Question 1

Rs 1,500 is divided into two parts such that if one part is invested at 6% per annum and the other part at 5% per annum, the total annual simple interest from both parts is Rs 85. How much money was invested at 5% per annum?

Accepted Answer

Introduction / Context: This question involves splitting a fixed amount into two parts and investing them at different simple interest rates such that the total yearly interest is known. Your task is to determine how much was placed at the lower rate. It is a linear equation problem combined with a simple interest concept, commonly seen in aptitude tests to assess algebraic setup skills. Given Data / Assumptions: Total amount = Rs 1,500. Let the amount at 6% per annum be x rupees. Then the amount at 5% per annum is (1500 - x) rupees. Total annual simple interest from both parts = Rs 85. Simple interest for one year = (Principal * Rate * 1) / 100. Concept / Approach: We express the yearly interest from each part in terms of x, sum them, and equate to the given total of Rs 85. This gives a linear equation in a single variable x. Solving the equation yields the amount invested at 6%. Subtracting that from 1500 gives the amount invested at 5%, which is what the question asks. Step-by-Step Solution: Step 1: Let amount at 6% per annum be x. Step 2: Then amount at 5% per annum is 1500 - x. Step 3: Yearly simple interest from the 6% part: I_6 = (x * 6 * 1) / 100 = 0.06x. Step 4: Yearly simple interest from the 5% part: I_5 = ((1500 - x) * 5 * 1) / 100 = 0.05(1500 - x). Step 5: Total yearly interest is I_6 + I_5 = 85. Step 6: Form the equation: 0.06x + 0.05(1500 - x) = 85. Step 7: Expand and simplify: 0.06x + 75 - 0.05x = 85. Step 8: Combine like terms: (0.06x - 0.05x) + 75 = 85 gives 0.01x + 75 = 85. Step 9: Subtract 75 from both sides: 0.01x = 10. Step 10: Therefore, x = 10 / 0.01 = 1000. Step 11: Amount at 6% is Rs 1,000, so amount at 5% is 1500 - 1000 = 500. Verification / Alternative check: Check yearly interest with these values. At 6%, interest on Rs 1000 = 1000 * 6 / 100 = 60. At 5%, interest on Rs 500 = 500 * 5 / 100 = 25. Total yearly interest = 60 + 25 = 85, matching the given value. This confirms the amounts are correct. Why Other Options Are Wrong: If the amount at 5% were Rs 245, 635, 750, or 1250, the remaining amount at 6% would lead to a total interest different from Rs 85. These alternatives arise from incorrect setup or algebraic manipulation of the equation and therefore do not satisfy the condition given. Common Pitfalls: A typical error is to mix up which part is invested at which rate or to forget that the time period is one year. Another frequent problem is miscalculating the coefficients when collecting like terms. Carefully defining the variable and writing out the contributions to interest from each part helps reduce such mistakes. Final Answer: The amount invested at 5% per annum is Rs 500.

Question 2

A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. What is the rate of interest per annum corresponding to this growth factor?

Accepted Answer

Introduction / Context: This question expresses the final amount as a fraction of the original principal under simple interest. When the amount becomes 7/6 of the principal in a certain time, you can use the relationship between amount, principal, and simple interest to find the annual rate. Such problems encourage you to work with fractions and ratios instead of only absolute rupee values. Given Data / Assumptions: Let principal P be the original sum of money. Time T = 3 years. Amount A after 3 years = (7/6) * P. Simple interest SI = A - P. Rate of interest per annum = r% (unknown). Simple interest formula: SI = (P * r * T) / 100. Concept / Approach: Since the amount is 7/6 of the principal, we can determine the fraction of the principal that constitutes the interest. That fraction over 3 years directly gives us the total interest in terms of P. Equating that to the simple interest formula yields an equation involving r that we then solve. Expressing r as a fraction ensures we match the options given in fractional percent form. Step-by-Step Solution: Step 1: Amount A after 3 years is given as (7/6)P. Step 2: Simple interest SI = A - P = (7/6)P - P. Step 3: Simplify SI = (7/6)P - (6/6)P = (1/6)P. Step 4: Thus, over 3 years the interest is (1/6) of the principal. Step 5: Using SI formula: SI = (P * r * T) / 100 = (P * r * 3) / 100. Step 6: Equate the two expressions for SI: (P * r * 3) / 100 = (1/6)P. Step 7: Cancel P from both sides (P is nonzero): (r * 3) / 100 = 1 / 6. Step 8: Multiply both sides by 100: 3r = 100 / 6. Step 9: Simplify 100 / 6 = 50 / 3, so 3r = 50 / 3. Step 10: Divide both sides by 3: r = (50 / 3) / 3 = 50 / 9. Step 11: Therefore, the rate of interest per annum is 50/9%. Verification / Alternative check: To verify, compute the amount using r = 50/9%. Simple interest for 3 years is SI = (P * (50/9) * 3) / 100 = (P * 50 * 3) / (9 * 100) = (150P) / 900 = (1/6)P. Amount A = P + SI = P + (1/6)P = (7/6)P, which matches the given growth factor, confirming the rate is correct. Why Other Options Are Wrong: Rates like 45/7%, 51/7%, 47/9%, or 40/9% do not produce an amount equal to 7/6 of the principal in 3 years under simple interest. Substituting any of these into the formula SI = (P * r * 3) / 100 gives a fraction of P different from 1/6. Hence, they are not consistent with the given condition. Common Pitfalls: Students sometimes miscalculate the difference between 7/6 and 1, or they forget to cancel the principal P before solving for r. Others incorrectly manipulate fractions when dividing by 3 and 100. Careful fraction handling and stepwise algebra help avoid these errors. Final Answer: The rate of interest per annum is 50/9%.

