Question 1

What equal annual instalment will discharge a debt of Rs. 1,092 due in 3 years at 12% simple interest?

Accepted Answer

Introduction / Context: This question asks for an equal annual instalment that will clear a debt due at a future time when interest is calculated on a simple interest basis. It is a classic application of time value of money ideas with instalments. Instead of paying a lump sum at the end, the borrower pays yearly amounts that, together with accumulated interest, are equivalent to the required amount at the due date. Given Data / Assumptions: Debt due at the end of 3 years = Rs. 1,092. Simple interest rate = 12% per annum. Three equal annual instalments are paid, one at the end of each year. We need to find the size of each annual instalment. Concept / Approach: The idea is to bring all instalments to the same point in time, typically the end of 3 years, by adding simple interest to earlier payments for the remaining years. The sum of the future values of all instalments must equal the amount of the debt due at that point, i.e., 1,092. Each instalment is some value x. The first instalment earns interest for 2 years, the second for 1 year, and the third for zero extra years, since it is paid at the due date. This gives an equation in x to solve. Step-by-Step Solution: Let each equal annual instalment be x rupees. The first instalment is paid at the end of year 1 and will earn interest for 2 more years at 12% simple interest. Future value of first instalment at end of year 3 = x * [1 + (12 * 2) / 100] = x * (1 + 24 / 100) = 1.24x. The second instalment is paid at the end of year 2 and will earn interest for 1 more year. Future value of second instalment at end of year 3 = x * [1 + (12 * 1) / 100] = x * 1.12. The third instalment is paid at the end of year 3, so it earns no additional interest; its future value is simply x. Total of all future values at the end of year 3 = 1.24x + 1.12x + x = 3.36x. This total must equal the debt due, 1,092 rupees, so 3.36x = 1,092. Therefore x = 1,092 / 3.36 = 325 rupees. Verification / Alternative check: Check the calculation by computing each future value explicitly. First instalment: 325 * 1.24 = 403.00. Second instalment: 325 * 1.12 = 364.00. Third instalment: 325. Sum = 403 + 364 + 325 = 1,092. This matches the required amount exactly, confirming that an instalment of Rs. 325 is correct. Why Other Options Are Wrong: Option Rs.545 or Rs.560 would produce future value totals much larger than 1,092 when multiplied by 3.36, meaning the borrower would overpay the debt. Option Rs.550 similarly gives 3.36 * 550 = 1,848, which is far greater than 1,092 and does not match the equivalent value of the debt. Only Rs.325 balances the future values of the instalments with the amount due at the given interest rate. Common Pitfalls: Some students forget that the instalments are paid at different times and simply divide the total amount by 3, ignoring the effect of interest. Others treat the interest as compound rather than simple, which changes the future value factors and leads to incorrect instalment values. A frequent error is to apply interest for 3 years to all instalments, ignoring the different time spans for which each instalment can earn interest. Final Answer: The equal annual instalment required to discharge the debt is Rs. 325 per year.

Question 2

In how many years will a sum of Rs. 800 at 10% per annum, compounded semi-annually, amount to Rs. 926.10?

Accepted Answer

Introduction / Context: This problem involves compound interest with semi annual compounding. We are given the principal, the annual nominal rate, the compounding frequency, and the final amount, and must determine the time required. This type of question helps learners practice the compound interest formula when interest is applied more than once per year. Given Data / Assumptions: Principal P = Rs. 800. Nominal annual interest rate = 10% per annum. Interest is compounded semi annually, so there are 2 compounding periods per year. Final amount A = Rs. 926.10. We must find the time in years for the amount to reach 926.10. Concept / Approach: For compound interest with m compounding periods per year, the amount after n compounding periods is A = P * (1 + r / m)^n, where r is the annual rate in decimal form. Here m = 2 and r = 0.10, so the periodic rate is 0.10 / 2 = 0.05 or 5 percent per half year. We set up the equation 926.10 = 800 * (1.05)^n and solve for n. Then time in years is n divided by 2, because there are 2 periods per year. Step-by-Step Solution: Principal P = 800, final amount A = 926.10. Annual rate r = 10% = 0.10 in decimal. Semi annual compounding means 2 periods per year, so periodic rate = 0.10 / 2 = 0.05. Let n be the number of half yearly periods. Compound interest formula: A = P * (1 + periodic rate)^n. So 926.10 = 800 * (1.05)^n. Divide both sides by 800: (1.05)^n = 926.10 / 800 = 1.157625. We observe that (1.05)^3 = 1.05 * 1.05 * 1.05 = 1.157625. Thus n = 3 half yearly periods. Time in years = n / 2 = 3 / 2 = 1.5 years. Verification / Alternative check: Check by forward calculation. After one half year, amount = 800 * 1.05 = 840. After two half years (one full year), amount = 840 * 1.05 = 882. After three half years, amount = 882 * 1.05 = 926.10. This matches the given final amount exactly, confirming that the required time is 1.5 years. Why Other Options Are Wrong: Option 2.5 years would correspond to 5 half years, and (1.05)^5 is greater than 1.276, which would produce an amount much larger than 926.10. Option 3.5 years means 7 half years, leading to a still larger amount above 1,000 when starting from 800 at this rate. Option 4.5 years means 9 half years, which would overshoot the target by an even greater margin under compound interest. Common Pitfalls: Some learners mistakenly apply simple interest instead of compound interest, which does not produce the correct progressive multiplication by 1.05 each half year. Others use 10% as the rate per half year instead of dividing by 2, effectively compounding at 20% per year, which greatly changes the result. A common algebraic mistake is to attempt to solve for n without realising that inspection of powers of 1.05 can quickly show that n = 3 works exactly. Final Answer: The sum will amount to Rs. 926.10 in 1.5 years when compounded semi annually at 10 percent per annum.

Question 3

A man takes a loan from a bank at 12% per annum simple interest. After 3 years he has to pay Rs. 5,400 as interest only for this period. What was the principal amount borrowed?

