 * 52 / 100 = 3,640 rupees. Second loan interest: 3,000 * 6.5 * 5 / 100 = 3,000 * 32.5 / 100 = 975 rupees. Total interest = 3,640 + 975 = 4,615 rupees, which matches the given total. This confirms that the annual simple interest rate is indeed 6.5 percent. Why Other Options Are Wrong: At 5.5 percent, the interest would be 7,000 * 5.5 * 8 / 100 + 3,000 * 5.5 * 5 / 100, which sums to less than 4,615 rupees. Similarly, 7.5 percent and 9.5 percent produce total interests larger than 4,615 rupees. Therefore, only 6.5 percent per annum yields the exact total interest specified in the problem statement. Common Pitfalls: A frequent mistake is to treat both loans as if they run for the same duration, ignoring that the second loan starts 3 years later. Another common error is to forget to divide by 100 when using the percentage rate in the formula, leading to very large interest values. Some learners also attempt to average time periods or principals without forming the correct linear equation. Writing separate expressions for each loan and then adding them is the safest and most systematic approach. Final Answer: The annual rate of simple interest charged by the lender is 6.5% per annum.

Question 17

A man borrows some money from a private organisation at 5% simple interest per annum. He lends the same money to another person at 10% compound interest per annum, compounded yearly. After 4 years, he makes a profit of Rs 26,410 from this transactio…

Accepted Answer

Introduction / Context: This question combines simple interest and compound interest in a single profit scenario. The man acts as an intermediary: he borrows at a lower simple interest rate and lends at a higher compound interest rate. His profit arises from the difference between what he receives and what he must repay after 4 years. This type of problem tests multi concept reasoning and the ability to model a real world financial transaction mathematically. Given Data / Assumptions: He borrows principal P from an organisation at 5 percent simple interest per annum He lends the same principal P to another person at 10 percent compound interest per annum, compounded yearly Total duration of both borrowing and lending is 4 years His net profit after 4 years is Rs 26,410 We assume no other fees or charges, only the stated interest flows Concept / Approach: First, compute the amount he must repay to the organisation after 4 years under simple interest: amount_out = P + P * 0.05 * 4. Next, compute the amount he receives from the borrower under compound interest for 4 years at 10 percent: amount_in = P * (1.10)^4. The profit is the difference amount_in minus amount_out. Set this equal to 26,410 and solve for P. This results in a linear equation because the compound factor (1.10)^4 is constant. Step-by-Step Solution: Step 1: Express the amount he must repay at simple interest. Simple interest rate = 5 percent per annum. Time T = 4 years. Simple interest on borrowing = P * 0.05 * 4 = 0.20 * P. Amount he repays to organisation = P + 0.20 * P = 1.20 * P. Step 2: Express the amount he receives under compound interest. Compound interest rate = 10 percent per annum. Compounding yearly for 4 years gives factor (1.10)^4. So amount received from borrower = P * (1.10)^4. Step 3: Compute (1.10)^4. (1.10)^2 = 1.21 and (1.10)^4 = (1.21)^2 = 1.4641. Thus amount_in = P * 1.4641. Step 4: Express profit as difference between amounts. Profit = amount_in - amount_out = P * 1.4641 - P * 1.20. Profit = P * (1.4641 - 1.20) = P * 0.2641. Step 5: Set profit equal to 26,410 and solve for P. 0.2641 * P = 26,410. P = 26,410 / 0.2641 = 100,000 rupees. Verification / Alternative check: To verify, assume P = Rs 1,00,000. Simple interest over 4 years at 5 percent is 1,00,000 * 0.05 * 4 = 20,000 rupees, so he must repay 1,20,000 rupees. Under 10 percent compound interest for 4 years, the amount received is 1,00,000 * 1.4641 = 1,46,410 rupees. The profit is 1,46,410 - 1,20,000 = 26,410 rupees, exactly as stated. This confirms that the original borrowed amount is indeed Rs 1,00,000. Why Other Options Are Wrong: If P were Rs 1,50,000 or Rs 2,00,000, the profit would scale proportionally and be significantly greater than 26,410 rupees. If P were Rs 1,32,050, the profit would be 0.2641 * 1,32,050, which does not equal 26,410. Only P = 1,00,000 rupees produces the exact profit of 26,410 under the given simple and compound interest conditions. Common Pitfalls: Some candidates mistakenly apply simple interest to both sides of the transaction or compound interest to both sides, losing the key asymmetry that generates profit. Others subtract the rates directly without accounting for the different interest calculation methods. A further error is miscomputing the compound factor (1.10)^4. It is important to compute the two amounts separately using the correct formulas and then subtract them to obtain the profit. Final Answer: The man originally borrows Rs 1,00,000 from the private organisation.

