Question 1

The difference between simple interest and compound interest, compounded annually, on a certain sum of money for 2 years at 4 percent per annum is Rs. 1. For this investment, what is the principal sum in rupees?

Accepted Answer

Introduction / Context:This is a small numerical question that again uses the standard formula for the difference between compound interest (CI) and simple interest (SI) for 2 years at a given rate. The difference is very small (only Rs. 1), which suggests that the principal is also relatively small. The rate and the difference are provided, and we must determine the principal. Such questions are designed to reinforce the use of the CI–SI difference shortcut in a quick calculation. Given Data / Assumptions: Annual interest rate r = 4 percent. Time period t = 2 years. Difference between CI and SI, D₂ = Rs. 1. Interest is compounded annually when calculating CI. Principal P is unknown and needs to be found. Concept / Approach:For 2 years at rate r percent per annum, the difference between compound interest and simple interest is:D₂ = P * (r/100)^2.This formula follows from expanding (1 + r/100)^2 and comparing it with 1 + 2r/100. Given D₂ and r, we substitute and solve directly for P. Because the rate is small and the difference is only Rs. 1, the principal will be easy to compute. Step-by-Step Solution:Step 1: Use the standard formula D₂ = P * (r/100)^2. Step 2: Substitute D₂ = 1 and r = 4: 1 = P * (4/100)^2. Step 3: Compute (4/100)^2 = 16/10000 = 0.0016. Step 4: So 1 = P * 0.0016. Step 5: Rearranging gives P = 1 / 0.0016. Step 6: Divide: 1 / 0.0016 = 625. Step 7: Therefore, the principal sum is Rs. 625. Verification / Alternative check:We can verify by calculating SI and CI for P = 625 at r = 4 percent over 2 years. Simple interest SI = (625 * 4 * 2) / 100 = (625 * 8) / 100 = 50. The compound amount A is A = 625 * (1.04)^2. Compute (1.04)^2 = 1.0816, so A = 625 * 1.0816 = 676.0. Compound interest CI = A − P = 676 − 625 = 51. The difference CI − SI = 51 − 50 = 1, which matches the given difference exactly. Why Other Options Are Wrong:If P were Rs. 600, then D₂ would be 600 * 0.0016 = 0.96, slightly less than 1. At P = 630, D₂ would be 630 * 0.0016 = 1.008, slightly more than 1. Similarly, 620 and 640 give differences that are close but not equal to 1. Only P = 625 yields exactly the required difference of Rs. 1 between CI and SI at 4 percent for 2 years. Common Pitfalls:Some students attempt to compute SI and CI from assumed principal values in the options rather than using the direct formula, which is slower. Others incorrectly compute (4/100)^2 as 4/100 or 16/100 instead of 16/10000, leading to large errors in P. Being careful with the square of the fraction and the decimal place is crucial in such small-difference problems. Final Answer:The principal sum on which the difference between simple interest and compound interest over 2 years at 4 percent per annum is Rs. 1 is Rs. 625.

Question 2

In aptitude (Simple Interest), what principal amount (in ₹) will yield a total simple interest of ₹60 at a rate of 6% per annum in 5 years? (Assume simple interest throughout and use the standard formula SI = P * r * t / 100.)

Accepted Answer

Introduction / Context: This aptitude question checks your understanding of basic simple interest calculations and how to rearrange the standard formula to find the missing principal amount. Such questions are common in banking exams, government job tests, and campus placement aptitude rounds, where you must quickly identify which quantity is unknown and solve for it using the relationship between principal, rate, time, and interest earned. Given Data / Assumptions: Simple interest (SI) earned = ₹60. Rate of interest per annum r = 6% per year. Time period t = 5 years. Interest is simple, so it is calculated only on the original principal for the full period. We need to find the principal amount P in rupees. Concept / Approach: In simple interest problems, the fundamental relationship between principal, rate, time, and interest is: SI = (P * r * t) / 100 Here SI is the simple interest, P is the principal, r is the annual rate in percent, and t is the time in years. When SI, r, and t are given, we solve this formula for P by rearranging it. This tests your ability to manipulate formulas and substitute known values correctly without making calculation errors. Step-by-Step Solution: Step 1: Start from the simple interest formula: SI = (P * r * t) / 100. Step 2: Substitute SI = 60, r = 6, and t = 5 into the formula. Step 3: So 60 = (P * 6 * 5) / 100. Step 4: Multiply the rate and time: 6 * 5 = 30, so 60 = (30 * P) / 100. Step 5: Rearrange to solve for P: P = 60 * 100 / 30. Step 6: Simplify the fraction: 60 * 100 = 6000 and 6000 / 30 = 200. Step 7: Therefore, the principal amount P is ₹200. Verification / Alternative check: We can verify the answer by plugging P = ₹200 back into the simple interest formula. Compute SI again: SI = (200 * 6 * 5) / 100 SI = (200 * 30) / 100 SI = 6000 / 100 = 60 The recalculated simple interest is ₹60, which matches the given data. This confirms that the principal of ₹200 is consistent and correct. Why Other Options Are Wrong: Option ₹250: If P were ₹250, SI would be (250 * 6 * 5) / 100 = ₹75, which is greater than ₹60. Option ₹150: This gives SI = (150 * 6 * 5) / 100 = ₹45, which is less than ₹60. Option ₹175: This gives SI = (175 * 6 * 5) / 100 = ₹52.5, not equal to ₹60. Option ₹300: This gives SI = (300 * 6 * 5) / 100 = ₹90, again not matching ₹60. Common Pitfalls: Students often forget to divide by 100 when using percentage rates or accidentally use 6 or 5 instead of the product 6 * 5 while rearranging the formula. Another frequent mistake is to misplace SI and P in the formula, trying to compute interest instead of the principal. Working step by step and writing the formula clearly before substituting values helps avoid such errors in exam conditions. Final Answer: Therefore, the required principal amount that yields a simple interest of ₹60 at 6% per annum in 5 years is ₹200.

