📘 Quiz

Test your skills & challenge yourself 🚀

Question 1 / 20
1:00
1
Goods were purchased for Rs. 600. They were sold for Rs. 688.50 on a 9-month credit. If this transaction resulted in a 2% gain, what is the annual rate of interest?
0:00
Solution: Step 1: The Cost Price (C.P.) of the goods is Rs. 600. Step 2: The desired Selling Price (S.P.) to achieve a 2% gain is: S.P. = C.P. * (1 + 2/100) = 600 * 1.02 = Rs. 612. Step 3: This Rs. 612 is the Present Worth (P.W.) of the credit sale amount, representing the value of the sale in cash today to achieve a 2% profit. Step 4: The actual amount due (Future Value) from the credit sale is Rs. 688.50. Step 5: The credit period (Time, T) is 9 months, which is 9/12 = 3/4 years. Step 6: The True Discount (T.D.) on the credit amount is the difference between the Future Value and the Present Worth. This T.D. is also the Simple Interest (S.I.) on the P.W. S.I. = T.D. = 688.50 - 612 = Rs. 76.50. Step 7: Now, use the Simple Interest formula (S.I. = (P * R * T) / 100) to find the Rate (R). Here, P = P.W. = Rs. 612, S.I. = Rs. 76.50, T = 3/4 years. 76.50 = (612 * R * (3/4)) / 100 76.50 = (612 * 3 * R) / 400 76.50 = (1836 * R) / 400 R = (76.50 * 400) / 1836 R = 30600 / 1836 = 16.666...% Step 8: Express the rate as a mixed fraction: R = 16 2/3%.
2
Calculate the difference between simple interest and compound interest at 10% per annum on a principal of Rs. 1000 over 3 years.
0:00
Solution: Step 1: Simple Interest (SI) = (1000 * 10 * 3) / 100 = Rs. 300 Step 2: Compound Interest (CI) = 1000 * (1 + 10/100)^3 - 1000 = Rs. 331 Step 3: Difference = CI - SI = 331 - 300 = Rs. 31
3
A trader owes a merchant Rs. 10,028, which is due in 1 year. The trader wishes to settle the account after 3 months. If the annual interest rate is 12%, how much cash should the trader pay at the time of settlement?
0:00
Solution: Step 1: The original amount due is Rs. 10,028, payable in 1 year (12 months). Step 2: The trader wants to settle after 3 months. Step 3: Calculate the remaining period until the original due date from the settlement date: 12 months - 3 months = 9 months. Step 4: Convert this time to years: T = 9/12 years = 3/4 years. Step 5: The annual interest rate (R) is 12%. Step 6: The amount the trader should pay is the Present Worth (P.W.) of Rs. 10,028 due 9 months hence. Formula for P.W. = Amount / (1 + (R * T / 100)) P.W. = 10028 / (1 + (12 * (9/12) / 100)) P.W. = 10028 / (1 + (9 / 100)) P.W. = 10028 / (1 + 0.09) P.W. = 10028 / 1.09 = Rs. 9200. Step 7: The trader should pay Rs. 9200.
4
A certain sum of money, invested at simple interest, amounts to Rs. 20925 after 2 years and Rs. 24412.50 after 5 years. Determine both the initial sum of money and the annual interest rate.
0:00
Solution: Step 1: Calculate the simple interest earned over the period from 2 years to 5 years (i.e., for 5 - 2 = 3 years). SI (3 years) = Amount at 5 years - Amount at 2 years SI (3 years) = 24412.50 - 20925 = Rs. 3487.50 Step 2: Calculate the simple interest earned for 1 year. SI (1 year) = SI (3 years) / 3 = 3487.50 / 3 = Rs. 1162.50 Step 3: Calculate the simple interest earned for the initial 2 years. SI (2 years) = SI (1 year) * 2 = 1162.50 * 2 = Rs. 2325 Step 4: Calculate the original principal (the sum). Principal = Amount at 2 years - SI (2 years) = 20925 - 2325 = Rs. 18600 Step 5: Calculate the rate of interest using the simple interest formula for the original principal and 2 years. Rate (R) = (SI * 100) / (P * T) R = (2325 * 100) / (18600 * 2) = 232500 / 37200 = 6.25% Step 6: The sum of money is Rs. 18600, and the rate of interest is 6.25%.