Question 18

Simple interest on a certain sum for 8 months at 6% per annum is Rs 340. What is the value of the principal sum, in rupees?

Accepted Answer

Introduction / Context: This question requires working backwards from the simple interest earned to find the original principal. Such reverse calculations are common when a bank statement shows interest credited for a partial year and a customer wants to know what principal produced that interest at a known annual rate. It reinforces the idea that the simple interest formula can be algebraically rearranged to solve for any one of its variables. Given Data / Assumptions: Simple interest I = Rs 340 Annual simple interest rate R = 6 percent per annum Time T = 8 months Interest is calculated using simple interest We need to find the principal P Concept / Approach: The simple interest formula is I = P * R * T, where R is in decimal form and T is in years. Since the time is given in months, convert 8 months into a fraction of a year. Then rearrange the formula to solve for P: P = I / (R * T). Substitute the known values and compute the principal. This demonstrates how time in months affects the total interest on a given sum. Step-by-Step Solution: Step 1: Convert the annual rate to decimal. R = 6 percent = 6 / 100 = 0.06. Step 2: Convert the time from months to years. T = 8 months = 8 / 12 years = 2 / 3 years. Step 3: Start from the simple interest formula I = P * R * T. 340 = P * 0.06 * (2 / 3). Step 4: Simplify the product of R and T. 0.06 * (2 / 3) = 0.06 * 0.6667 ≈ 0.04. More exactly, 6 / 100 * 2 / 3 = 12 / 300 = 4 / 100 = 0.04. Step 5: So the equation is 340 = P * 0.04. Step 6: Solve for P: P = 340 / 0.04. Step 7: P = 8,500 rupees. Verification / Alternative check: To check, compute the interest on 8,500 rupees at 6 percent per annum for 8 months. First, annual interest on 8,500 at 6 percent is 8,500 * 0.06 = 510 rupees. Since 8 months is 8 / 12 of a year, the interest is 510 * (8 / 12) = 510 * 2 / 3 = 340 rupees. This matches the given interest, confirming that the principal is correctly calculated as 8,500 rupees. Why Other Options Are Wrong: If the principal were Rs 9,500, simple interest for 8 months at 6 percent per annum would be greater than 340 rupees. A principal of Rs 8,000 would give annual interest of 480 rupees and 8 month interest of 320 rupees, which is too low. A principal of Rs 6,800 would produce even less interest. Only a principal of 8,500 rupees yields exactly 340 rupees of interest under the given rate and time. Common Pitfalls: Learners sometimes forget to convert months to years and instead treat T as 8, which inflates the principal estimate. Others may incorrectly approximate the fraction 8 / 12 or make arithmetic mistakes when dividing 340 by 0.04. Carefully converting the time unit and simplifying the fraction for the product R * T helps maintain accuracy in such reverse interest problems. Final Answer: The principal sum invested or borrowed is Rs 8,500.

Question 19

Ravi invests Rs P in Scheme A, which offers simple interest at 10% per annum for 2 years. He then invests the entire amount received from Scheme A (principal plus interest) in Scheme B, which offers simple interest at 12% per annum for 5 years. If t…