Question 3

Manu invested Rs 14,800 at 7% per annum simple interest. After how many years will she earn a simple interest of Rs 15,800 on this amount?

Accepted Answer

Introduction / Context: Here, you are given a principal, a rate of simple interest, and the total interest desired, and you must find the time required. This type of problem is very common and helps you learn how to rearrange the simple interest formula to solve for time when the other variables are known. Given Data / Assumptions: Principal P = Rs 14,800. Rate of interest per annum R = 7%. Desired simple interest SI = Rs 15,800. Time T in years is unknown. Simple interest formula: SI = (P * R * T) / 100. Concept / Approach: Since the target is to earn Rs 15,800 as interest, and simple interest grows linearly with time, we substitute the given values into SI = (P * R * T) / 100 and solve for T. The resulting T will be a decimal value, and we then express it in years with the appropriate fractional part to match the closest option. Step-by-Step Solution: Step 1: Write SI = (P * R * T) / 100. Step 2: Substitute SI = 15800, P = 14800, R = 7. Step 3: 15800 = (14800 * 7 * T) / 100. Step 4: Compute 14800 * 7 = 103600. Step 5: So 15800 = (103600 * T) / 100 = 1036T. Step 6: Therefore, T = 15800 / 1036. Step 7: Divide to find T: 15800 / 1036 ≈ 15.25096 years. Step 8: This is approximately 15.25 years (15 and one quarter years). Verification / Alternative check: Check by recomputing the interest using T = 15.25 years. SI = (14800 * 7 * 15.25) / 100. First compute 14800 * 7 = 103600. Then 103600 * 15.25 = 158,000 (because 103600 * 15.25 / 100 simplifies exactly to 15800). Thus, SI = 15800, which matches the required interest, confirming that 15.25 years is correct. Why Other Options Are Wrong: Times such as 16.75, 14, 13.5, or 18 years would give interest amounts different from Rs 15,800 when substituted into the formula. For example, at 14 years, SI = (14800 * 7 * 14) / 100 = 14,504, which is less than 15,800. Therefore, those options do not satisfy the condition. Common Pitfalls: Learners sometimes confuse the interest with the final amount or neglect to divide by 100 at the correct stage. Others may approximate too early and round off in the middle of calculations, causing slight mismatches with the given options. Keeping the calculation in fractional or exact form until the final step helps avoid such issues. Final Answer: Manu will earn the required simple interest after approximately 15.25 years.

Question 4

A sum of money invested at 8% per annum simple interest grows to Rs 180 in a certain number of years. The same sum of money invested for the same number of years at 4% per annum simple interest grows to Rs 120. For how many years is the money invest…

Accepted Answer

Introduction / Context: This question gives two different amounts obtained from the same principal over the same time but at two different simple interest rates. Using these two scenarios, you can form simultaneous equations and solve for both the principal and the time period. It highlights how changing the rate affects the final amount under simple interest and how to use the resulting equations to solve for unknowns. Given Data / Assumptions: Principal P is the same in both cases. Time T (in years) is the same in both cases. In the first case, rate R1 = 8% per annum and amount A1 = Rs 180. In the second case, rate R2 = 4% per annum and amount A2 = Rs 120. Simple interest formula: SI = (P * R * T) / 100, and Amount A = P + SI. Concept / Approach: We write down expressions for the amounts at each rate in terms of P and T. This gives two equations: one for A1 and one for A2. Solving these equations simultaneously allows us to determine P and T. Once T is known, we choose the option that matches this value. This is a standard two-variable simple interest system. Step-by-Step Solution: Step 1: For rate 8%, amount after T years is A1 = P + (P * 8 * T) / 100. Step 2: This can be written as A1 = P * (1 + 8T / 100). Step 3: Given A1 = 180, so P * (1 + 8T / 100) = 180. Step 4: For rate 4%, amount after T years is A2 = P + (P * 4 * T) / 100 = P * (1 + 4T / 100). Step 5: Given A2 = 120, so P * (1 + 4T / 100) = 120. Step 6: We now have two equations: P(1 + 8T / 100) = 180 and P(1 + 4T / 100) = 120. Step 7: Divide the first equation by the second to eliminate P: (1 + 8T / 100) / (1 + 4T / 100) = 180 / 120. Step 8: Simplify 180 / 120 to 3 / 2. Step 9: Let a = 8T / 100 and b = 4T / 100 for clarity. Then (1 + a) / (1 + b) = 3 / 2. Step 10: Substitute a and b: (1 + 0.08T) / (1 + 0.04T) = 3 / 2. Step 11: Cross-multiply: 2(1 + 0.08T) = 3(1 + 0.04T). Step 12: Expand: 2 + 0.16T = 3 + 0.12T. Step 13: Rearrange: 0.16T - 0.12T = 3 - 2, giving 0.04T = 1. Step 14: Therefore, T = 1 / 0.04 = 25 years. Verification / Alternative check: Once T = 25 is known, find P from the second equation. A2 = 120 = P * (1 + 4 * 25 / 100) = P * (1 + 1) = 2P. Thus, P = 60. Check the first scenario: SI at 8% for 25 years = (60 * 8 * 25) / 100 = 60 * 2 = 120, so A1 = 60 + 120 = 180, which matches the given amount. This confirms that T = 25 years and P = 60 are correct. Why Other Options Are Wrong: If T were 15, 20, 22, or 18 years, substituting these values into the equations would not yield consistent values for P that satisfy both amounts 180 and 120 simultaneously. Only T = 25 years works for both scenarios. Common Pitfalls: A common mistake is to subtract the equations incorrectly or to attempt to solve them without eliminating one variable first, leading to algebraic errors. Some students also confuse amount with interest and set up formulas incorrectly. Carefully define amount and interest for each rate, form two equations, and then use either substitution or division to eliminate P and solve for T. Final Answer: The money is invested for 25 years in both cases.