5
Person A loaned Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years, both at the same simple interest rate. If A received a total of Rs. 2200 in interest from both loans, what was the annual interest rate?
0:00
Solution: Step 1: Let the common rate of interest be R% per annum. Step 2: Calculate the simple interest (SI) for the loan given to B: SI_B = (Principal_B * R * Time_B) / 100 = (5000 * R * 2) / 100 = 100R. Step 3: Calculate the simple interest (SI) for the loan given to C: SI_C = (Principal_C * R * Time_C) / 100 = (3000 * R * 4) / 100 = 120R. Step 4: The total interest received from both loans is the sum of SI_B and SI_C: Total SI = 100R + 120R = 220R. Step 5: We are given that the total interest received is Rs. 2200. Set up the equation: 220R = 2200. Step 6: Solve for R: R = 2200 / 220 = 10. Step 7: The rate of interest per annum is 10%.
6
At an annual simple interest rate of 16 2/3%, how many years will it take for the simple interest earned on a sum of money to become equal to the original principal amount?
0:00
Solution: Step 1: Let the principal be P. According to the problem, the simple interest (SI) is equal to the principal, i.e., SI = P. Step 2: The rate of interest is R = 16 2/3% = 50/3 %. Step 3: Use the simple interest formula: SI = (P * R * T) / 100. Substitute SI = P and R = 50/3: P = (P * (50/3) * T) / 100 Step 4: Solve for T. Divide both sides by P (assuming P is not zero): 1 = ((50/3) * T) / 100 1 = (50 * T) / 300 1 = T / 6 T = 6 Step 5: It will take 6 years.
7
At a constant simple interest rate per annum, a certain sum of money accumulates to Rs. 5182 in 2 years and Rs. 5832 in 3 years. What is the original principal amount in rupees?
0:00
Solution: Step 1: Understand that simple interest is constant for each year on the original principal. Step 2: The difference in the total amount between consecutive years represents the simple interest for one year. Amount after 3 years = Rs. 5832 Amount after 2 years = Rs. 5182 Simple Interest for 1 year = Amount after 3 years - Amount after 2 years Simple Interest for 1 year = 5832 - 5182 = Rs. 650. Step 3: Calculate the simple interest for 2 years. Simple Interest for 2 years = 1-year SI * 2 = 650 * 2 = Rs. 1300. Step 4: The amount after 2 years is the principal plus the simple interest for 2 years. Amount after 2 years = Principal + SI for 2 years 5182 = Principal + 1300 Step 5: Solve for the Principal. Principal = 5182 - 1300 Principal = Rs. 3882.
8
A stock that pays a 12% dividend yields a 10% return on investment. At what price is this stock quoted (per Rs. 100 face value)?
0:00
Solution: Step 1: Understand the terms. A '12% stock' means that for every Rs. 100 of face value, it pays a dividend of Rs. 12. 'Yielding 10%' means that the income generated (Rs. 12) represents 10% of the actual market value (investment) of the stock. Step 2: Let the market value of the Rs. 100 face value stock be 'M'. The income (dividend) on Rs. 100 face value stock is Rs. 12. This income of Rs. 12 is 10% of the market value (M). So, 10% of M = Rs. 12. (10/100) * M = 12. M = (12 * 100) / 10. M = 1200 / 10. M = Rs. 120. Step 3: The market value (quoted price) of the stock is Rs. 120 for every Rs. 100 face value.
9
A child lends Rs. 10 to a friend, to be repaid through 11 monthly installments of Rs. 1 each, with simple interest applied. Determine the annual simple interest rate.