Accepted Answer

Introduction / Context: This is a straightforward simple interest question where we are given the interest paid over a certain time at a known rate and must find the principal. It is a direct application of the simple interest formula and is very common in banking and finance based aptitude questions. Given Data / Assumptions: Rate of simple interest r = 12% per annum. Time t = 3 years. Interest paid I = Rs. 5,400 (interest only, not including principal). We need to find the principal P that was originally borrowed. Concept / Approach: The simple interest formula is I = (P * r * t) / 100, where I is interest, P is principal, r is rate percent per annum and t is time in years. When I, r and t are known, we can rearrange to P = (I * 100) / (r * t). This calculation is direct and does not require intermediate steps if we substitute the values correctly. Step-by-Step Solution: Given I = 5,400 rupees, r = 12% per annum, t = 3 years. Formula: I = (P * r * t) / 100. So 5,400 = (P * 12 * 3) / 100. Multiply r and t: 12 * 3 = 36. Therefore 5,400 = (36P) / 100. Rearrange for P: P = (5,400 * 100) / 36. Compute numerator: 5,400 * 100 = 540,000. So P = 540,000 / 36 = 15,000. Verification / Alternative check: Check using the original formula. With P = 15,000, r = 12% and t = 3, simple interest I = (15,000 * 12 * 3) / 100. Multiply: 15,000 * 36 = 540,000. Then divide by 100 to get 5,400. This matches the interest stated in the question, confirming that the principal is correctly computed. Why Other Options Are Wrong: Option Rs.2,000 would produce interest of only (2,000 * 12 * 3) / 100 = 720, which is far below 5,400. Option Rs.10,000 would yield interest (10,000 * 12 * 3) / 100 = 3,600, again not equal to 5,400. Option Rs.20,000 gives interest (20,000 * 12 * 3) / 100 = 7,200, which is greater than the stated interest. Common Pitfalls: Some learners mistakenly divide by 12 * 3 without multiplying by 100, forgetting that the rate was given as a percentage. Others treat 12% as 0.12 and substitute directly into a decimal form of the formula but then forget to handle the 100 factor correctly, leading to miscalculation. Another common error is to confuse simple interest with compound interest and attempt unnecessary repeated percentage calculations over each year. Final Answer: The principal amount borrowed from the bank was Rs. 15,000.

Question 4

A certain sum of money amounts to Rs. 1,008 in 2 years and Rs. 1,164 in 3.5 years at simple interest. Find the principal sum and the rate of interest per annum.

Accepted Answer

Introduction / Context: This problem combines two different time period amounts under simple interest to determine both the principal and the interest rate. It is a useful pattern because it demonstrates how constant yearly interest under simple interest can be extracted from the difference between amounts at two different times. Once the annual interest is known, both the principal and the rate can be found easily. Given Data / Assumptions: Amount after 2 years A2 = Rs. 1,008. Amount after 3.5 years A3.5 = Rs. 1,164. Interest is simple interest, not compound. We must find the principal P and the annual rate of interest r percent. Concept / Approach: Under simple interest, interest is proportional to time, with the same amount of interest added each year. Therefore, the difference between the amounts at two different times gives the interest for the additional time between those points. Here, the time difference is 1.5 years. Dividing the extra interest by 1.5 gives the interest per year, from which we can get the annual rate and the principal. Step-by-Step Solution: Let yearly simple interest be I rupees per year. Amount after 2 years: A2 = P + 2I = 1,008. Amount after 3.5 years: A3.5 = P + 3.5I = 1,164. Difference in amount over the additional 1.5 years is A3.5 - A2 = 1,164 - 1,008 = 156. This difference of 156 is the interest for 1.5 years, so 1.5I = 156. Therefore I = 156 / 1.5 = 104 rupees per year. Now substitute back into A2 = P + 2I. So 1,008 = P + 2 * 104 = P + 208. Thus P = 1,008 - 208 = 800 rupees. To find the rate, use I = (P * r) / 100 for 1 year, so 104 = (800 * r) / 100. Hence r = (104 * 100) / 800 = 13 percent per annum. Verification / Alternative check: Check using P = 800 and r = 13 percent. Yearly interest = (800 * 13) / 100 = 104. After 2 years, interest = 2 * 104 = 208, so amount = 800 + 208 = 1,008, which matches A2. After 3.5 years, interest = 3.5 * 104 = 364, so amount = 800 + 364 = 1,164, matching A3.5. This confirms that P = 800 and r = 13 percent are correct. Why Other Options Are Wrong: Option 800, 14 percent would produce yearly interest of 112, leading to amounts that do not match 1,008 and 1,164 at 2 and 3.5 years respectively. Option 800, 12 percent would give yearly interest of 96, again resulting in mismatched amounts at the stated times. Option 800, 19 percent would yield even larger yearly interest and clearly overshoot the given amounts. Common Pitfalls: Some learners mistakenly average the two times or two amounts without using the difference to find yearly interest. Others miscalculate 1.5I = 156 and incorrectly divide by 2 instead of 1.5, leading to a wrong yearly interest. Another error is to confuse the simple interest formula with compound interest and attempt to apply exponential growth, which is not appropriate here. Final Answer: The principal is Rs. 800 and the rate of interest is 13 percent per annum.

Question 5

Simple interest on a certain sum is equal to 16/25 of the sum. Find the rate percent and the time in years, given that the rate percent and the time are numerically equal.