Question 3

In aptitude (Simple Interest), at what annual rate of simple interest (in % per annum) will a sum of money become exactly double of itself in 16 2/3 years? (Assume simple interest and that doubling means Amount = 2 * Principal.)

Accepted Answer

Introduction / Context: This question explores how long term growth works under simple interest and asks you to connect the idea of doubling an amount with the simple interest rate. Many competitive exams include this type of problem to test whether you can interpret phrases like amount doubles and translate them into an algebraic condition involving principal, rate, and time. Given Data / Assumptions: The amount becomes exactly double of the original principal. Time period t = 16 2/3 years. Interest is calculated using simple interest, not compound interest. We need to find the annual simple interest rate r in percent. Let the principal be P; then the final amount A is 2P. Concept / Approach: For simple interest, the amount A after time t is related to the principal P through: A = P + SI and SI = (P * r * t) / 100 If the amount doubles, then A = 2P, which means: 2P = P + (P * r * t) / 100 This simplifies to a direct relation between r and t. The goal is to insert the value of t in years and solve for r. The mixed fraction 16 2/3 years must be converted into an improper fraction before using it in the formula. Step-by-Step Solution: Step 1: Write the doubling condition: A = 2P. Step 2: Since A = P + SI, we have 2P = P + SI, so SI = P. Step 3: Use the simple interest formula SI = (P * r * t) / 100. Step 4: Substitute SI = P into the formula: P = (P * r * t) / 100. Step 5: Cancel P from both sides (P is nonzero), giving 1 = (r * t) / 100. Step 6: Rearrange to get r = 100 / t. Step 7: Convert 16 2/3 years to an improper fraction: 16 2/3 = (50 / 3) years. Step 8: Substitute t = 50 / 3 into r = 100 / t: r = 100 / (50 / 3) = 100 * 3 / 50. Step 9: Simplify: 100 * 3 / 50 = 300 / 50 = 6. Step 10: Therefore, r = 6% per annum. Verification / Alternative check: We can check the result numerically. Assume P = ₹100 for simplicity. With r = 6% and t = 16 2/3 years, simple interest is: SI = (100 * 6 * (50 / 3)) / 100 = (600 * 50 / 3) / 100 SI = (30000 / 3) / 100 = 10000 / 100 = 100 So the amount A = P + SI = 100 + 100 = 200, which is exactly double the principal. This confirms that 6% per annum is consistent with the doubling condition. Why Other Options Are Wrong: 4%: At 4% per annum, the product r * t is less than 100, so the amount would not double in 16 2/3 years. 5%: With 5%, r * t becomes about 83.33, still not enough to double the principal. 6.5%: Here r * t is greater than 100, meaning the amount would increase to more than double. 3%: This rate is too low and would result in much less than doubling over the given time. Common Pitfalls: A frequent mistake is to treat the mixed fraction 16 2/3 as 16.2 or 16.67 without using the exact fractional form, which can introduce rounding errors. Some learners also forget that doubling implies SI equals the principal and instead try to write separate expressions for amount and interest. Always convert mixed fractions properly and simplify the condition A = 2P to SI = P before applying the simple interest formula. Final Answer: The required annual simple interest rate that doubles the sum in 16 2/3 years is 6% per annum.

Question 4

In aptitude (Simple Interest), for what principal sum (in ₹) will the simple interest at R% per annum for 2 years be exactly ₹R? (Here R is both the numerical value of the rate in percent and the simple interest amount in rupees.)