0:00
Solution: Step 1: Calculate the total amount repaid and the total interest. Total principal borrowed = Rs. 10. Total amount repaid = 11 installments × Rs. 1/installment = Rs. 11. Total Simple Interest (SI) paid = Total amount repaid - Principal borrowed = 11 - 10 = Rs. 1. Step 2: Determine the equivalent principal on which this interest is charged over the loan period. Interest is charged on the outstanding balance each month. Month 1: Rs. 10 is outstanding for 1 month. Month 2: After the first Rs. 1 installment, Rs. 9 is outstanding for 1 month. Month 3: After the second Rs. 1 installment, Rs. 8 is outstanding for 1 month. ...and so on. Month 11: After the tenth Rs. 1 installment, Rs. 1 is outstanding for 1 month (this is the final installment). Step 3: Sum the outstanding principals for each month to find the equivalent principal for one month, or total 'principal-months'. Sum of principals = 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55 (principal-months). Step 4: Convert the 'principal-months' to 'principal-years' for the annual rate formula. Equivalent principal-years = 55 months / 12 months/year = 55/12 years (with a principal of Rs. 1). So, the effective principal for the entire duration if it were a single sum outstanding for a year is 55/12 times the rate. Step 5: Use the simple interest formula: SI = (P_effective × R × T_effective) / 100. Here, P_effective is the loan amount, T_effective is the sum of time periods for each Rs. 1 unit of principal outstanding. Alternatively, Total SI = (Sum of [Principal outstanding each month × Rate × 1/12]) / 100. 1 = ( (10 × R × 1/12) + (9 × R × 1/12) + ... + (1 × R × 1/12) ) / 100. 1 = (R/1200) × (10 + 9 + ... + 1). 1 = (R/1200) × 55. Step 6: Solve for R (annual rate). R = 1200 / 55. R = 240 / 11. R = 21 9/11 % per annum. Step 7: The rate of interest is 21 9/11 %.
10
An amount grows to Rs. 9800 after 5 years and Rs. 12005 after 8 years, both under the same simple interest rate. Determine the annual interest rate.
0:00
Solution: Step 1: The difference in the amounts over the difference in the time periods represents the simple interest for that duration. Step 2: Calculate the time difference = 8 years - 5 years = 3 years. Step 3: Calculate the simple interest (SI) for 3 years = Rs. 12005 - Rs. 9800 = Rs. 2205. Step 4: Calculate the simple interest for 1 year = Rs. 2205 / 3 = Rs. 735. Step 5: Calculate the simple interest for 5 years = Rs. 735 * 5 = Rs. 3675. Step 6: Find the principal (P) by subtracting the 5 years' interest from the amount after 5 years: P = Rs. 9800 - Rs. 3675 = Rs. 6125. Step 7: Use the Simple Interest formula to find the Rate (R): R = (SI * 100) / (P * T). Step 8: Using the SI for 5 years, P=Rs. 6125, T=5 years: R = (3675 * 100) / (6125 * 5). Step 9: Perform the calculation: R = 367500 / 30625 = 12. Step 10: The rate of interest is 12% per annum.
11
An investor places equal sums in two accounts, one earning simple interest and the other compound interest. Both accounts have the same 2-year term and 4% annual interest rate. After the term, the compound interest exceeds the simple interest by Rs. 50. What was the original sum invested in each account?
0:00
Solution: Step 1: Let the principal sum = P Step 2: Simple Interest (SI) = (P * 4 * 2) / 100 = 0.08P Step 3: Compound Interest (CI) = P * [1 + (4/100)]^2 - P = P * (1.04)^2 - P = 0.0816P Step 4: Difference = CI - SI = 0.0816P - 0.08P = 0.0016P Step 5: Set up equation: 0.0016P = 50 Step 6: Solve for P: P = 50 / 0.0016 = 31250 Step 7: Verify: SI = 0.08 * 31250 = 2500, CI = 0.0816 * 31250 = 2560, Difference = 60 - 50 = 60
12
A sum of Rs. 725 is lent at the beginning of a year at an initial interest rate. Eight months later, an additional Rs. 362.50 is lent at a rate that is double the initial rate. If the total interest earned from both loans by the end of the year is Rs. 33.50, what was the original annual interest rate?
0:00
Solution: Step 1: Let the original rate of interest be R% per annum. Step 2: The second loan's rate is 2R% per annum. Step 3: The first loan of Rs. 725 was outstanding for the entire year (12 months), so T1 = 1 year. Step 4: The second loan of Rs. 362.50 was lent after 8 months, meaning it was outstanding for (12 - 8) = 4 months. Convert 4 months to years: T2 = 4/12 = 1/3 year. Step 5: Calculate Simple Interest from the first loan (SI1): SI1 = (P1 * R1 * T1) / 100 = (725 * R * 1) / 100 = 7.25R. Step 6: Calculate Simple Interest from the second loan (SI2): SI2 = (P2 * R2 * T2) / 100 = (362.50 * 2R * (1/3)) / 100 = (725R / 3) / 100 = 7.25R / 3. Step 7: The total interest earned from both loans is Rs. 33.50. Total Interest = SI1 + SI2. Step 8: Formulate the equation: 7.25R + (7.25R / 3) = 33.50. Step 9: To eliminate the fraction, multiply the entire equation by 3: 3 * (7.25R) + 7.25R = 33.50 * 3. Step 10: 21.75R + 7.25R = 100.5. Step 11: Combine like terms: 29R = 100.5. Step 12: Solve for R: R = 100.5 / 29 = 3.4655... Step 13: Since the exact value is not among the main options and 'None of these' is available, the original rate of interest is approximately 3.46%.