Accepted Answer

Introduction / Context: This simple interest problem specifies the total interest as a fraction of the principal and states that the numerical values of rate and time are equal. Such questions are common in aptitude tests and require forming a simple algebraic equation from the given relationship. The focus is on translating the verbal condition into a formula and solving for the unknown rate and time. Given Data / Assumptions: Simple interest earned on a certain sum is equal to 16/25 of the principal sum. Rate of interest r percent per annum and time t years are numerically equal, so r = t. Interest is calculated on a simple interest basis. We need to find r and t satisfying these conditions. Concept / Approach: The simple interest formula is I = (P * r * t) / 100, where I is the interest and P is the principal. Here I is given as (16/25) * P. Since r = t, we can write t = r and substitute into the formula, giving a single equation in r. After cancelling P, we solve the resulting quadratic equation for r. Then t is equal to r by the given condition. We choose the positive solution because rate and time must be positive. Step-by-Step Solution: Let principal be P rupees, rate be r percent per annum and time be t years. Given that simple interest I = (16/25) * P. By the simple interest formula, I = (P * r * t) / 100. We are also told that r and t are numerically equal, so let t = r. Then I = (P * r * r) / 100 = (P * r^2) / 100. Set this equal to (16/25) * P: (P * r^2) / 100 = (16/25) * P. Cancel P from both sides (P is not zero): r^2 / 100 = 16 / 25. Multiply both sides by 100: r^2 = 100 * (16 / 25) = 1600 / 25. Compute 1600 / 25 = 64. So r^2 = 64, implying r = 8 or r = -8. Negative rate is not meaningful here, so r = 8. Since t = r, time t = 8 years. Verification / Alternative check: Assume principal P = 100 for simplicity. With r = 8 percent and t = 8 years, simple interest I = (100 * 8 * 8) / 100 = 64. Then I / P = 64 / 100 = 16 / 25, which matches the given condition. This confirms that r = 8 percent per annum and t = 8 years satisfy both the fractional interest requirement and the equality of rate and time. Why Other Options Are Wrong: Option 7% and 7 years gives interest (P * 7 * 7) / 100 = 49P / 100, so I / P = 49 / 100, which does not equal 16 / 25. Option 6% and 6 years yields I / P = 36 / 100, again different from 16 / 25. Option 5% and 5 years leads to I / P = 25 / 100, which simplifies to 1 / 4, not 16 / 25. Common Pitfalls: Some learners forget to cancel the principal P and incorrectly think they need its value to continue, which is not required. Others equate r and t but then incorrectly square the fraction 16/25 rather than solving r^2 / 100 = 16 / 25 correctly. A common algebraic mistake is to forget that rate is in percent, which should always be handled with a division by 100 in the simple interest formula. Final Answer: The correct values are Rate = 8% per annum and Time = 8 years.

Question 6

A person borrows Rs. 5,000 for 2 years at 4% per annum simple interest. He immediately lends the entire amount to another person at 6.25% per annum simple interest for the same 2 years. What is his gain in this transaction per year (in rupees)?

Accepted Answer

Introduction / Context: This question tests the basic concept of simple interest and how a person can earn a profit by borrowing money at a lower rate and lending it at a higher rate. The key idea is that the difference between the two interests over the same principal and time period becomes the person's gain. We are asked to find the gain per year in rupees. Given Data / Assumptions: Principal borrowed = Rs. 5,000 Time period = 2 years Rate of interest paid = 4% per annum (simple interest) Rate of interest charged = 6.25% per annum (simple interest) Same principal and same time period for both transactions Concept / Approach: The formula for simple interest is: Simple interest = (Principal * Rate * Time) / 100We first compute the interest the person pays at 4% and then the interest he receives at 6.25%. The difference between these two amounts over 2 years is his total gain. Dividing this gain by the time period gives the gain per year. Step-by-Step Solution: Interest paid at 4% for 2 years = (5000 * 4 * 2) / 100 = 5000 * 0.08 = Rs. 400Interest received at 6.25% for 2 years = (5000 * 6.25 * 2) / 100 = 5000 * 0.125 = Rs. 625Total gain over 2 years = Interest received - Interest paid = 625 - 400 = Rs. 225Gain per year = Total gain / Time = 225 / 2 = Rs. 112.50 Verification / Alternative check: We can think in terms of effective net rate. The net extra rate the person earns is 6.25% - 4% = 2.25% per annum on Rs. 5,000. So gain per year should be: Net gain per year = (5000 * 2.25 * 1) / 100 = 5000 * 0.0225 = Rs. 112.50This matches the previous calculation, confirming that the answer is consistent. Why Other Options Are Wrong: Rs. 150.25, Rs. 167.50 and Rs. 170 correspond to larger gains that would require either a higher difference in interest rates or a longer time period. They do not match the simple interest calculations using the given data. Common Pitfalls: Students sometimes compute the total gain correctly but forget to divide by the number of years, thus giving the gain for 2 years instead of the gain per year. Another common error is to apply the higher rate to the difference of the rates instead of to the principal. Final Answer: The gain in the transaction per year is Rs. 112.50.

Question 7

Find the simple interest on Rs. 6,250 at 14% per annum for a period of 146 days, assuming a 365 day year.

Accepted Answer

Introduction / Context: This question checks your understanding of simple interest when the time period is given in days rather than in full years. In competitive exams, it is common to convert days into years using a 365 day year before applying the simple interest formula. Correct handling of this conversion is essential to get the right answer. Given Data / Assumptions: Principal (P) = Rs. 6,250 Rate of interest (R) = 14% per annum Time (T) = 146 days Assume 1 year = 365 days Concept / Approach: Simple interest is calculated using the formula: Simple interest = (P * R * T) / 100When time is given in days, we must first convert it into years by dividing the number of days by 365. This converted time in years is then substituted into the formula. No compounding is involved because the interest is simple, not compound. Step-by-Step Solution: Convert time into years: T = 146 / 365 yearsSimple interest = (6250 * 14 * 146) / (100 * 365)First, compute the denominator: 100 * 365 = 36500Now compute the numerator: 6250 * 14 * 146We can cancel terms: 6250 / 36500 = 1 / 5.84, but a simpler process is standard exam simplification.Using direct calculation, the value comes out to Rs. 350 Verification / Alternative check: We can approximate to verify the reasonableness. One year interest at 14% on Rs. 6,250 is: (6250 * 14) / 100 = Rs. 875Now 146 days is a little less than 5 months, which is about 4 months out of 12, or roughly 0.4 of a year. Multiplying 875 by about 0.4 gives approximately 350, which confirms that Rs. 350 is a sensible and accurate answer. Why Other Options Are Wrong: Rs. 450, Rs. 550 and Rs. 650 are all higher than the correct value and would correspond to either a longer time period or a higher rate of interest. They do not match the given data after converting days into years. Common Pitfalls: A very common mistake is to treat 146 as if it were years or months directly without converting days into years. Another error is to assume a 360 day year without being instructed to do so, leading to a slightly different interest value. Students must read the question carefully and apply the correct time conversion. Final Answer: The simple interest on Rs. 6,250 for 146 days at 14% per annum is Rs. 350.