Accepted Answer

Introduction / Context: This question is a classic algebra based simple interest puzzle where a symbol R is used both as the annual rate of interest in percent and as the simple interest amount in rupees. The goal is to express the principal in terms of R and to understand how the formula behaves when the same symbol appears in different roles. Such questions test algebraic manipulation and conceptual clarity rather than heavy calculation. Given Data / Assumptions: Simple interest rate per annum = R%. Time period t = 2 years. Simple interest amount SI = ₹R. We must find the principal sum P in rupees. Interest is simple, not compound. Concept / Approach: The simple interest formula is: SI = (P * r * t) / 100 Here SI is the interest, P is the principal, r is the rate in percent, and t is the time in years. In this question, SI is given as R and r is also R. Therefore, the formula becomes an equation with P and R. We will substitute SI = R, r = R, t = 2 and solve for P algebraically. The presence of the same symbol R in two places should not confuse us; we treat it simply as a number that remains unspecified. Step-by-Step Solution: Step 1: Start from the standard formula SI = (P * r * t) / 100. Step 2: Substitute SI = R, r = R, and t = 2. Step 3: This gives R = (P * R * 2) / 100. Step 4: Simplify the right side: R = (2 * P * R) / 100. Step 5: Since R is nonzero, cancel R from both sides of the equation. Step 6: This yields 1 = (2 * P) / 100. Step 7: Rearrange for P: P = 100 / 2. Step 8: Therefore, P = 50. Step 9: So the principal sum is ₹50, which does not depend on the specific value of R as long as R is nonzero. Verification / Alternative check: To verify, pick any convenient value for R, for example R = 10. Then P should be ₹50. Compute SI using the formula: SI = (50 * 10 * 2) / 100 = (1000) / 100 = 10 The interest is ₹10, which matches SI = R = 10. Try another value, say R = 8. Then: SI = (50 * 8 * 2) / 100 = 800 / 100 = 8 Again, interest equals ₹8, which is consistent with SI = R. This confirms that P = ₹50 is correct for all valid R values. Why Other Options Are Wrong: ₹100: Substituting P = 100 leads to SI = (100 * R * 2) / 100 = 2R, which is double the required interest. ₹200: With P = 200, SI becomes 4R, far larger than the given interest R. ₹50/R: This wrongly introduces division by R and does not satisfy the equation for general R values. ₹100/R: This also fails for general R and leads to inconsistent interest values when tested with specific R examples. Common Pitfalls: Learners sometimes confuse the symbol R being used in two different roles and mistakenly try to substitute a random numeric value before solving algebraically. Others forget to cancel R from both sides and end up with an expression that still contains R in the principal. A safe strategy is to work symbolically until the very end and cancel common nonzero factors carefully. Always double check the result by substituting one or two trial values for R to ensure consistency. Final Answer: The principal amount for which the simple interest at R% per annum for 2 years equals ₹R is ₹50.

Question 5

In aptitude (Simple Interest), a certain sum amounts to ₹5,182 in 2 years and to ₹5,832 in 3 years at the same simple interest rate. What is the original principal amount (in ₹) invested at simple interest?

Accepted Answer

Introduction / Context: This question uses two different future amounts at the same simple interest rate to help you work backwards and find the original principal. It highlights an important simple interest idea: the interest added each year is constant, so the difference between successive years amounts is equal to the interest for one year. Recognizing this shortcut can help you solve many banking and aptitude questions quickly. Given Data / Assumptions: Amount after 2 years, A2 = ₹5,182. Amount after 3 years, A3 = ₹5,832. The interest rate is simple and unchanged throughout. Let the principal be P and the annual simple interest be I per year. We must find the principal P in rupees. Concept / Approach: Under simple interest, interest added every year is a fixed amount I. Thus: A2 = P + 2I A3 = P + 3I The difference between the amounts in consecutive years is: A3 - A2 = (P + 3I) - (P + 2I) = I So the increase from year 2 to year 3 directly gives the yearly interest I. Once I is known, we can use A2 = P + 2I to solve for the principal P without needing the rate explicitly. Step-by-Step Solution: Step 1: Compute the difference between the amounts for year 3 and year 2. Step 2: A3 - A2 = 5,832 - 5,182 = 650. Step 3: This difference equals the annual simple interest I, so I = ₹650 per year. Step 4: Use the 2 year amount expression A2 = P + 2I. Step 5: Substitute A2 = 5,182 and I = 650 into the equation: 5,182 = P + 2 * 650. Step 6: Compute 2 * 650 = 1,300. Step 7: Rearrange for P: P = 5,182 - 1,300 = 3,882. Step 8: Therefore the original principal is ₹3,882. Verification / Alternative check: We can verify by checking both years. From P = 3,882, year 1 interest is I = 650. Amount after 2 years: A2 = 3,882 + 2 * 650 = 3,882 + 1,300 = 5,182 Amount after 3 years: A3 = 3,882 + 3 * 650 = 3,882 + 1,950 = 5,832 Both match the given amounts exactly, confirming that ₹3,882 is correct. Why Other Options Are Wrong: ₹4,000: This would give A2 = 4,000 plus 2 years of interest, which cannot equal 5,182 while keeping the same difference to reach 5,832. ₹2,882: This principal is too small and would require a much larger yearly interest than the 650 implied by the difference of 650 between A2 and A3. ₹5,000 and ₹3,500: Both fail to produce the correct pair of amounts 5,182 and 5,832 when combined with a constant annual interest value. Common Pitfalls: Learners sometimes try to find the interest rate first using complicated algebra instead of noticing that the difference between consecutive yearly amounts is simply the annual interest. Another common mistake is subtracting in the wrong order, leading to a negative interest, or using the 3 year amount expression incorrectly. Always remember that under simple interest, the difference between amounts in successive years is constant and equal to the yearly interest. Use that fact to simplify problems like this. Final Answer: The principal amount invested at simple interest is ₹3,882.

Question 6

In aptitude (Simple Interest), a sum earns a total simple interest of ₹1,200 at a rate of 7.5% per annum in 4 years. What is the original principal sum (in ₹) that was invested?