13
A sum of money was invested at simple interest for 3 years at a specific rate. If the interest rate had been 1% higher, the investment would have yielded Rs. 5100 more. What was the original sum?
0:00
Solution: Step 1: Let the principal sum be P and the original interest rate be R% per annum. The time period is 3 years. Original Simple Interest (SI_original) = (P * R * 3) / 100 Step 2: If the rate was (R + 1)% per annum, the new simple interest (SI_new) would be: SI_new = (P * (R + 1) * 3) / 100 Step 3: The difference in interest is Rs. 5100. SI_new - SI_original = 5100 (P * (R + 1) * 3) / 100 - (P * R * 3) / 100 = 5100 Step 4: Simplify and solve for P. (3PR + 3P - 3PR) / 100 = 5100 3P / 100 = 5100 3P = 5100 * 100 3P = 510000 P = 510000 / 3 P = 170000 Step 5: The sum is Rs. 170000.
14
Calculate the difference between the simple interest earned on Rs. 500 at 5% per annum for 3 years and the simple interest earned on the same principal at 4% per annum for 4 years.
0:00
Solution: Step 1: Calculate the simple interest (SI1) for the first case: Principal (P) = Rs. 500, Rate (R1) = 5% per annum, Time (T1) = 3 years. Step 2: SI1 = (P × T1 × R1) / 100 = (500 × 3 × 5) / 100 = 5 × 15 = Rs. 75. Step 3: Calculate the simple interest (SI2) for the second case: Principal (P) = Rs. 500, Rate (R2) = 4% per annum, Time (T2) = 4 years. Step 4: SI2 = (P × T2 × R2) / 100 = (500 × 4 × 4) / 100 = 5 × 16 = Rs. 80. Step 5: Find the difference between the two simple interests: Difference = SI2 - SI1 = 80 - 75 = Rs. 5.
15
Calculate the simple interest accrued on a principal of Rs. 16,800 over 9 months, given an annual interest rate of 6 1/4%.
0:00
Solution: Step 1: Identify the given values. Principal (P) = Rs. 16,800 Time (T) = 9 months Rate (R) = 6 1/4% p.a. Step 2: Convert the rate from mixed fraction to improper fraction. R = 6 1/4% = (6 * 4 + 1) / 4 % = 25/4 % p.a. Step 3: Convert time from months to years. T = 9 months = 9/12 years = 3/4 year. Step 4: Calculate the Simple Interest (SI) using the formula SI = (P * R * T) / 100. SI = (16800 * (25/4) * (3/4)) / 100 SI = (16800 * 25 * 3) / (4 * 4 * 100) SI = (16800 * 75) / 1600 SI = (168 * 75) / 16 SI = 12600 / 16 = Rs. 787.50
16
An individual invested Rs. 12,000 in a bank fixed deposit at a simple annual interest rate of 10%. Due to urgent requirements, the entire sum was withdrawn after three years, resulting in a reduced interest rate being applied by the bank. If the amount received was Rs. 3,320 less than what would have been earned after five years at the original rate, what was the actual interest rate provided by the bank?
0:00
Solution: Step 1: Identify the Principal (P) = Rs. 12,000 and the original Rate (R_original) = 10% per annum. Step 2: Calculate the Simple Interest (SI) that would have been earned if the money stayed for 5 years: SI_5_years = (P * R_original * 5) / 100 = (12000 * 10 * 5) / 100 = Rs. 6,000. Step 3: The problem states that the actual interest received was Rs. 3,320 less than SI_5_years. Step 4: Calculate the actual interest received (SI_actual): SI_actual = 6000 - 3320 = Rs. 2,680. Step 5: This actual interest was earned over Time (T_actual) = 3 years. Step 6: Use the simple interest formula SI_actual = (P * R_actual * T_actual) / 100 to find the actual rate (R_actual). Step 7: Substitute the values: 2680 = (12000 * R_actual * 3) / 100. Step 8: Simplify the equation: 2680 = 120 * 3 * R_actual = 360 * R_actual. Step 9: Solve for R_actual: R_actual = 2680 / 360 = 268 / 36 = 67 / 9. Step 10: Convert the improper fraction to a mixed number: R_actual = 7 4/9 %.