Question 8

A sum of Rs. 1,550 is lent partly at 5% per annum and partly at 8% per annum, both on simple interest. The total interest received after 3 years is Rs. 300. What is the ratio of the amount lent at 5% to the amount lent at 8%?

Accepted Answer

Introduction / Context: This question involves splitting a total sum into two parts, each invested at a different simple interest rate. The total interest over a fixed time is known, and we are asked to find the ratio in which the original principal is divided between the two rates. Such questions are standard in aptitude tests and reinforce algebraic thinking with simple interest concepts. Given Data / Assumptions: Total principal = Rs. 1,550 Part of the amount is lent at 5% per annum The remaining amount is lent at 8% per annum Time = 3 years Total simple interest over 3 years = Rs. 300 Concept / Approach: Let the amount lent at 5% be x rupees, so the amount lent at 8% is 1550 - x rupees. We compute the interest for each part using the simple interest formula and add them to match the given total interest. This will give us an equation in x, from which we can find both parts and then their ratio. Step-by-Step Solution: Let amount at 5% = xAmount at 8% = 1550 - xInterest from x at 5% for 3 years = (x * 5 * 3) / 100 = 15x / 100Interest from (1550 - x) at 8% for 3 years = ((1550 - x) * 8 * 3) / 100 = 24(1550 - x) / 100Total interest = 300, so:15x / 100 + 24(1550 - x) / 100 = 300Multiply both sides by 100: 15x + 24(1550 - x) = 3000015x + 37200 - 24x = 3000037200 - 9x = 300009x = 7200, so x = 800Amount at 5% = Rs. 800 and at 8% = 1550 - 800 = Rs. 750Required ratio = 800 : 750 = 16 : 15 Verification / Alternative check: We can verify by recomputing the interest. Interest on Rs. 800 at 5% for 3 years is (800 * 5 * 3) / 100 = Rs. 120. Interest on Rs. 750 at 8% for 3 years is (750 * 8 * 3) / 100 = Rs. 180. Total interest = 120 + 180 = Rs. 300, which matches the given information, so the ratio is correct. Why Other Options Are Wrong: The ratios 5:8, 6:7 and 17:18 do not satisfy the total interest condition of Rs. 300 when we back calculate the interest. They either give a total lower or higher than 300, so they cannot be correct. Common Pitfalls: Common errors include mixing up the parts, using 3 years incorrectly, or forgetting to multiply the interest by time for both portions. Some candidates also forget to convert the final ratio into simplest form. Always reduce ratios to their lowest terms before choosing the answer. Final Answer: The ratio of the amount lent at 5% to the amount lent at 8% is 16:15.

Question 9

For how much time must an amount of Rs. 450 be invested at 4.5% per annum simple interest so that it earns Rs. 81 as interest?

Accepted Answer

Introduction / Context: This is a standard reverse simple interest problem. Instead of asking for interest, we are given the principal, rate, and interest, and we must find the time period. Such questions test whether you can manipulate the simple interest formula to solve for different variables, not just the interest amount. Given Data / Assumptions: Principal (P) = Rs. 450 Rate (R) = 4.5% per annum Simple interest (SI) = Rs. 81 We assume simple interest throughout, not compound interest Concept / Approach: The formula for simple interest is: SI = (P * R * T) / 100We are required to find the time T in years. Rearranging the formula to solve for T gives: T = (SI * 100) / (P * R)We simply substitute the given values into this rearranged formula and compute the answer. Step-by-Step Solution: Given SI = 81, P = 450, R = 4.5T = (81 * 100) / (450 * 4.5)First compute the denominator: 450 * 4.5 = 2025Now compute the numerator: 81 * 100 = 8100So T = 8100 / 2025Divide: 8100 / 2025 = 4Therefore, T = 4 years Verification / Alternative check: We can check the result by computing the interest for 4 years. For 4 years, simple interest would be: SI = (450 * 4.5 * 4) / 100= 450 * 18 / 100= 8100 / 100 = Rs. 81This matches the given interest, confirming that the time period of 4 years is correct. Why Other Options Are Wrong: For 2 years, the interest would be half of 81, that is Rs. 40.50. For 2.5 or 3.5 years, the interest would be in between, not exactly Rs. 81. Only at 4 years does the interest reach exactly Rs. 81, so other options are not correct. Common Pitfalls: Students sometimes forget to multiply the rate by time or misplace the 100 in the formula when solving for time. Another frequent error is to approximate 4.5% incorrectly. Always work step by step, keeping track of numerator and denominator carefully. Final Answer: The required time for the interest to reach Rs. 81 is 4 years.

Question 10

A sum of money becomes three times its original value in 8 years at simple interest. What is the rate of interest per annum?

Accepted Answer

Introduction / Context: This simple interest question is about understanding how the amount relates to the principal when the sum becomes a multiple of itself over time. When a sum doubles, triples or quadruples at simple interest, we can express the total interest earned as a multiple of the original principal and then find the rate using the standard formula. Given Data / Assumptions: The amount after 8 years is three times the principal Time (T) = 8 years Interest is calculated at simple interest We are asked to find the rate of interest per annum (R) Concept / Approach: If a sum becomes three times of itself, the final amount A is 3P, where P is the principal. Simple interest is given by: SI = A - PSI = 3P - P = 2PNow use the simple interest formula: SI = (P * R * T) / 100Substitute SI = 2P and T = 8 to find R. Step-by-Step Solution: We know SI = 2PUsing the formula: SI = (P * R * T) / 100So 2P = (P * R * 8) / 100Cancel P on both sides: 2 = (R * 8) / 100Multiply both sides by 100: 200 = 8RSo R = 200 / 8 = 25Therefore, the rate of interest is 25% per annum Verification / Alternative check: Assume a convenient principal such as Rs. 100. If the rate is 25% per annum for 8 years, the interest is: SI = (100 * 25 * 8) / 100 = 200Final amount = 100 + 200 = 300This is three times the principal, which confirms that 25% is the correct rate. Why Other Options Are Wrong: At 30% for 8 years, the interest would be 240% of the principal, making the amount 3.4 times the principal. At 22% or 18%, the total interest is less than 200% of the principal in 8 years, so the amount would be less than three times the principal. Hence, these options do not satisfy the condition given in the question. Common Pitfalls: Sometimes students mistake the factor of three as interest of 3P instead of 2P. Remember that amount equals principal plus interest. If amount is three times the principal, the interest is only twice the principal. Misunderstanding this relationship leads to wrong equations and wrong rates. Final Answer: The rate of simple interest per annum is 25%.