Accepted Answer

Introduction / Context: This is a straightforward simple interest problem where the total interest, rate, and time are given, and you must find the principal. Questions like this appear frequently in aptitude tests because they check quick application of the standard formula without any complex reasoning. Mastering these basics is important for clearing the quantitative section efficiently. Given Data / Assumptions: Total simple interest SI = ₹1,200. Annual simple interest rate r = 7.5% per annum. Time period t = 4 years. We must find the principal amount P in rupees. Interest is calculated using simple interest, not compound interest. Concept / Approach: The standard simple interest formula is: SI = (P * r * t) / 100 Here SI is the simple interest, P is the principal, r is the rate in percent per annum, and t is time in years. When SI, r, and t are known, we can rearrange to solve for P: P = (SI * 100) / (r * t) The main task is accurate substitution and careful handling of the decimal rate 7.5%. Step-by-Step Solution: Step 1: Write the formula SI = (P * r * t) / 100. Step 2: Substitute SI = 1,200, r = 7.5, and t = 4. Step 3: 1,200 = (P * 7.5 * 4) / 100. Step 4: Multiply rate and time: 7.5 * 4 = 30. Step 5: So 1,200 = (P * 30) / 100. Step 6: Rearrange for P: P = 1,200 * 100 / 30. Step 7: Compute 1,200 * 100 = 120,000. Step 8: Divide 120,000 by 30 to get P = 4,000. Step 9: Therefore, the required principal is ₹4,000. Verification / Alternative check: Check by recomputing SI from P = ₹4,000: SI = (4,000 * 7.5 * 4) / 100 SI = (4,000 * 30) / 100 SI = 120,000 / 100 = 1,200 The calculated simple interest matches the given value of ₹1,200, so the principal is correct. Why Other Options Are Wrong: ₹6,000: This gives SI = (6,000 * 7.5 * 4) / 100 = 1,800, which is higher than ₹1,200. ₹7,500: This leads to even larger interest and does not match the required total. ₹8,000: This produces SI = 2,400, exactly double the given interest. ₹5,000: This gives SI = (5,000 * 7.5 * 4) / 100 = 1,500, which again is not equal to ₹1,200. Common Pitfalls: One common mistake is mishandling the decimal rate 7.5%; some students approximate it poorly or forget to multiply it correctly by time. Others try to directly guess the principal from the options without using the formula, which can waste time. Writing the formula first, simplifying r * t, and then performing clean arithmetic reduces errors. Avoid using shortcuts unless you are very confident with percentage mental math. Final Answer: The principal sum that earns ₹1,200 as simple interest at 7.5% per annum over 4 years is ₹4,000.

Question 7

Albert invests ₹x in a fixed deposit account. The bank applies 10% interest for the first year and 15% interest for the second year, compounded annually. If the final amount after 2 years is ₹20,240, what is the value of x (in ₹)?

Accepted Answer

Introduction / Context: This problem is about compound interest with different interest rates in each year. Instead of a single constant rate, the bank offers 10% in the first year and 15% in the second year. The question asks you to reverse the compounding process to find the original investment. Such questions strengthen your understanding of how compound growth works when the rate changes over time, which is very relevant to real world financial products. Given Data / Assumptions: Initial principal = ₹x (unknown). Year 1 interest rate = 10% per annum. Year 2 interest rate = 15% per annum. Interest is compounded annually. Final amount after 2 years = ₹20,240. We need to find x, the original principal. Concept / Approach: Under compound interest with variable rates, each year multiplies the amount by a factor 1 + r/100 corresponding to that year. Therefore: Amount after Year 1 = x * (1 + 10 / 100) = x * 1.10 Amount after Year 2 = Amount after Year 1 * (1 + 15 / 100) = x * 1.10 * 1.15 The final amount after 2 years is given as ₹20,240, so we set: x * 1.10 * 1.15 = 20,240 Then we solve for x by dividing the final amount by the combined growth factor 1.10 * 1.15. Step-by-Step Solution: Step 1: Write the compound growth expression: Final amount = x * 1.10 * 1.15. Step 2: Given final amount = 20,240, so x * 1.10 * 1.15 = 20,240. Step 3: Compute the combined growth factor: 1.10 * 1.15 = 1.265. Step 4: Rearrange for x: x = 20,240 / 1.265. Step 5: Perform the division: 20,240 divided by 1.265 equals 16,000. Step 6: Therefore, the original principal x is ₹16,000. Verification / Alternative check: Verify by forward computation. Starting from x = ₹16,000: Amount after Year 1 = 16,000 * 1.10 = 17,600. Amount after Year 2 = 17,600 * 1.15 = 20,240. This final amount exactly matches the value given in the question, so the principal is confirmed as ₹16,000. Why Other Options Are Wrong: ₹14,000: Compounding 14,000 with 10% and then 15% yields a final amount less than 20,240. ₹15,000: This also grows to a value lower than 20,240 under the same sequence of rates. ₹18,000 and ₹17,000: Both would produce final amounts greater than 20,240 when compounded at 10% and then 15%, so they do not satisfy the given condition. Common Pitfalls: A common error is to wrongly treat the problem as simple interest by adding 10% and 15% and using a combined 25% on the principal. That approach ignores the compounding effect and leads to the wrong answer. Another pitfall is to add interest amounts year by year in rupees without using the multiplicative factors. Always express each year as multiplication by 1 plus the rate, then multiply the factors and solve backward when the final amount is known. Final Answer: The original investment amount that grows to ₹20,240 under 10% interest in the first year and 15% interest in the second year is ₹16,000.