Question 5

On a principal of ₹3,500 invested at a simple interest rate of 7% per annum, ₹500 is earned as interest in a certain number of years. For the same time period, what annual rate of simple interest is required on ₹4,900 so that the interest earned bec…

Accepted Answer

Introduction: This question tests the core idea of simple interest (SI) and how the same time period can be reused to find a new interest rate. In simple interest, interest grows linearly with principal, rate, and time, so we can first compute the time from the first investment and then reuse that time to find the required rate in the second investment. Given Data / Assumptions: First case: P1 = ₹3,500, r1 = 7% per annum, SI1 = ₹500 Second case: P2 = ₹4,900, SI2 = ₹800 Time period is the same in both cases Simple interest formula: SI = (P * r * t) / 100 Concept / Approach: Step 1: Use the first case to compute time t. Step 2: Substitute the same t into the second case and solve for the unknown rate r2. Since SI is directly proportional to r when P and t are fixed, the calculation becomes straightforward after t is known. Step-by-Step Solution: From SI = (P * r * t) / 100, we get t = (SI * 100) / (P * r) t = (500 * 100) / (3500 * 7) t = 50000 / 24500 = 100 / 49 years (approximately 2.0408 years) Now use SI2 = (P2 * r2 * t) / 100 800 = (4900 * r2 * (100/49)) / 100 800 = (4900 * r2) / 49 r2 = (800 * 49) / 4900 = 8 Verification / Alternative check: Using proportionality: with same time, SI is proportional to P*r. Compare the two cases: SI1 corresponds to 3500*7, and SI2 corresponds to 4900*r2. Solving gives the same result r2 = 8%. Why Other Options Are Wrong: 7.5% and 8.5% are close distractors but do not produce exactly ₹800 for the same time. 9% gives too much interest, and 6.5% gives too little. Common Pitfalls: Forgetting that the time period is the same, mixing up simple interest with compound interest, or using years incorrectly without computing t from the first scenario. Final Answer: The required simple interest rate is 8% per annum.

Question 6

A person lends ₹5,000 to B for 2 years and ₹3,000 to C for 4 years at the same annual rate of simple interest. If the total interest received from both borrowers together is ₹2,200, what is the rate of simple interest per annum?

Accepted Answer

Introduction: This problem checks whether you can combine simple interest from multiple loans when the interest rate is the same. Since simple interest adds linearly, total interest is the sum of the interests on each loan. We form one equation in the unknown rate and solve it. Given Data / Assumptions: Loan 1: P1 = ₹5,000, t1 = 2 years Loan 2: P2 = ₹3,000, t2 = 4 years Same rate r% per annum for both loans Total simple interest received = ₹2,200 Formula: SI = (P * r * t) / 100 Concept / Approach: Compute interest from each loan in terms of r, add them, and set the sum equal to ₹2,200. This produces a single linear equation in r because all other quantities are known. Step-by-Step Solution: Interest from B: SI1 = (5000 * r * 2) / 100 SI1 = (10000r) / 100 = 100r Interest from C: SI2 = (3000 * r * 4) / 100 SI2 = (12000r) / 100 = 120r Total interest: SI1 + SI2 = 100r + 120r = 220r Given total interest = 2200, so 220r = 2200 r = 2200 / 220 = 10 Verification / Alternative check: Notice that total interest equals r times (5000*2 + 3000*4)/100. The combined principal-time is 10000 + 12000 = 22000, so interest is (22000*r)/100 = 220r, matching the derivation. Why Other Options Are Wrong: 5% and 7% produce total interest less than ₹2,200. 12% produces more than ₹2,200. 7.5% and similar values are plausible but do not satisfy the exact total interest equation. Common Pitfalls: Adding principals directly without weighting by time, forgetting to divide by 100 in the simple interest formula, or mistakenly compounding interest. Final Answer: The required simple interest rate is 10% per annum.