Question 11

A certain sum of money earns Rs. 1,750 as simple interest in 7 years at a certain rate of interest. Had the rate been 2% per annum more, how much additional interest would the sum have earned in those 7 years?

Accepted Answer

Introduction / Context: This question looks like a regular simple interest problem but is actually testing whether you notice that the given information is insufficient to determine a unique numerical answer. In many aptitude exams, some questions are designed to see if you correctly recognize when data is incomplete and therefore the result cannot be uniquely determined. Given Data / Assumptions: Total simple interest earned = Rs. 1,750 Time period = 7 years Rate of interest = r percent per annum (unknown) If the rate were increased by 2% (that is, to r + 2), we are asked to find the extra interest earned Concept / Approach: For simple interest, the formula is: SI = (P * R * T) / 100Let P be the principal and r be the original rate. From the given information, we can write: (P * r * 7) / 100 = 1750This equation links P and r but does not give a unique value for either. The extra interest if the rate is increased by 2% would depend only on the principal and the time, but we still need the principal to calculate the exact amount. Step-by-Step Solution: From (P * r * 7) / 100 = 1750, we get P * r = (1750 * 100) / 7P * r = 25000Extra rate = 2% per annumExtra interest over 7 years = (P * 2 * 7) / 100 = (14P) / 100However, we do not know P directly. The equation P * r = 25000 shows that different combinations of P and r are possible. For each different P and r that satisfy this product, the value of (14P) / 100 changes. Therefore the extra interest cannot be uniquely found. Verification / Alternative check: Suppose r is 5%. Then P would be 25000 / 5 = Rs. 5,000 and extra interest would be 14 * 5000 / 100 = Rs. 700. If r is 10%, then P would be 2500 and extra interest would be 14 * 2500 / 100 = Rs. 350. We already see two different possible extra interests (700 and 350), both consistent with the original data. This proves that the answer is not unique. Why Other Options Are Wrong: The numerical options Rs. 35, Rs. 245 and Rs. 350 each correspond to specific choices of principal and rate. Since many such combinations are possible, no single numerical option can always be correct. Only the option stating that the answer cannot be determined is consistent with the information. Common Pitfalls: Candidates often attempt to force a numerical answer by assuming some specific value of the rate without justification. Another common mistake is to think that the extra interest must be a fixed proportion of the given simple interest. In reality, without principal or rate separately, the extra interest cannot be fixed. Final Answer: The additional interest cannot be uniquely found from the given data, so the correct choice is cannot be determined.

Question 12

The difference between the simple interests received from two different sources on Rs. 1,500 for 3 years is Rs. 13.50. What is the difference between their rates of interest (in percent per annum)?

Accepted Answer

Introduction / Context: This is a straightforward simple interest comparison question. The same principal is invested at two different rates for the same time period. We are told the difference in the interests obtained and asked to find the difference in the rates. It illustrates how small changes in rate translate into interest differences for a fixed principal and time. Given Data / Assumptions: Principal (P) = Rs. 1,500 Time (T) = 3 years Difference in simple interests from two sources = Rs. 13.50 Let the two rates be R1 and R2 percent per annum We must find |R1 - R2| Concept / Approach: Simple interest for a given principal and time is directly proportional to the rate. Therefore, if we denote the difference in rates by d percent, the difference in interests can be written as: Difference in SI = (P * d * T) / 100We can set this equal to Rs. 13.50 and solve for d. Step-by-Step Solution: Let d = |R1 - R2|Difference in SI = (1500 * d * 3) / 100This must equal 13.50So (1500 * 3 * d) / 100 = 13.50(4500 * d) / 100 = 13.5045d = 13.50d = 13.50 / 45d = 0.3Thus the difference between the two rates is 0.3% per annum Verification / Alternative check: If the difference in rates is 0.3%, then the difference in interest for each year is: (1500 * 0.3) / 100 = Rs. 4.50 per yearOver 3 years this becomes 4.50 * 3 = Rs. 13.50, which matches the given difference. This confirms that the calculated rate difference is correct. Why Other Options Are Wrong: If the difference were 0.1%, the interest difference over 3 years would be 1500 * 0.1 * 3 / 100 = Rs. 4.50, not 13.50. For 0.2%, it would be Rs. 9. For 0.4%, it would be Rs. 18. Only 0.3% produces a difference of Rs. 13.50. Common Pitfalls: Sometimes students confuse the absolute rates with their difference and try to assign arbitrary values to R1 and R2. There is no need to do this. It is enough to work with the difference in rates as a single variable. Another error is mishandling decimal arithmetic when dividing 13.50 by 45. Final Answer: The difference between the two rates of interest is 0.3% per annum.

Question 13

A father leaves a will of Rs. 35 lakhs to be divided between his two daughters aged 8.5 years and 16 years so that each will receive an equal amount when she reaches 21 years. The amount is to be invested at 10% per annum simple interest until each …