Accepted Answer

Introduction / Context: This question deals with successive investments in two simple interest schemes. Ravi first invests in a lower rate scheme, then reinvests the accumulated amount (principal plus interest) into a higher rate scheme for a longer period. The problem provides the difference between the interest earned in the second scheme and the first scheme and asks for the original principal. It combines basic simple interest calculations with algebraic reasoning about successive stages of investment. Given Data / Assumptions: Initial principal in Scheme A = Rs P Scheme A rate = 10 percent per annum, time = 2 years Amount from Scheme A is reinvested in Scheme B Scheme B rate = 12 percent per annum, time = 5 years Difference in interest (Scheme B minus Scheme A) = Rs 1,300 Both schemes use simple interest Concept / Approach: First, compute the simple interest earned in Scheme A in terms of P. Then determine the amount carried forward to Scheme B. Use that amount to compute the interest earned in Scheme B, again in terms of P. Finally, form an equation using the information that interest from Scheme B minus interest from Scheme A equals 1,300 rupees, and solve for P. The principal P will appear in both interest expressions but with different coefficients, which leads to a straightforward linear equation. Step-by-Step Solution: Step 1: Compute interest in Scheme A. Rate = 10 percent per annum, time = 2 years. I_A = P * 10 * 2 / 100 = P * 20 / 100 = 0.20 * P. Step 2: Compute amount after Scheme A. Amount after A = P + I_A = P + 0.20 * P = 1.20 * P. Step 3: Use this amount as principal in Scheme B. Principal in Scheme B = 1.20 * P. Rate in Scheme B = 12 percent per annum, time = 5 years. Step 4: Compute interest in Scheme B. I_B = (1.20 * P) * 12 * 5 / 100. I_B = 1.20 * P * 60 / 100 = 1.20 * P * 0.60 = 0.72 * P. Step 5: Difference between interests is given. I_B - I_A = 1,300 rupees. 0.72 * P - 0.20 * P = 1,300. Step 6: Simplify the left side: (0.72 - 0.20) * P = 0.52 * P. 0.52 * P = 1,300. Step 7: Solve for P: P = 1,300 / 0.52 = 2,500 rupees. Verification / Alternative check: Verify by substituting P = 2,500. Scheme A interest: I_A = 2,500 * 10 * 2 / 100 = 500 rupees. Amount after A = 2,500 + 500 = 3,000 rupees. Scheme B interest: I_B = 3,000 * 12 * 5 / 100 = 3,000 * 60 / 100 = 1,800 rupees. Difference I_B - I_A = 1,800 - 500 = 1,300 rupees, which matches the given condition. This confirms that the original principal is 2,500 rupees. Why Other Options Are Wrong: If P were 2,000, the difference in interests would be 0.52 * 2,000 = 1,040 rupees, not 1,300 rupees. For P = 3,000, the difference would be 1,560 rupees. For P = 3,500, the difference would be 1,820 rupees. None of these match the specified difference of 1,300 rupees. Only P = 2,500 rupees leads to the correct difference. Common Pitfalls: A common error is to treat Scheme B interest as if it were calculated on the original principal P rather than on the increased amount after Scheme A. Others might compute the difference between amounts instead of the difference between interests, which changes the equation. Another mistake is forgetting to divide by 100 when converting from percentage to decimal. Carefully tracking the flow of money from one scheme to the next and writing the algebraic expressions step by step is essential. Final Answer: The original principal invested by Ravi in Scheme A is Rs 2,500.

Question 20

The difference between the simple interest earned when Rs P is invested for 4 years at 9% per annum and when the same sum Rs P is invested for 2 years at 12% per annum is Rs 480. What is the value of P?

Accepted Answer

Introduction / Context: This question compares two different simple interest scenarios for the same principal but with different rates and time periods. The difference between the two interest amounts is given, and the task is to find the principal P. Such problems demonstrate how simple interest scales directly with both rate and time and are frequently used to test algebraic manipulation with percentages in aptitude exams. Given Data / Assumptions: Principal in both cases = Rs P Case 1: Rate = 9 percent per annum, time = 4 years Case 2: Rate = 12 percent per annum, time = 2 years Difference between interest in Case 1 and Case 2 = Rs 480 Both cases use simple interest Concept / Approach: Use the simple interest formula I = P * r * t / 100 for each case. Express I1 and I2 in terms of P, then write an equation representing the difference I1 minus I2 equal to 480 rupees. Solving this linear equation yields the value of P. Because the same principal is used in both cases, P appears as a common factor and the equation simplifies nicely. Step-by-Step Solution: Step 1: Express interest in Case 1. I1 = P * 9 * 4 / 100 = P * 36 / 100 = 0.36 * P. Step 2: Express interest in Case 2. I2 = P * 12 * 2 / 100 = P * 24 / 100 = 0.24 * P. Step 3: The difference between the two interests is given. I1 - I2 = 480. Step 4: Substitute the expressions in terms of P. 0.36 * P - 0.24 * P = 480. Step 5: Simplify the left side. (0.36 - 0.24) * P = 0.12 * P. Step 6: So 0.12 * P = 480. Step 7: Solve for P: P = 480 / 0.12. Step 8: P = 4,000 rupees. Verification / Alternative check: Check by substituting P = 4,000. Case 1 interest at 9 percent for 4 years: I1 = 4,000 * 9 * 4 / 100 = 4,000 * 36 / 100 = 1,440 rupees. Case 2 interest at 12 percent for 2 years: I2 = 4,000 * 12 * 2 / 100 = 4,000 * 24 / 100 = 960 rupees. Difference I1 - I2 = 1,440 - 960 = 480 rupees, which matches the given difference and confirms that P is 4,000 rupees. Why Other Options Are Wrong: If P were Rs 2,000, then 0.12 * P would be only 240 rupees, not 480 rupees. For P = 2,500, 0.12 * P = 300 rupees. For P = 3,500, 0.12 * P = 420 rupees. None of these match the given difference. Only P = 4,000 rupees produces the required difference of 480 rupees between the two simple interest amounts. Common Pitfalls: Some learners mistakenly subtract rates or times directly without forming proper interest expressions. Others may reverse the difference and set I2 - I1 equal to 480, which leads to a negative coefficient for P. Additionally, incorrect handling of percentages, such as forgetting to divide by 100, can distort results. Writing out the formula clearly for each case and then carefully subtracting the expressions helps to prevent such errors. Final Answer: The principal P invested in both cases is Rs 4,000.

Simple Interest Questions