Question 7

Consider a sum of money invested at simple interest. The following information is given: I. The sum amounts to ₹690 in 3 years at simple interest. II. The sum amounts to ₹750 in 5 years at simple interest. III. The rate of interest is 5% per annum. …

Accepted Answer

Introduction: This is a data-sufficiency style question about finding the principal under simple interest. The key idea is that the amount under simple interest is A = P * (1 + r*t/100). Depending on which statements you have, you may be able to solve for the unknowns P and r. We must check whether each pair of statements removes ambiguity. Given Data / Assumptions: Statement I: A = ₹690 when t = 3 years Statement II: A = ₹750 when t = 5 years Statement III: r = 5% per annum Simple interest amount formula: A = P * (1 + r*t/100) Concept / Approach: Test each combination: (I + III), (II + III), and (I + II). If each pair allows solving for P uniquely, then “Any two of the three” is correct. Under simple interest, with known r and t, one amount is enough to find P. With two amounts at two times, you can solve for both P and r even if r is not given. Step-by-Step Solution: Check I + III: 690 = P * (1 + 5*3/100) = P * 1.15 P = 690 / 1.15 = 600 Check II + III: 750 = P * (1 + 5*5/100) = P * 1.25 P = 750 / 1.25 = 600 Check I + II (without III): 690 = P * (1 + 3r/100) 750 = P * (1 + 5r/100) Subtracting eliminates P after rearranging, giving a unique r, then P is unique. Verification / Alternative check: From I and II, the increase in amount from 3 to 5 years is ₹60 over 2 years, so yearly interest is ₹30. Then amount at 3 years is P + 3*30 = 690, giving P = 600. This confirms uniqueness without needing statement III. Why Other Options Are Wrong: I and III only is sufficient (so choosing it alone is not the best statement if the correct choice is broader). II and III only is also sufficient. I and II only is sufficient as well, so the best answer is that any two statements are enough. Common Pitfalls: Assuming you must always know the rate, or forgetting that two amounts at two times can determine both rate and principal in simple interest because the growth is linear. Final Answer: Any two of the three statements are sufficient to determine the principal.

Question 8

How much time (in years) will it take for a principal of ₹450 to earn ₹81 as simple interest at an annual rate of 4.5% per annum?

Accepted Answer

Introduction: This question tests direct use of the simple interest formula to find time. When principal, interest, and rate are known, time can be computed by rearranging SI = (P * r * t) / 100. Because it is a single formula substitution with no tricky conversions (rate is annual and time is requested in years), this is an easy-level problem. Given Data / Assumptions: Principal P = ₹450 Simple interest SI = ₹81 Rate r = 4.5% per annum Formula: SI = (P * r * t) / 100 Concept / Approach: Rearrange the formula to isolate t: t = (SI * 100) / (P * r). Substitute the given values and compute. Ensure that the rate is used as a percentage (not decimal) because the formula already divides by 100. Step-by-Step Solution: SI = (P * r * t) / 100 t = (SI * 100) / (P * r) t = (81 * 100) / (450 * 4.5) t = 8100 / 2025 t = 4 Verification / Alternative check: Check by forward calculation: SI = (450 * 4.5 * 4) / 100 = (450 * 18) / 100 = 8100 / 100 = ₹81, which matches exactly. Why Other Options Are Wrong: 3 years and 3.5 years give less than ₹81. 4.5 and 5 years give more than ₹81 because interest increases linearly with time at simple interest. Common Pitfalls: Using 0.045 instead of 4.5 while still dividing by 100 (double division), or mixing months and years without converting (not needed here). Final Answer: It will take 4 years.

Question 9

In a simple interest setup on the same principal amount: If increasing the rate of simple interest by 2 percentage points increases the interest by ₹108, and increasing the time period by 2 years increases the interest by ₹180, which of the followin…

Accepted Answer

Introduction: This question checks whether the given changes in rate and time provide enough information to uniquely determine the principal under simple interest. Simple interest depends on three variables: principal P, rate r, and time t. If the problem only gives information about how interest changes when r or t changes, we must see if those constraints uniquely identify P, or if multiple combinations of P, r, and t can satisfy them. Given Data / Assumptions: Original principal = P Original rate = r% per annum Original time = t years Increase in rate by 2% increases interest by ₹108 Increase in time by 2 years increases interest by ₹180 Formula: SI = (P * r * t) / 100 Concept / Approach: Translate each “increase” into an equation. A 2% increase in rate changes SI by (P * 2 * t)/100. A 2-year increase in time changes SI by (P * r * 2)/100. These produce relationships involving P*t and P*r, but do not directly give P alone unless we can also relate r and t uniquely. Step-by-Step Solution: Rate increase condition: (P * 2 * t) / 100 = 108 So P * t = 108 * 100 / 2 = 5400 Time increase condition: (P * r * 2) / 100 = 180 So P * r = 180 * 100 / 2 = 9000 We now know P*t and P*r, but we do not know r or t individually. Many pairs (r, t) can satisfy these while giving different P values. Verification / Alternative check: Example 1: If t = 6 years, then P = 5400/6 = 900, and r = 9000/900 = 10%. Example 2: If t = 9 years, then P = 5400/9 = 600, and r = 9000/600 = 15%. Both satisfy the given increases, but P is different. Hence P is not uniquely determined. Why Other Options Are Wrong: ₹540, ₹415, ₹404, and ₹450 are specific values, but the information allows multiple valid principals, so no single number can be confirmed as the only answer. Common Pitfalls: Assuming the original rate or time is implicitly known, or trying to compute SI without enough independent equations. Another mistake is to treat “increase by 2%” as “multiply by 1.02” (that would be a different interpretation than 2 percentage points). Final Answer: Data is not sufficient to uniquely determine the principal.