Question 8

In aptitude (Simple Interest vs Compound Interest), the simple interest (SI) and compound interest (CI) on the same principal for 2 years at the same annual rate are ₹1,000 and ₹1,040 respectively. What is the annual rate of interest (in % per annum…

Accepted Answer

Introduction / Context: This problem compares simple interest and compound interest on the same principal and time period and asks you to determine the rate of interest from the difference between them. Such questions are popular in aptitude exams because they highlight the extra amount generated by compounding and test your ability to use known relationships between simple interest and compound interest over two years. Given Data / Assumptions: Simple interest SI for 2 years = ₹1,000. Compound interest CI for 2 years = ₹1,040. The principal P is the same in both cases. The annual rate of interest r% is the same for SI and CI. Time period t = 2 years. We need to find r in percent per annum. Concept / Approach: For 2 years, the simple interest is: SI = (P * r * 2) / 100 For compound interest compounded annually, the interest for 2 years can be written as: CI = P * ((1 + r / 100)^2 - 1) There is a useful relationship: CI = SI + extra interest where the extra interest for 2 years is: extra = P * (r / 100)^2 The question gives SI and CI, so the difference CI - SI directly equals this extra term, which depends on P and r. At the same time, SI gives us P * r through its own formula. We combine both facts to solve for r. Step-by-Step Solution: Step 1: Use the SI formula for 2 years: SI = (P * r * 2) / 100 = 1,000. Step 2: Simplify to get P * r = 1,000 * 100 / 2 = 50,000. Step 3: Now compute the difference between CI and SI: CI - SI = 1,040 - 1,000 = 40. Step 4: This difference equals P * (r / 100)^2. Step 5: Write this as P * r^2 / 10,000 = 40. Step 6: Substitute P from Step 2: P = 50,000 / r. Step 7: Then (50,000 / r) * r^2 / 10,000 = 40. Step 8: Simplify the expression: 50,000 * r / 10,000 = 5 * r = 40. Step 9: Solve for r: 5 * r = 40 gives r = 8. Step 10: Therefore the annual interest rate is 8% per annum. Verification / Alternative check: Choose P so that the SI calculation is simple using r = 8%. We know P * r = 50,000 from Step 2, so: P = 50,000 / 8 = 6,250. Check SI for 2 years: SI = (6,250 * 8 * 2) / 100 = (6,250 * 16) / 100 = 100,000 / 100 = 1,000. Check CI for 2 years: Amount = 6,250 * (1 + 8 / 100)^2 = 6,250 * 1.08^2 = 6,250 * 1.1664 = 7,290. CI = Amount - Principal = 7,290 - 6,250 = 1,040. The values match the given SI and CI, confirming that r = 8% is correct. Why Other Options Are Wrong: 10%, 9%, 11%, and 7%: For each of these, if you compute SI and CI for 2 years on any principal, the difference CI - SI will not equal ₹40 under the given SI = ₹1,000 condition. They fail to satisfy both equations simultaneously. Common Pitfalls: Students sometimes try to guess the principal and test rates randomly, which is slow and error prone. Another typical mistake is ignoring the specific 2 year relationship and treating CI as if it grows linearly like SI. Remember that for 2 years, the extra compound interest over simple interest is P * (r / 100)^2, which leads directly to r when combined with the SI expression. Final Answer: The annual rate of interest that produces SI = ₹1,000 and CI = ₹1,040 in 2 years is 8% per annum.

Question 9

In aptitude (Simple Interest and Compound Interest), in 2 years at simple interest a principal increases by 18% in total. What will be the compound interest (in ₹) on ₹7,000 for 3 years at the same annual rate, compounded annually?

Accepted Answer

Introduction / Context: This question links simple interest and compound interest by giving you the total percentage increase over 2 years under simple interest and then asking for the actual rupee compound interest on a different principal and time period. It tests your ability to infer the annual rate from simple interest information and then correctly apply that rate for compound interest calculations. Given Data / Assumptions: Under simple interest, the principal increases by 18% in 2 years. This means total simple interest over 2 years is 18% of the principal. The underlying annual rate r is the same for simple and compound interest cases. New principal for compound interest calculation P = ₹7,000. Time for compound interest t = 3 years, compounded annually. We must find the compound interest in rupees for these new conditions. Concept / Approach: From the given simple interest statement, 18% increase in 2 years means: Total SI in 2 years = 18% of principal = P * 18 / 100. Simple interest for t years is given by: SI = (P * r * t) / 100. Thus, for 2 years: (P * r * 2) / 100 = P * 18 / 100. By comparing coefficients, we get r * 2 = 18, so r = 9% per annum. Then we use compound interest for 3 years on ₹7,000: Amount = P * (1 + r / 100)^t. Compound interest is Amount minus Principal. Step-by-Step Solution: Step 1: From simple interest, write (P * r * 2) / 100 = 18 * P / 100. Step 2: Cancel P / 100 from both sides to get 2r = 18. Step 3: Solve for r: r = 18 / 2 = 9% per annum. Step 4: For compound interest on ₹7,000 for 3 years at 9%, use Amount A = P * (1 + 9 / 100)^3. Step 5: Compute the growth factor: 1 + 9 / 100 = 1.09. Step 6: Calculate 1.09^3 = 1.09 * 1.09 * 1.09 ≈ 1.295029. Step 7: Amount A = 7,000 * 1.295029 ≈ 9,065.203. Step 8: Compound interest CI = A - P = 9,065.203 - 7,000 ≈ 2,065.203. Step 9: Rounded to one decimal place, CI ≈ ₹2,065.2. Verification / Alternative check: We can approximate the compound interest by using annual interest additions. Year 1 interest: 9% of 7,000 = 630. New amount = 7,630. Year 2 interest: 9% of 7,630 ≈ 686.7, amount ≈ 8,316.7. Year 3 interest: 9% of 8,316.7 ≈ 748.5, amount ≈ 9,065.2. The total interest is about 9,065.2 - 7,000 = 2,065.2, confirming the earlier calculation. Why Other Options Are Wrong: ₹1,765.2, ₹1,865.2, and ₹1,965.2: These values are all lower than the correct compound interest and correspond to either lower rates or shorter durations. ₹2,165.2: This is higher than the correct CI, which would require a higher effective rate or more years than the given 3 years at 9%. Common Pitfalls: One common mistake is to treat the 18% increase over 2 years as an annual rate of 18%, forgetting to divide by 2 for simple interest. Another error is to compute 3 * 9% and apply 27% directly on ₹7,000 as if it were simple interest, which ignores compounding. Always separate the tasks clearly: first infer the annual rate, then apply compound interest formulas carefully, especially when calculators are not allowed and approximations need to be precise. Final Answer: The compound interest on ₹7,000 for 3 years at the same rate, compounded annually, is approximately ₹2,065.2.