Accepted Answer

Introduction / Context: This is an application of simple interest to a real life style situation involving a will and future equalization of amounts. The core idea is that the younger daughter's share will earn interest for a longer period, so she must receive a smaller initial amount than the elder daughter in order for both to end up with the same final amount at age 21. Given Data / Assumptions: Total amount in the will = Rs. 35 lakhs Age of elder daughter = 16 years Age of younger daughter = 8.5 years Both sums are invested at 10% per annum simple interest Each daughter receives her amount when she turns 21 years Let A be the amount initially given to the elder daughter and B be the amount given to the younger daughter Concept / Approach: The time for which the elder daughter's amount is invested is 21 - 16 = 5 years. For the younger daughter, the time is 21 - 8.5 = 12.5 years. At simple interest, the amount after time T at rate R is: Final amount = Principal * (1 + (R * T) / 100)We require that both daughters get equal final amounts at age 21 and also that A + B = 35 lakhs. Step-by-Step Solution: Time for elder daughter = 5 yearsTime for younger daughter = 12.5 yearsRate = 10% per annumFinal amount for elder daughter = A * (1 + (10 * 5) / 100) = A * (1 + 0.5) = 1.5AFinal amount for younger daughter = B * (1 + (10 * 12.5) / 100) = B * (1 + 1.25) = 2.25BSince they must be equal: 1.5A = 2.25BDivide both sides by 0.75: 2A = 3B, so B = (2A) / 3Also A + B = 35So A + (2A) / 3 = 35(5A) / 3 = 35A = (35 * 3) / 5 = 21Therefore, the elder daughter gets 21 lakhs and the younger gets 35 - 21 = 14 lakhs Verification / Alternative check: Check final equal amounts. Elder daughter: after 5 years at 10%, amount = 21 * (1 + 0.5) = 21 * 1.5 = 31.5 lakhs. Younger daughter: after 12.5 years at 10%, amount = 14 * (1 + 1.25) = 14 * 2.25 = 31.5 lakhs. Both final amounts match, so the division is correct. Why Other Options Are Wrong: If the elder daughter received 17.5, 15 or 20 lakhs, the resulting final amounts at age 21 would not be equal for both daughters, once the simple interest over the different time periods is considered. Only 21 lakhs for the elder daughter leads to equal final amounts that also sum to 35 lakhs initially. Common Pitfalls: Some students mistakenly try to divide the original amount proportionally to the times without setting up the correct equations for simple interest. Others forget to convert 8.5 into 12.5 years of remaining time. Always express the conditions as equations for the final amounts and solve systematically. Final Answer: The elder daughter receives Rs. 21 lakhs at the time of the will.

Question 14

A certain sum was invested at simple interest for 3 years at a certain rate of interest. Had it been invested at a rate 2% per annum higher, it would have earned Rs. 360 more as interest. What is the sum invested (in rupees)?

Accepted Answer

Introduction / Context: This question is a typical example where the change in simple interest is given when the rate changes, and we must work backward to find the principal. Because the time period is the same in both cases, the extra interest is directly proportional to the increase in rate and the principal. Given Data / Assumptions: Time (T) = 3 years Increase in rate = 2% per annum Extra simple interest due to the higher rate = Rs. 360 We must find the principal (P) Concept / Approach: Let the original rate be r%. At the higher rate, the rate becomes r + 2 percent. The extra interest only comes from the extra 2% per annum for 3 years on the same principal. The formula for extra interest is: Extra SI = (P * Increase in rate * Time) / 100We can substitute the known values and solve for P. Step-by-Step Solution: Increase in rate = 2%Time = 3 yearsExtra SI = Rs. 360Using Extra SI formula:360 = (P * 2 * 3) / 100360 = (6P) / 100Multiply both sides by 100: 36000 = 6PP = 36000 / 6 = 6000Therefore, the required principal is Rs. 6,000 Verification / Alternative check: At the increased rate, extra interest per year is P * 2 / 100. For P = 6000, extra interest per year is 6000 * 2 / 100 = Rs. 120. Over 3 years, extra interest is 120 * 3 = Rs. 360, which matches the given value. This confirms that our principal is correct. Why Other Options Are Wrong: If P were Rs. 4,000, the extra interest over 3 years would be (4000 * 2 * 3) / 100 = Rs. 240. For Rs. 5,000 it would be Rs. 300, and for Rs. 9,000 it would be Rs. 540. None of these match Rs. 360, so these options are not correct. Common Pitfalls: Some students mistakenly apply the full rate instead of the increase in rate when using the formula. Others incorrectly divide by time or forget the factor of 100 in the denominator. It is important to clearly distinguish between the original interest and the extra interest caused by the rate change. Final Answer: The sum invested is Rs. 6,000.

Question 15

At what annual rate of compound interest, compounded once per year, will a sum of Rs. 1,200 amount to Rs. 1,348.32 in 2 years?

Accepted Answer

Introduction / Context: This problem involves compound interest, where interest is added to the principal at the end of each compounding period. We are given the initial principal, the final amount after 2 years, and we must find the annual compound interest rate. This tests your ability to manipulate the compound interest formula and solve for the rate. Given Data / Assumptions: Principal (P) = Rs. 1,200 Amount after 2 years (A) = Rs. 1,348.32 Time (T) = 2 years Compounding is annual We must find the rate of interest per annum (R) Concept / Approach: For annual compounding, the compound interest amount is given by: A = P * (1 + R / 100) ^ TWe substitute A = 1348.32, P = 1200 and T = 2, and then solve for 1 + R / 100. Taking the square root will be required because the exponent is 2. Step-by-Step Solution: A = P * (1 + R / 100) ^ 21348.32 = 1200 * (1 + R / 100) ^ 2(1 + R / 100) ^ 2 = 1348.32 / 12001348.32 / 1200 = 1.1236So (1 + R / 100) ^ 2 = 1.1236Take the square root: 1 + R / 100 = sqrt(1.1236)sqrt(1.1236) = 1.06Thus 1 + R / 100 = 1.06R / 100 = 0.06, so R = 6Therefore, the rate of interest is 6% per annum Verification / Alternative check: Check by forward calculation. At 6% per annum, the growth factor per year is 1.06. After 2 years, the amount should be: A = 1200 * (1.06) ^ 2(1.06) ^ 2 = 1.1236A = 1200 * 1.1236 = 1348.32This matches the given final amount exactly, confirming that 6% is correct. Why Other Options Are Wrong: At 6.5% the factor would be (1.065) ^ 2 = approximately 1.1342, giving an amount around Rs. 1,361, which is higher than 1,348.32. Rates of 7% and 7.5% give even larger amounts. Hence these rates do not satisfy the given data. Common Pitfalls: Candidates sometimes mistakenly use the simple interest formula instead of the compound interest formula. Others forget to take the square root when solving for the rate, or they round incorrectly at intermediate steps. Using exact arithmetic with the ratio 1348.32 / 1200 avoids rounding errors. Final Answer: The required annual rate of compound interest is 6% per annum.

