Question 1

One-eighth of a number is 41.5. What will 69% of that number be?

Accepted Answer

Concept & Strategy: The problem requires finding a base number from a given fractional part and then calculating a percentage of that base number. The strategy is to set up a simple algebraic equation to find the base number, then apply the required percentage. Base = Part × Denominator Step-by-Step Solution: Given: • (1/8) of a number is 41.5. • We need to find 69% of this same number. Calculation / Deduction: • Let the unknown number be N. • According to the problem statement: (1/8) × N = 41.5 • Multiply both sides by 8 to isolate N: N = 41.5 × 8 • Calculate the product to find the base number: N = 332 • Now, find 69% of 332: (69/100) × 332 • Multiply 69 by 332: 69 × 332 = 22908 • Divide by 100 to apply the percentage: (22908/100) = 229.08 Exam Strategy & Shortcut: Instead of performing the full multiplication for the final step, use unit digit analysis to save time. The final calculation is 332 × 0.69. Ignore the decimal temporarily and look at the unit digits of the numbers: 2 × 9 = 18. This means the final product must end with an 8. Looking at the provided options, only 229.08 ends with an 8. This allows you to skip the tedious arithmetic entirely. Common Pitfall: A frequent mistake is finding the base number (332) and forgetting to perform the second half of the problem (finding 69%). Another pitfall is misplacing the decimal point during the final multiplication, leading to an answer off by a factor of ten. Final Answer: Therefore, the correct answer is 229.08.

Question 2

Ten percent of twenty plus twenty percent of ten equals

Accepted Answer

Concept & Formula: This question tests the commutative property of percentages. The fundamental rule of percentages is that x% of y is always equal to y% of x. This principle makes seemingly complex summations much easier to resolve mentally. x% × y = y% × x Step-by-Step Solution: Given: • First term: 10% of 20 • Second term: 20% of 10 Calculation / Deduction: • Calculate the first term: 10% of 20 = (10/100) × 20 = 2 • Calculate the second term: 20% of 10 = (20/100) × 10 = 2 • Add the two results together: 2 + 2 = 4 • Now, evaluate the given options to find which one equals 4: (a) 10% of 20 = 2 (b) 20% of 10 = 2 (c) 1% of 200 = 2 (d) 2% of 200 = (2/100) × 200 = 4 • Option (d) is the only expression that evaluates to the sum of 4. Exam Strategy & Shortcut: Using the rule A% of B = B% of A, you can immediately see that "10% of 20" is the exact same value as "20% of 10". Therefore, you are simply calculating 2 × (10% of 20). Since 10% of 20 is 2, the total is obviously 4. Scanning the options, 2% of 200 clearly yields 4. This requires zero paper calculation. Common Pitfall: Students often skim the options and hastily select (a) or (b), mistaking one part of the question for the total sum. Always remember to complete the addition operation before checking the options. Final Answer: Therefore, the correct answer is 2 percent of 200.

Question 3

60% of 264 is the same as

Accepted Answer

Concept & Strategy: This problem tests the concept of equivalent percentages through proportional scaling. If you divide a percentage by a certain factor, you must multiply the base number by that exact same factor to keep the total value identical. (P \div x)% of (B × x) = P% of B Step-by-Step Solution: Given: • The target expression is 60% of 264. Calculation / Deduction: • Calculate the exact numerical value of the target expression: (60/100) × 264 = 0.6 × 264 • 0.6 × 264 = 158.4 • Now, test each option to find the matching value: • Test Option (a): 10% of 44 0.1 × 44 = 4.4 (Incorrect) • Test Option (b): 15% of 1056 (15/100) × 1056 = 0.15 × 1056 15 × 10.56 = 158.4 (Correct) • Test Option (c): 30% of 132 0.3 × 132 = 39.6 (Incorrect) Exam Strategy & Shortcut: Instead of calculating 158.4, use factor scaling. Look at the options and compare them to the original 60%. Option (b) uses 15%. How do you get from 60% to 15%? You divide by 4. To keep the value the same, you must multiply the base (264) by 4. 264 × 4 = 1056. Therefore, 60% of 264 is mathematically identical to 15% of 1056. This logical deduction is much faster than brute-force decimal multiplication. Common Pitfall: A standard error is attempting to calculate every single option fully, which consumes too much time. Another mistake is miscalculating the decimals when checking the options, especially when dealing with numbers like 1056. Final Answer: Therefore, the correct answer is 15% of 1056.