Question 10

In aptitude (Simple Interest and Compound Interest), in 3 years at simple interest a principal increases by 15% in total. What is the approximate compound interest (in ₹ lakhs) on ₹15 lakhs for 3 years at the same annual rate, compounded annually?

Accepted Answer

Introduction / Context: This question again uses the link between simple interest and compound interest. The total simple interest over a certain time is used to infer the underlying annual rate, and that rate is then applied to compute compound interest on a larger principal. The result is expressed in lakhs, which is common in Indian financial aptitude questions. Given Data / Assumptions: In 3 years under simple interest, a principal increases by 15%. This implies total simple interest over 3 years is 15% of the principal. The annual rate r is the same when we later use compound interest. New principal P = ₹15 lakhs. Time for CI t = 3 years, compounded annually. We must find the approximate compound interest in lakhs of rupees. Concept / Approach: Under simple interest: SI = (P * r * t) / 100. We know that total SI in 3 years is 15% of P, so: (P * r * 3) / 100 = 15 * P / 100. After cancelling P / 100 from both sides, we get 3r = 15, hence r = 5% per annum. For compound interest on ₹15 lakhs for 3 years at 5%: Amount A = P * (1 + r / 100)^3 = 15,00,000 * (1.05)^3. Compound interest CI is A minus P. Finally we convert this rupee value into lakhs and approximate according to the options. Step-by-Step Solution: Step 1: From simple interest, write (P * r * 3) / 100 = 15 * P / 100. Step 2: Cancel P / 100 on both sides to get 3r = 15. Step 3: Solve for r: r = 15 / 3 = 5% per annum. Step 4: For CI, use P = ₹15,00,000 and t = 3 years with r = 5%. Step 5: Compute the growth factor: 1 + 5 / 100 = 1.05. Step 6: Calculate 1.05^3 = 1.05 * 1.05 * 1.05 = 1.157625. Step 7: Amount A = 15,00,000 * 1.157625 = 17,36,437.5 rupees. Step 8: Compound interest CI = A - P = 17,36,437.5 - 15,00,000 = 2,36,437.5 rupees. Step 9: Convert to lakhs: 2,36,437.5 rupees ≈ 2.364 lakhs, which is approximately ₹2.36 lakhs. Verification / Alternative check: We can check using a simpler mental estimate. Over 3 years, simple interest at 5% would give 15% or 0.15 of the principal. On ₹15 lakhs, that would be ₹2.25 lakhs. Since compound interest is only slightly higher than simple interest for modest rates and short periods, we expect the CI to be a bit more than ₹2.25 lakhs. The calculated value of about ₹2.36 lakhs fits this expectation and matches the closest option available. Why Other Options Are Wrong: ₹2.87 lakhs and ₹3.38 lakhs: Both are too high and would require a higher rate than 5% or a longer time period to be correct. ₹7.81 lakhs: This is far too high compared to a principal of ₹15 lakhs and is not realistic for 3 years at a modest rate. ₹2.10 lakhs: This is slightly lower than the simple interest benchmark of about ₹2.25 lakhs, so it cannot represent compound interest, which should exceed simple interest for the same rate and period. Common Pitfalls: A frequent error is to assume that 15% in 3 years means 15% per year, forgetting that simple interest distributes the total percentage gain evenly over the years. Another pitfall is computing compound interest as 15% of the principal plus small corrections without using the proper exponential form. Always isolate the annual rate carefully from the simple interest information before applying compound interest formulas. Final Answer: The approximate compound interest on ₹15 lakhs for 3 years at the same rate, compounded annually, is ₹2.36 lakhs.

Question 11

In aptitude (Compound Interest), A invests ₹x in a bank for 2 years. The bank gives 5% interest in year 1 and 6% interest in year 2, compounded annually. If the amount received after 2 years is ₹24,486, what is the value of x (in ₹)?