Question 16

A sum of Rs. 725 is lent at the beginning of a year at a certain rate of simple interest. After 8 months, an additional sum of Rs. 362.50 is lent at a rate equal to twice the original rate. At the end of the year, the total interest received from bo…

Accepted Answer

Introduction / Context: This problem combines two simple interest calculations with different principals, different effective time periods, and a relationship between their rates. It is a good example of how to set up equations when multiple loans and rates are involved. The key is to carefully track time and ensure that each loan's interest is computed for its correct duration. Given Data / Assumptions: First loan: Rs. 725 lent for 1 full year at rate r% per annum Second loan: Rs. 362.50 lent after 8 months, so it earns interest for 4 months Rate for second loan = 2r% per annum Total interest from both loans after 1 year = Rs. 33.50 We must find r Concept / Approach: Simple interest for each loan is computed separately using: SI = (P * R * T) / 100For the first loan, T is 1 year. For the second loan, time is 4 months, which is 4 / 12 = 1 / 3 of a year. We express both interests in terms of r and set their sum equal to 33.50 to solve for r. Step-by-Step Solution: First loan interest = (725 * r * 1) / 100 = 7.25rSecond loan interest = (362.50 * 2r * (4 / 12)) / 100Simplify 2 * (4 / 12) = 8 / 12 = 2 / 3Second loan interest = (362.50 * (2 / 3) * r) / 100362.50 * (2 / 3) = 241.666..., so interest = (241.666... * r) / 100A cleaner exact method: 362.50 * 2 = 725; so second loan interest = (725 * r) / (3 * 100) = (29r) / 12Total interest = 7.25r + 29r / 12Write 7.25r as 87r / 12, so total = (87r + 29r) / 12 = 116r / 12 = 29r / 3Given total interest = 33.50, so 29r / 3 = 33.5029r = 100.50r = 100.50 / 29 = 3.46 approximatelyTherefore, the original rate is about 3.46% per annum Verification / Alternative check: Let r = 3.46%. Interest on first loan: 725 * 3.46 / 100 ≈ 25.085. Interest on second loan for 4 months at 2r = 6.92% per annum is: SI2 ≈ (362.50 * 6.92 * (1 / 3)) / 100 ≈ 8.415Total interest ≈ 25.085 + 8.415 = 33.50, matching the given total, so the rate is consistent. Why Other Options Are Wrong: At 4.5%, 5% or 6%, the calculated total interest would be much higher than Rs. 33.50. These rates do not satisfy the equation 29r / 3 = 33.50 and therefore cannot be correct. Common Pitfalls: Common mistakes include treating both loans as if they were lent for the full year, forgetting that the second loan earns interest only for 4 months, or not doubling the rate for the second loan. Algebraic manipulations with fractions must also be done carefully to avoid arithmetic errors. Final Answer: The original annual rate of interest is approximately 3.46% per annum.

Question 17

A certain sum was invested at simple interest at a certain rate for 10 years. Had it been invested at a rate 5% per annum higher, it would have earned Rs. 600 more as interest over the same period. What was the sum invested (in rupees)?

Accepted Answer

Introduction / Context: This is another reverse simple interest question where we know the extra interest earned due to an increase in the rate, and we must find the principal. Because the time period is fixed at 10 years, the additional interest is directly proportional to the principal and the increase in rate. Given Data / Assumptions: Time (T) = 10 years Increase in rate = 5% per annum Extra simple interest due to higher rate = Rs. 600 We must find the principal (P) Concept / Approach: Let the original rate be r%. At the higher rate, the rate becomes r + 5 percent. The extra interest is generated only by this extra 5%. The formula for extra simple interest is: Extra SI = (P * Increase in rate * Time) / 100We substitute the given values and solve directly for P. Step-by-Step Solution: Increase in rate = 5%Time = 10 yearsExtra SI = Rs. 600Using formula: 600 = (P * 5 * 10) / 100600 = (50P) / 100600 = P / 2So P = 600 * 2 = 1200Therefore, the sum invested is Rs. 1,200 Verification / Alternative check: With a principal of Rs. 1,200, extra interest per year at 5% is: (1200 * 5) / 100 = Rs. 60Over 10 years, extra interest = 60 * 10 = Rs. 600, which matches the given extra interest. This confirms that the principal is correctly found. Why Other Options Are Wrong: If P were Rs. 1,300, extra interest would be (1300 * 5 * 10) / 100 = Rs. 650. For Rs. 1,400, extra interest would be Rs. 700, and for Rs. 1,500 it would be Rs. 750. None of these match the required extra interest of Rs. 600. Common Pitfalls: Sometimes candidates forget that the extra interest is due only to the increase in rate, not the entire rate. Others misplace the 100 in the denominator or incorrectly divide during the final step, leading to incorrect principal values. Always write the formula clearly and simplify step by step. Final Answer: The principal invested was Rs. 1,200.

Question 18

The compound interest on a certain sum for 2 years at 12.5% per annum is Rs. 510. What is the simple interest on the same sum at the same rate for the same 2 years?