17
A sum is lent at 4% per annum for the initial 3 years, 8% per annum for the subsequent 4 years, and 12% per annum for any period beyond 7 years. If the total simple interest obtained over an 11-year period is Rs. 27,600, what is the original sum (in Rs.)?
0:00
Solution: Step 1: Determine the time duration for each interest rate. Period 1: 3 years at 4% p.a. Period 2: 4 years at 8% p.a. Period 3: Remaining years = 11 - 3 - 4 = 4 years at 12% p.a. Step 2: Set up the equation for total simple interest (SI), where P is the principal. Total SI = SI (Period 1) + SI (Period 2) + SI (Period 3) 27,600 = (P * 4 * 3) / 100 + (P * 8 * 4) / 100 + (P * 12 * 4) / 100 27,600 = 12P / 100 + 32P / 100 + 48P / 100. Step 3: Combine terms and solve for P. 27,600 = (12P + 32P + 48P) / 100 27,600 = 92P / 100 P = (27,600 * 100) / 92 P = Rs. 30,000.
18
Under simple interest, a sum of money doubles itself in 5 years at one rate, and becomes three times its original value in 12 years at a different rate. Identify the lower of these two annual simple interest rates.
0:00
Solution: Step 1: Calculate the first rate (R1) for the sum doubling in 5 years. If a sum P doubles, the Simple Interest (SI) = P. Using SI = (P * R * T) / 100: P = (P * R1 * 5) / 100 1 = (5 * R1) / 100 R1 = 100 / 5 = 20% p.a. Step 2: Calculate the second rate (R2) for the sum becoming three times in 12 years. If a sum P becomes three times, the Simple Interest (SI) = 3P - P = 2P. Using SI = (P * R * T) / 100: 2P = (P * R2 * 12) / 100 2 = (12 * R2) / 100 R2 = (2 * 100) / 12 = 200 / 12 = 50 / 3 = 16 and 2/3 % p.a. Step 3: Compare the two rates and identify the lower one. R1 = 20% R2 = 16 and 2/3 % (approximately 16.67%) The lower rate is 16 and 2/3%.
19
Given that the simple interest earned on a principal amount at 8% annual rate over 6 years is half of the principal amount, determine the original sum.
0:00
Solution: Step 1: Let the sum (principal) be P. Step 2: Given Simple Interest (SI) = P/2. Step 3: Given Rate (R) = 8% per annum. Step 4: Given Time (T) = 6 years. Step 5: Use the simple interest formula: SI = (P * R * T) / 100. Step 6: Substitute the given values into the formula: P/2 = (P * 8 * 6) / 100. Step 7: Simplify the right side of the equation: P/2 = 48P / 100. Step 8: Further simplify the fraction: P/2 = 12P / 25. Step 9: Multiply both sides by 50 (the least common multiple of 2 and 25) to clear denominators: 25P = 24P. Step 10: Rearrange the equation: 25P - 24P = 0, which results in P = 0. Step 11: This outcome indicates that the equation holds true only if the principal is zero, or that the principal (P) cancels out from both sides, meaning the condition is true for any principal, making it impossible to determine a specific value for the sum. Therefore, the data provided is inadequate to find a unique sum.
20
An item priced at Rs. 20000 can be purchased with a Rs. 4000 down payment and four equal monthly installments. If the annual interest rate is 8%, what is the monthly installment amount?
0:00
Solution: Step 1: Total cost = Rs. 20000 Step 2: Down payment = Rs. 4000 Step 3: Remaining amount = 20000 - 4000 = Rs. 16000 Step 4: Monthly interest rate = 8%/12 = 0.6667% Step 5: Use installment formula: Installment = (Remaining Amount * Monthly Rate) / (1 - (1 + Monthly Rate)^-Number of Payments) Step 6: Installment = (16000 * 0.006667) / (1 - (1 + 0.006667)^-4) Step 7: Calculate: Installment ≈ Rs. 4066.01
📊 Questions Status
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20