Question 10

In simple interest, let J be the simple interest earned on a principal amount K, and let K be the simple interest earned on a principal amount L. If the rate of interest and time period are the same in both cases, what is the correct relation betwee…

Accepted Answer

Introduction: This question tests algebraic manipulation using the simple interest formula when the same rate and time apply to different principals. The twist is that one interest value becomes the principal in the next statement. By writing both statements using SI = (P * r * t) / 100, we can eliminate the common factor (r*t/100) and derive the required relationship among J, K, and L. Given Data / Assumptions: J is SI on principal K at rate r% for time t K is SI on principal L at the same rate r% for the same time t Simple interest: SI = (P * r * t) / 100 Let m = (r * t) / 100 (a common multiplier) Concept / Approach: Express both interests using the same multiplier m. Then substitute one equation into the other, and simplify to get a clean identity involving only J, K, and L. The common multiplier cancels, which is the main simplification trick. Step-by-Step Solution: Let m = (r * t) / 100 J = K * m K = L * m Substitute K = L * m into J = K * m: J = (L * m) * m = L * m^2 Now compute K^2: K^2 = (L * m)^2 = L^2 * m^2 Compute J * L: J * L = (L * m^2) * L = L^2 * m^2 Hence K^2 = J * L Verification / Alternative check: Pick a sample m = 0.2 and L = 100. Then K = 20, J = 4. Check: K^2 = 400 and J*L = 4*100 = 400. Relationship holds, confirming the derivation. Why Other Options Are Wrong: J*J = K*L would imply J proportional to sqrt(K*L), which does not match the chain definition. L*L = J*K is not consistent with the multiplier cancellation. J*K*L = 1 is dimensionally meaningless here. J = K + L is unrelated to simple interest structure. Common Pitfalls: Forgetting that K is used as a principal in the first statement but is an interest in the second, or not factoring out the common term (r*t/100). Final Answer: The correct relation is K * K = J * L.

Question 11

A sum of money placed at simple interest at a rate of 13.5% per annum amounts to ₹2,502.50 after 4 years. What is the original principal (initial sum) invested?

Accepted Answer

Introduction: This problem tests how to find the principal when the final amount is given under simple interest. Under simple interest, the amount A equals principal plus interest, and interest is linear in time. We use A = P * (1 + r*t/100) and solve for P. Because it is one main formula with careful percentage handling, it is medium difficulty. Given Data / Assumptions: Final amount A = ₹2,502.50 Rate r = 13.5% per annum Time t = 4 years Simple interest amount formula: A = P * (1 + r*t/100) Concept / Approach: Compute the interest factor (1 + r*t/100). Then divide the amount by this factor to get P. Ensure the rate is treated as 13.5 (not 0.135) because the formula already divides by 100. Step-by-Step Solution: A = P * (1 + r*t/100) Compute r*t/100 = (13.5 * 4) / 100 = 54 / 100 = 0.54 So A = P * (1 + 0.54) = 1.54P P = A / 1.54 = 2502.50 / 1.54 P = 1625 Verification / Alternative check: Compute SI = (P * r * t)/100 = (1625 * 13.5 * 4)/100 = 1625 * 0.54 = 877.50. Amount = 1625 + 877.50 = 2502.50, matching perfectly. Why Other Options Are Wrong: ₹1,525 and ₹1,425 would produce a smaller amount than ₹2,502.50 at the same rate and time. ₹1,700 would produce a larger amount. ₹1,325 is too low by a large margin. Common Pitfalls: Using 0.135 in place of 13.5 while still dividing by 100, or mistakenly compounding interest rather than using the linear simple interest amount formula. Final Answer: The original principal is ₹1,625.

Question 12

A car is purchased on hire purchase with simple interest charged on the balance. The cash price is $21,000. The buyer pays a deposit of 10% of the cash price and agrees to pay the remaining balance over 60 equal monthly instalments. If simple intere…

Accepted Answer

Introduction: This question tests hire purchase calculations where simple interest is charged on the financed balance, and the total payable is then split into equal monthly instalments. The key is to compute the deposit, determine the balance, compute simple interest on that balance for the full term, then divide the total repayable by the number of instalments. Given Data / Assumptions: Cash price = $21,000 Deposit = 10% of $21,000 Balance is paid in 60 equal monthly instalments Simple interest rate = 12% per annum on the balance 60 months = 5 years Formula: SI = (P * r * t) / 100 Concept / Approach: Compute financed principal (balance) after deposit. Then compute total interest on that balance using simple interest for 5 years at 12% per annum. Add interest to balance to get total amount to be repaid via instalments. Divide by 60 to get each monthly instalment. Step-by-Step Solution: Deposit = 10% of 21000 = (10/100) * 21000 = 2100 Balance financed = 21000 - 2100 = 18900 Time = 60 months = 5 years Interest on balance: SI = (18900 * 12 * 5) / 100 SI = 18900 * 60 / 100 = 18900 * 0.60 = 11340 Total repayable through instalments = 18900 + 11340 = 30240 Monthly instalment = 30240 / 60 = 504 Verification / Alternative check: Monthly instalment of $504 over 60 months gives 504 * 60 = $30,240, which matches the computed total repayable (balance + interest). Consistency confirms correctness. Why Other Options Are Wrong: $503 and $505 are near distractors but do not sum to the exact total repayable. $506 gives too high a total. $520 is far too high compared to the computed financed total. Common Pitfalls: Charging interest on the full cash price instead of only the balance, forgetting to convert months to years, or dividing the balance alone (without adding interest) by 60. Final Answer: The monthly instalment is $504.