Accepted Answer

Introduction / Context: This question involves compound interest with different rates applied in each year. Instead of a single flat rate, the first year grows at 5% and the second year at 6%. You are required to work backwards from the final amount to find the initial principal. This situation models real bank products where promotional rates or changing economic conditions affect annual returns. Given Data / Assumptions: Initial principal invested = ₹x (unknown). Year 1 interest rate = 5% per annum. Year 2 interest rate = 6% per annum. Interest is compounded annually. Final amount after 2 years = ₹24,486. We need to determine x, the original investment. Concept / Approach: For compound interest with varying rates, each year multiplies the previous year amount by a factor of 1 plus the rate. Thus: Amount after Year 1 = x * (1 + 5 / 100) = x * 1.05. Amount after Year 2 = Amount after Year 1 * (1 + 6 / 100) = x * 1.05 * 1.06. This final amount is given as ₹24,486. So we have: x * 1.05 * 1.06 = 24,486. To find x, divide the final amount by the product 1.05 * 1.06. Step-by-Step Solution: Step 1: Express the final amount: Final amount = x * 1.05 * 1.06. Step 2: Set this equal to 24,486: x * 1.05 * 1.06 = 24,486. Step 3: Compute the combined growth factor: 1.05 * 1.06 = 1.113. Step 4: Rearrange to get x = 24,486 / 1.113. Step 5: Perform the division: 24,486 divided by 1.113 equals 22,000. Step 6: Therefore, the initial principal x is ₹22,000. Verification / Alternative check: Verify by forward calculation using x = ₹22,000. After year 1: Amount after Year 1 = 22,000 * 1.05 = 23,100. After year 2 at 6%: Amount after Year 2 = 23,100 * 1.06 = 24,486. This matches the given final amount perfectly, confirming that ₹22,000 is correct. Why Other Options Are Wrong: ₹21,500, ₹22,500, ₹23,000, and ₹24,000 all yield different final amounts when multiplied by factors 1.05 and 1.06; none of them produce exactly ₹24,486. Only ₹22,000 leads to the correct final amount, so it is the only valid choice. Common Pitfalls: Students sometimes incorrectly add the rates to get 11% and then apply that single rate for 2 years, treating the problem like simple interest. Others forget that multiplication order matters and may round intermediate values too early. Always use the multiplicative factors year by year and postpone rounding until the end to keep accuracy high. Final Answer: The principal amount invested so that it grows to ₹24,486 under 5% in the first year and 6% in the second year, compounded annually, is ₹22,000.

Question 12

In aptitude (Simple Interest vs Compound Interest), the difference between compound interest (CI) and simple interest (SI) on a certain sum for 2 years at 8% per annum is ₹40. What is the principal sum (in ₹)?

Accepted Answer

Introduction / Context: Here you are given the difference between compound interest and simple interest on the same principal, at the same rate, over the same period of 2 years. This is a standard type of aptitude question that relies on a compact formula relating that difference directly to the principal and rate, making the solution quick once you know the relationship. Given Data / Assumptions: The rate of interest r = 8% per annum. Time period t = 2 years. Difference between CI and SI for 2 years = ₹40. Principal P is the same for both CI and SI. Interest is compounded annually for the CI calculation. We must find P in rupees. Concept / Approach: For 2 years at rate r%, the difference between compound interest and simple interest on principal P is: CI - SI = P * (r / 100)^2. This happens because compound interest for 2 years can be written as: CI = SI + extra interest, and that extra interest equals P * (r / 100)^2. Since r is known and the difference CI - SI is given as ₹40, we can directly solve for P using this formula without computing the full CI and SI separately. Step-by-Step Solution: Step 1: Use the difference formula: CI - SI = P * (r / 100)^2. Step 2: Substitute CI - SI = 40 and r = 8. Step 3: Compute (r / 100)^2 = (8 / 100)^2 = 0.08^2 = 0.0064. Step 4: So the equation becomes 40 = P * 0.0064. Step 5: Rearrange for P: P = 40 / 0.0064. Step 6: Compute 40 / 0.0064 = 6,250. Step 7: Therefore, the principal sum P is ₹6,250. Verification / Alternative check: Verify by computing SI and CI for P = ₹6,250 at 8% for 2 years. Simple interest: SI = (6,250 * 8 * 2) / 100 = (6,250 * 16) / 100 = 100,000 / 100 = 1,000. Compound interest: Amount A = 6,250 * (1 + 8 / 100)^2 = 6,250 * 1.08^2. Compute 1.08^2 = 1.1664, so A = 6,250 * 1.1664 = 7,290. CI = A - P = 7,290 - 6,250 = 1,040. Difference CI - SI = 1,040 - 1,000 = 40, which matches the given difference. Why Other Options Are Wrong: ₹12,500, ₹18,750, ₹25,000, and ₹10,000 all produce differences between CI and SI that are either larger or smaller than ₹40 when the rate is 8% and the time is 2 years. Only the principal of ₹6,250 yields exactly a ₹40 difference, so the other options are not valid. Common Pitfalls: Many learners ignore the direct formula for CI - SI in 2 years and instead try to compute SI and CI for several trial principals, which is slow and error prone. Another mistake is to use the formula for longer periods incorrectly or to miscalculate (r / 100)^2. Always remember that for exactly 2 years, the difference between CI and SI depends only on P and the square of the rate fraction, making these problems fast to solve once you know the relationship. Final Answer: The principal sum for which the difference between compound interest and simple interest at 8% per annum over 2 years is ₹40 is ₹6,250.

Question 13

In aptitude (Simple Interest), a sum earns a total simple interest of ₹9,648 at the rate of 12% per annum in 6 years. What is the principal sum (in ₹) on which this interest is earned?