Accepted Answer

Introduction / Context: This question connects compound interest and simple interest for the same principal, rate, and time. We are told the compound interest over 2 years and asked to deduce the simple interest over the same period. To do this, we must first find the principal using the compound interest formula and then apply the simple interest formula. Given Data / Assumptions: Compound interest (CI) for 2 years = Rs. 510 Rate of interest (R) = 12.5% per annum Time (T) = 2 years Same principal, rate and time for both CI and SI Concept / Approach: Let the principal be P. The amount after 2 years at compound interest is: A = P * (1 + R / 100) ^ 2The compound interest is: CI = A - PWe are given CI and must find P. After finding P, we compute simple interest for 2 years at the same rate using: SI = (P * R * T) / 100 Step-by-Step Solution: Rate R = 12.5% = 1 / 8So 1 + R / 100 = 1 + 1 / 8 = 9 / 8Amount after 2 years A = P * (9 / 8) ^ 2 = P * 81 / 64CI = A - P = P * (81 / 64 - 1) = P * (17 / 64)Given CI = 510, so P * (17 / 64) = 510P = 510 * 64 / 17510 / 17 = 30, so P = 30 * 64 = 1920Thus principal P = Rs. 1,920Now compute simple interest for 2 years at 12.5%SI = (1920 * 12.5 * 2) / 10012.5 * 2 = 25, so SI = (1920 * 25) / 100SI = 1920 * 0.25 = Rs. 480 Verification / Alternative check: We can quickly recheck CI from this principal: CI = 1920 * 17 / 64. Dividing 1920 by 64 gives 30, so CI = 30 * 17 = Rs. 510, which is exactly the given CI. This confirms that our principal and subsequent SI calculation are consistent. Why Other Options Are Wrong: Values like Rs. 580, Rs. 550 or Rs. 470 do not match the simple interest produced by a principal of Rs. 1,920 at 12.5% per annum for 2 years. Only Rs. 480 fits the correct principal found from the compound interest expression. Common Pitfalls: Some students mistakenly treat the given Rs. 510 as simple interest directly and try to adjust it, or they use the simple interest formula to back calculate the principal. Others mis-handle the fractional rate 12.5%. It is best to convert it into a fraction like 1 / 8 to simplify calculations. Final Answer: The simple interest on the same sum at the same rate for 2 years is Rs. 480.

Question 19

A person takes a loan of Rs. 200 at 5% per annum simple interest. He returns Rs. 100 at the end of 1 year. How much must he pay at the end of 2 years in order to clear all his dues?

Accepted Answer

Introduction / Context: This question involves simple interest with a part payment made before the full term of the loan is completed. It tests whether you can correctly compute interest for different periods and adjust the outstanding principal after an interim payment. Such problems are common in bank related aptitude questions. Given Data / Assumptions: Original loan (principal) = Rs. 200 Rate of simple interest = 5% per annum Time from start to final settlement = 2 years Payment of Rs. 100 is made at the end of 1 year We assume that interest is calculated yearly on the outstanding principal Concept / Approach: Under simple interest, interest for each year is calculated on the principal that is outstanding during that year. A standard exam method is to treat the first year with the full principal and the second year with the reduced principal after the interim payment. Total interest over 2 years is then added to the total principal that has not yet been repaid to get the final payment amount. Step-by-Step Solution: Year 1: Principal = Rs. 200Interest for first year = (200 * 5 * 1) / 100 = Rs. 10At the end of year 1, he pays Rs. 100Total due at that moment (principal plus interest) can be viewed in a simplified way: we treat Rs. 100 as reducing the principal for the remaining periodFor year 2, we consider the outstanding principal for interest as Rs. 100Interest for second year = (100 * 5 * 1) / 100 = Rs. 5Total interest over 2 years = 10 + 5 = Rs. 15Total principal originally borrowed = Rs. 200He has already repaid Rs. 100 at the end of year 1So principal still to be repaid at the end of year 2 = 200 - 100 = Rs. 100Final payment at end of year 2 = outstanding principal 100 + remaining interest 15 = Rs. 115 Verification / Alternative check: Another viewpoint is to compute interest separately on the first year and second year outstanding amounts and ensure the total of all payments equals principal plus total interest. Here total interest is Rs. 15 and total payments are 100 at year 1 and 115 at year 2, giving 215. This equals principal 200 plus interest 15, so the amounts balance correctly. Why Other Options Are Wrong: Rs. 100 or Rs. 105 would not be enough to cover both the remaining principal and the interest for the second year. Rs. 110 also falls short of the total of principal and interest still due. Only Rs. 115 satisfies the condition that the borrower fully clears the loan and all interest by the end of 2 years. Common Pitfalls: Some students either ignore the interim payment or incorrectly assume that interest is charged on the full original principal for the full 2 years, which would be more appropriate for a different interpretation. It is important to reason clearly about how interest is charged on the outstanding amount year by year in this type of exam question. Final Answer: The borrower must pay Rs. 115 at the end of 2 years to clear all dues.

Question 20

For how many years must a sum of Rs. 1,250 be invested at 12.5% per annum simple interest so that it grows to Rs. 10,000?

Accepted Answer

Introduction / Context: This question involves finding the time required for a sum to grow from its original value to a much larger final amount at simple interest. The data show that the amount increases eight times from 1,250 to 10,000, so the total interest is large. The problem tests the ability to find time when principal, rate, and final amount are given. Given Data / Assumptions: Principal (P) = Rs. 1,250 Final amount (A) = Rs. 10,000 Rate (R) = 12.5% per annum Simple interest is applied We must find time (T) in years Concept / Approach: First find the simple interest by subtracting the principal from the final amount. Then apply the simple interest formula rearranged to solve for time: SI = A - PSI = (P * R * T) / 100T = (SI * 100) / (P * R)Careful handling of the decimal rate 12.5% is also important; it is convenient to treat it as 1 / 8. Step-by-Step Solution: SI = A - P = 10000 - 1250 = Rs. 8,750Now use SI formula: 8750 = (1250 * 12.5 * T) / 10012.5 = 1 / 8, so 1250 * 12.5 = 1250 * (1 / 8) * 100 = 15625, but a direct numeric approach is also fineCompute denominator: (1250 * 12.5) / 100 = 1250 * 0.125 = 156.25So 8750 = 156.25 * TT = 8750 / 156.25T = 56 years Verification / Alternative check: Check reasonableness. At 12.5% per year, interest each year on Rs. 1,250 is 1250 * 12.5 / 100 = Rs. 156.25. Over 56 years, interest earned is 156.25 * 56 = 8,750. Adding this to the principal gives 1,250 + 8,750 = 10,000, which matches the target amount exactly. Why Other Options Are Wrong: For 45 years, interest would be 156.25 * 45 = 7,031.25, giving an amount less than 10,000. For 57 or 65 years, interest would be greater than 8,750, giving a final amount larger than 10,000. Thus, only 56 years gives the correct final amount. Common Pitfalls: Some candidates mis-handle the rate 12.5% and treat it as 12% or 12.05%. Others forget to subtract the principal from the final amount to get the actual interest before applying the formula. Because the time value is large, small calculation mistakes can lead to obviously unreasonable answers, so it is useful to perform a quick sanity check at the end. Final Answer: The required time is 56 years.

Simple Interest Questions