Question 13

Under simple interest, an amount becomes ₹812 in 2 years and ₹924 in 4 years. What is the annual rate of simple interest on the original principal?

Accepted Answer

Introduction: This question tests how amounts grow under simple interest across different time periods. Under simple interest, the increase in amount per year is constant because interest added each year is the same. By comparing amounts at 2 years and 4 years, we can find the yearly interest, then compute principal and finally the rate. Given Data / Assumptions: Amount after 2 years: A2 = ₹812 Amount after 4 years: A4 = ₹924 Simple interest implies constant yearly interest Amount relation: A = P + SI, with SI = (P * r * t) / 100 Concept / Approach: Compute the difference A4 - A2 to find interest earned in the extra 2 years. Divide by 2 to get interest per year. Then subtract 2 years of interest from A2 to obtain the principal. Finally compute r using yearly interest = (P * r)/100. Step-by-Step Solution: Difference in amount from 2 to 4 years = 924 - 812 = 112 This 112 is interest for 2 years, so yearly interest = 112 / 2 = 56 At 2 years, total interest = 2 * 56 = 112 Principal P = A2 - interest in 2 years = 812 - 112 = 700 Yearly interest = (P * r) / 100, so 56 = (700 * r) / 100 r = (56 * 100) / 700 = 8 Verification / Alternative check: Check using A4: interest in 4 years = 4 * 56 = 224, so A4 = 700 + 224 = 924, matching the given value. Why Other Options Are Wrong: 7.2% yields yearly interest 50.4 on principal 700, which would not match the observed increase. 8.5% and 9.3% produce larger increases and would overshoot the amounts. 6.8% is too low. Common Pitfalls: Treating the growth as compound interest, or forgetting that the difference between amounts corresponds only to interest over the additional years under simple interest. Final Answer: The annual simple interest rate is 8%.

Question 14

A sum of ₹2,600 is invested at two different simple interest rates. The difference between the simple interest amounts earned after 4 years at these two rates is ₹402.80. What is the difference between the two rates of interest (in percentage points…

Accepted Answer

Introduction: This problem checks how simple interest changes when only the rate changes while principal and time remain fixed. Under simple interest, SI is directly proportional to the rate. Therefore, the difference in interest earned equals the principal-time factor multiplied by the difference in rates. We use SI difference to solve reinforcing the idea of linearity in simple interest. Given Data / Assumptions: Principal P = ₹2,600 Time t = 4 years Difference in simple interest = ₹402.80 Let the difference in rates be Δr percentage points Formula: SI = (P * r * t) / 100 Concept / Approach: Compute the interest difference formula: ΔSI = (P * Δr * t) / 100. Rearrange to solve Δr = (ΔSI * 100) / (P * t). Substitute values and compute carefully. Step-by-Step Solution: ΔSI = (P * Δr * t) / 100 Δr = (ΔSI * 100) / (P * t) Δr = (402.80 * 100) / (2600 * 4) Δr = 40280 / 10400 Δr = 3.8730769...% Rounded to two decimals: 3.87% Verification / Alternative check: If Δr = 3.87%, then ΔSI = (2600 * 3.87 * 4)/100 = (2600 * 15.48)/100 = 402.48 (close due to rounding). Using the exact ratio gives ₹402.80 exactly. Why Other Options Are Wrong: 2.63% and 1.58% produce smaller interest differences than ₹402.80. 4.02% produces a larger difference. 3.25% is also short of the required value. Common Pitfalls: Forgetting to multiply by time, dividing by 100 incorrectly, or treating ₹402.80 as the total interest rather than the difference between two interests. Final Answer: The difference between the two rates is 3.87 percentage points.

Question 15

Under simple interest, the simple interest earned on a certain principal is three times the principal itself when invested for 16 years. What is the annual rate of simple interest offered (in % per annum)?