Accepted Answer

Introduction / Context: This is a direct application of the simple interest formula where total interest, rate, and time are given and you must find the original principal. Such problems are very common in quantitative aptitude exams and are designed to test your speed and accuracy with percentage calculations and algebraic rearrangement. Given Data / Assumptions: Total simple interest SI = ₹9,648. Annual interest rate r = 12% per annum. Time period t = 6 years. We need to determine the principal P in rupees. Interest is calculated under simple interest, not compound interest. Concept / Approach: The basic simple interest formula is: SI = (P * r * t) / 100. Here SI is the interest amount, P is the principal, r is the rate in percent, and t is time in years. When SI, r, and t are known, we rearrange the formula to find P: P = (SI * 100) / (r * t). The key is to substitute correctly and simplify step by step. Step-by-Step Solution: Step 1: Start with SI = (P * r * t) / 100. Step 2: Substitute SI = 9,648, r = 12, and t = 6. Step 3: 9,648 = (P * 12 * 6) / 100. Step 4: Multiply rate and time: 12 * 6 = 72. Step 5: So 9,648 = (P * 72) / 100. Step 6: Rearrange for P: P = 9,648 * 100 / 72. Step 7: Compute 9,648 * 100 = 964,800. Step 8: Divide 964,800 by 72 to get P = 13,400. Step 9: Therefore, the principal sum is ₹13,400. Verification / Alternative check: Verify by recomputing SI using P = ₹13,400, r = 12%, t = 6 years: SI = (13,400 * 12 * 6) / 100. Compute 13,400 * 12 = 160,800. Then 160,800 * 6 = 964,800. Finally, divide by 100: 964,800 / 100 = 9,648. The simple interest matches the given value, confirming the principal is correct. Why Other Options Are Wrong: ₹16,080, ₹10,720, ₹8,040, and ₹12,000 all produce simple interest amounts that differ from ₹9,648 when plugged into the formula with r = 12% and t = 6 years. Only the principal of ₹13,400 yields exactly the specified interest. Common Pitfalls: Some students mistakenly divide by r or t alone instead of the product r * t, or forget to multiply by 100. Another error is miscalculating the product 12 * 6 or the division step at the end. Writing each arithmetic step clearly reduces the risk of such mistakes during time pressured exams. Final Answer: The sum on which a simple interest of ₹9,648 is earned at 12% per annum for 6 years is ₹13,400.

Question 14

In aptitude (Simple Interest), Dev lends ₹8,000 to Jairam for 17 years and ₹4,700 to Karnik for 16 years at the same simple interest rate. If Dev receives a total interest of ₹21,120 from both loans together, what is the annual rate of interest (in …

Accepted Answer

Introduction / Context: This problem combines simple interest from two separate loans given at the same rate but for different principals and time periods. You are asked to find the common rate of interest from the total interest received. Such questions are common in banking aptitude sections and test your ability to set up equations that combine multiple simple interest amounts. Given Data / Assumptions: Loan 1: Principal P1 = ₹8,000, time t1 = 17 years. Loan 2: Principal P2 = ₹4,700, time t2 = 16 years. Common rate of interest = r% per annum (simple interest). Total interest received from both loans = ₹21,120. We must find r in percent per annum. Concept / Approach: Under simple interest, interest on one loan is: SI1 = (P1 * r * t1) / 100. Similarly, interest on the second loan is: SI2 = (P2 * r * t2) / 100. Total interest is the sum: SI_total = SI1 + SI2. Because r is the same for both, we can factor it out: SI_total = (r / 100) * (P1 * t1 + P2 * t2). We know SI_total and the principals and times, so we can compute the combined term and solve for r. Step-by-Step Solution: Step 1: Compute P1 * t1 = 8,000 * 17 = 136,000. Step 2: Compute P2 * t2 = 4,700 * 16 = 75,200. Step 3: Add these to obtain P1 * t1 + P2 * t2 = 136,000 + 75,200 = 211,200. Step 4: Use the formula SI_total = (r / 100) * (P1 * t1 + P2 * t2). Step 5: Substitute SI_total = 21,120: 21,120 = (r / 100) * 211,200. Step 6: Rearrange for r: r = (21,120 * 100) / 211,200. Step 7: Simplify the fraction: 21,120 * 100 / 211,200 = 2,112,000 / 211,200 = 10. Step 8: Therefore, r = 10% per annum. Verification / Alternative check: We can verify by computing the individual interests at r = 10%. Loan 1: SI1 = (8,000 * 10 * 17) / 100 = (8,000 * 170) / 100 = 1,360,000 / 100 = 13,600. Loan 2: SI2 = (4,700 * 10 * 16) / 100 = (4,700 * 160) / 100 = 752,000 / 100 = 7,520. Total interest: SI_total = 13,600 + 7,520 = 21,120. This matches the given total, confirming that the rate is 10% per annum. Why Other Options Are Wrong: 10.5%, 11%, 11.5%, and 9.5% all produce total interest amounts larger or smaller than ₹21,120 when substituted into the formula. Only 10% results in the exact total interest given in the question, so the other rates must be rejected. Common Pitfalls: A common error is to calculate each simple interest separately but make arithmetic mistakes when multiplying or adding large numbers. Another mistake is to average the time periods or principals incorrectly instead of using the combined expression. Keeping the formula in the factored form (r / 100) * (sum of P * t) helps organize the work and reduces the risk of error. Final Answer: The annual simple interest rate that makes the total interest from both loans equal to ₹21,120 is 10% per annum.

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