Accepted Answer

Introduction: This question tests the relationship between simple interest and principal over time. When interest is expressed as a multiple of the principal, the simple interest formula becomes a clean proportion. Since SI = (P * r * t) / 100 and here SI equals 3P, we can cancel P and solve directly for r. This makes it an easy, direct-recall algebra problem. Given Data / Assumptions: Principal = P Time t = 16 years Simple interest SI = 3P Formula: SI = (P * r * t) / 100 Concept / Approach: Set (P * r * t)/100 = 3P and cancel P from both sides (P is non-zero). Then solve r = (3 * 100) / t. Substitute t = 16 years. Step-by-Step Solution: SI = (P * r * t) / 100 Given SI = 3P, so (P * r * 16) / 100 = 3P Cancel P: (r * 16) / 100 = 3 r * 16 = 300 r = 300 / 16 = 18.75 Verification / Alternative check: If r = 18.75%, then SI in 16 years is (P * 18.75 * 16)/100 = P * 3, exactly matching “three times the principal.” Why Other Options Are Wrong: 13.33% and 14.25% produce SI less than 3P in 16 years. 16.98% also produces less than 3P. Only 18.75% gives exactly 3P when multiplied by 16 and divided by 100. Common Pitfalls: Forgetting to cancel P, mixing up “three times the principal” with “principal plus three times,” or using 16 as months instead of years. Final Answer: The annual simple interest rate is 18.75%.

Question 16

Find the simple interest on ₹600 for 11 months if the rate of interest is 5 paise per rupee per month (that is, 5% per month) under simple interest.

Accepted Answer

Introduction: This question tests converting a non-standard rate statement (“paise per rupee per month”) into a percentage and applying simple interest for a time given in months. The phrase 5 paise per rupee per month means interest is 5 paise for every 1 rupee each month, which equals 5% per month. Then we apply SI = (P * r * t) / 100 using monthly time units consistently. Given Data / Assumptions: Principal P = ₹600 Time t = 11 months Rate r = 5% per month (since 5 paise per rupee = 5/100 = 5%) Simple interest formula: SI = (P * r * t) / 100 Concept / Approach: Because the rate is explicitly “per month,” we can keep time in months (no need to convert to years). Substitute P = 600, r = 5, t = 11 into the simple interest formula and compute. Step-by-Step Solution: SI = (P * r * t) / 100 SI = (600 * 5 * 11) / 100 SI = (600 * 55) / 100 SI = 33000 / 100 SI = 330 Verification / Alternative check: 5% of ₹600 per month is ₹30 per month. Over 11 months, interest = 30 * 11 = ₹330, matching the formula result. Why Other Options Are Wrong: ₹30 is only one month’s interest. ₹33 and ₹3.30 come from decimal mistakes. ₹300 is close but does not match 11 months exactly. Only ₹330 fits correctly. Common Pitfalls: Converting to annual rate unnecessarily (which can still work if done correctly), confusing paise with rupees, or forgetting to multiply by 11 months. Final Answer: The simple interest is ₹330.

Question 17

In how many years will ₹200 produce the same amount of simple interest at 5% per annum as ₹900 produces in 2 years at 3.5% per annum (simple interest in both cases)?

Accepted Answer

Introduction: This question tests equating two simple interest amounts from different principals, rates, and times. The core idea is that simple interest is SI = (P * r * t)/100. If two investments produce the same simple interest, we can set their SI expressions equal and solve for the unknown time. Because it involves setting up an equation and solving for time, it is medium difficulty. Given Data / Assumptions: Case 1 (unknown time): P1 = ₹200, r1 = 5% per annum, time = t years Case 2: P2 = ₹900, r2 = 3.5% per annum, time = 2 years Both are under simple interest Formula: SI = (P * r * t) / 100 Concept / Approach: Compute SI from case 2 first since all values are known. Then set SI(case 1) equal to that value and solve for t. Keep percentages consistent and remember to divide by 100 only once in each SI formula. Step-by-Step Solution: SI2 = (900 * 3.5 * 2) / 100 SI2 = (900 * 7) / 100 = 6300 / 100 = 63 Now set SI1 = SI2: (200 * 5 * t) / 100 = 63 (1000 * t) / 100 = 63 10t = 63 t = 63 / 10 = 6.3 Verification / Alternative check: At 5% on ₹200, yearly interest is ₹10. To reach ₹63, time must be 63/10 = 6.3 years, confirming the equation result. Why Other Options Are Wrong: 5.2 years gives only ₹52 interest. 7 years gives ₹70 interest. 7.9 years gives ₹79 interest. 4.5 years gives ₹45 interest. Only 6.3 years yields ₹63. Common Pitfalls: Using 3.5% as 35%, forgetting to multiply by 2 years in case 2, or mixing up principal amounts between the two cases. Final Answer: It will take 6.3 years.

Question 18

The difference between compound interest (compounded every 6 months) and simple interest on a certain sum after 2 years is ₹248.10. If the annual rate of interest is 10%, what is the principal sum invested?

Accepted Answer

Introduction: This question tests understanding of the difference between compound interest (CI) and simple interest (SI) when compounding is done semi-annually. For the same principal, rate, and time, CI is slightly higher than SI due to interest-on-interest. The given difference lets us solve for the principal by expressing both CI and SI in terms of P and isolating P using the computed factor. Given Data / Assumptions: Difference (CI - SI) after 2 years = ₹248.10 Annual rate = 10% Compounding every 6 months (semi-annually) Time = 2 years = 4 half-year periods Semi-annual rate = 10%/2 = 5% per half-year Concept / Approach: Compute SI for 2 years at 10%: SI = P * 10 * 2 / 100 = 0.2P. Compute CI factor for semi-annual compounding: amount factor = (1 + 5/100)^4 = 1.05^4. Then CI = P * (1.05^4 - 1). Difference is P * [(1.05^4 - 1) - 0.2]. Set this equal to ₹248.10 and solve for P. Step-by-Step Solution: SI for 2 years at 10%: SI = (P * 10 * 2) / 100 = 0.2P CI factor (semi-annual): (1.05)^4 (1.05)^2 = 1.1025, so (1.05)^4 = 1.1025^2 = 1.21550625 CI = P * (1.21550625 - 1) = P * 0.21550625 Difference CI - SI = P * (0.21550625 - 0.2) = P * 0.01550625 Given P * 0.01550625 = 248.10 P = 248.10 / 0.01550625 = 16000 Verification / Alternative check: For P = 16000: SI = 0.2P = 3200. CI = 16000 * 0.21550625 = 3448.10. Difference = 3448.10 - 3200 = ₹248.10, matching exactly. Why Other Options Are Wrong: ₹12,000 and ₹14,000 yield smaller differences than ₹248.10. ₹18,000 and ₹20,000 yield larger differences because the difference scales directly with P for fixed rate and time. Common Pitfalls: Using annual compounding instead of semi-annual, forgetting to use 4 half-year periods, or incorrectly computing the compound factor 1.05^4. Final Answer: The principal sum is ₹16,000.

Question 19

₹750 is invested for 3 months and earns simple interest of ₹18. What is the annual rate of simple interest per annum (in %)?

Accepted Answer

Introduction: This question tests finding an annual simple interest rate when time is given in months. The simple interest formula SI = (P * r * t) / 100 expects time in years when r is per annum. So we first convert 3 months into years, then solve for r. This involves one conversion plus a formula rearrangement, so it is medium difficulty. Given Data / Assumptions: Principal P = ₹750 Simple interest SI = ₹18 Time = 3 months = 3/12 years = 0.25 years Rate r = ? % per annum Formula: SI = (P * r * t) / 100 Concept / Approach: Convert time to years because the rate is annual. Then rearrange r = (SI * 100) / (P * t). Substitute values carefully, keeping r as a percentage (not a decimal) since the formula divides by 100. Step-by-Step Solution: t = 3/12 = 0.25 years SI = (P * r * t) / 100 r = (SI * 100) / (P * t) r = (18 * 100) / (750 * 0.25) Denominator: 750 * 0.25 = 187.5 r = 1800 / 187.5 = 9.6 Verification / Alternative check: At 9.6% per annum on ₹750, yearly interest is ₹72. In 3 months (1/4 year), interest is 72/4 = ₹18, matching the given interest. Why Other Options Are Wrong: 12% would give yearly interest 90 and quarterly interest 22.5. 7.2% gives quarterly interest 13.5. 2.4% and 8% are also too low to produce ₹18 in 3 months on ₹750. Common Pitfalls: Forgetting to convert months to years, using t = 3 instead of 0.25, or treating 9.6% as 0.096 while still dividing by 100 again. Final Answer: The annual simple interest rate is 9.6% per annum.

Question 20

A sum of ₹15,200 is divided into two parts. For 1 year at simple interest: The simple interest on the first part at 25% per annum equals the simple interest on the second part at 13% per annum. What is the simple interest (in rupees) earned on each …

Accepted Answer

Introduction: This problem tests splitting a total principal into two parts such that the simple interest earned on each part (for the same time) becomes equal even though the rates differ. Because the time is the same (1 year), equal interest implies the principals are inversely proportional to the rates. We use a variable split, set the two simple interests equal, solve for the parts, and then compute the interest value. Given Data / Assumptions: Total sum = ₹15,200 First part earns SI at 25% per annum for 1 year Second part earns SI at 13% per annum for 1 year Interests are equal for the same time Formula: SI = (P * r * t) / 100 with t = 1 Concept / Approach: Let first part be x and second part be (15200 - x). Since t is 1 year, SI1 = 0.25x and SI2 = 0.13(15200 - x). Set SI1 = SI2 and solve for x. Then compute SI for either part for 1 year (they will match by construction). Step-by-Step Solution: Let first principal = x, second principal = 15200 - x SI1 for 1 year at 25%: SI1 = (x * 25 * 1) / 100 = 0.25x SI2 for 1 year at 13%: SI2 = ((15200 - x) * 13 * 1) / 100 = 0.13(15200 - x) Given SI1 = SI2: 0.25x = 0.13(15200 - x) 0.25x = 1976 - 0.13x 0.38x = 1976 x = 1976 / 0.38 = 5200 Then second part = 15200 - 5200 = 10000 Interest on each part: SI1 = 0.25 * 5200 = 1300 (and SI2 = 0.13 * 10000 = 1300) Verification / Alternative check: Compute both interests directly: 25% of 5200 for 1 year = 1300, and 13% of 10000 for 1 year = 1300. Equal as required, confirming correctness. Why Other Options Are Wrong: ₹2,500 and ₹3,250 are too high for one-year interest under these splits. ₹1,625 and ₹1,520 come from incorrect splitting or wrong equality setup. Only ₹1,300 satisfies both rates with the correct split. Common Pitfalls: Forgetting that time is 1 year (so SI is directly rate percent of principal), setting up equality on amounts instead of interest, or swapping the rates for the two parts. Final Answer: The simple interest on each part for 1 year is ₹1,300.

Simple Interest Questions