Question 4

270 candidates appeared for an examination, of which 252 passed. The pass percentage is:

Accepted Answer

Concept & Formula: This is a fundamental percentage calculation based on a part-to-whole relationship. To find the percentage of a subset within a total, divide the subset by the total and multiply by 100. Percentage = ( \frac{Part}{Whole} ) × 100 Step-by-Step Solution: Given: • Total candidates appeared (Whole) = 270 • Candidates passed (Part) = 252 Calculation / Deduction: • Set up the fraction for the pass percentage: (252/270) × 100 • Simplify the fraction (252/270) by finding common divisors. Both end in an even number or zero, and their digits sum to multiples of 9 (2+5+2=9, 2+7+0=9), so they are divisible by 18. • Divide numerator and denominator by 18: 252 \div 18 = 14 270 \div 18 = 15 • The simplified fraction is (14/15). • Now calculate the percentage: (14/15) × 100 • Simplify by dividing 100 and 15 by 5: 14 × (20/3) = (280/3) • Convert the improper fraction to a mixed number: 280 \div 3 = 93 with a remainder of 1. • This gives 93(1/3)%. Exam Strategy & Shortcut: Avoid heavy division by looking at the difference. The total is 270 and passed is 252. The number of failed candidates is 270 - 252 = 18. Now, find the failure percentage: (18/270). This easily simplifies to (1/15). The pass percentage is simply 100% - ((1/15) as a percent). We know (1/15) is equivalent to 6(2/3)%. 100% - 6(2/3)% = 93(1/3)%. Working with smaller numbers (18 instead of 252) dramatically increases calculation speed. Common Pitfall: Students often struggle with reducing large fractions like (252/270) and resort to long division early on (e.g., dividing 25200 by 270), which takes significantly more time and introduces a higher risk of arithmetic errors. Final Answer: Therefore, the correct answer is 93(1/3)%.

Question 5

5 out of 2250 parts of earth is sulphur. What is the percentage of sulphur in earth?

Accepted Answer

Concept & Formula: This problem requires converting a standard ratio or fraction into a percentage. The concept is identical to standard percentage formulas: isolate the specific part, divide it by the total parts, and multiply the outcome by 100. Percentage = ( \frac{Given Parts}{Total Parts} ) × 100 Step-by-Step Solution: Given: • Sulphur parts = 5 • Total parts of earth = 2250 Calculation / Deduction: • Construct the fraction representing the ratio of sulphur to the total: (5/2250) • Simplify the fraction by dividing the numerator and the denominator by 5: (1/450) • To convert this fraction into a percentage, multiply by 100: (1/450) × 100 • Simplify the expression by cancelling a zero from the numerator and denominator: (10/45) • Further simplify by dividing both numbers by their greatest common divisor, which is 5: (2/9) • The result is (2/9)%. The options represent the numerical value of the percentage. Exam Strategy & Shortcut: Write down the expression directly as (5/2250) × 100. Cancel the zeroes immediately to get (50/225). Knowing your multiples of 25 is extremely helpful here. 50 is 2 × 25, and 225 is 9 × 25. Cancelling the 25 from the top and bottom instantly leaves you with (2/9). Common Pitfall: A very common mistake is confusing the fractional part with the percentage itself. Students might simplify (5/2250) to (1/450) and then incorrectly look for that answer, forgetting the final crucial step of multiplying by 100 to convert it to a percentage format. Final Answer: Therefore, the correct answer is (2/9).

Question 6

What percent of 88 is 33?

Accepted Answer

Concept & Logic: The phrasing "what percent of X is Y" means you are finding the ratio of Y to X, and then scaling it to a percentage format. It is a fundamental part-to-whole relationship. Percentage = ( \frac{Part}{Whole} ) × 100 Step-by-Step Solution: Given: • Whole (Base) = 88 • Part = 33 Calculation / Deduction: • Construct the fraction representing the ratio of the part to the whole: (33/88) • Notice that both the numerator and the denominator are multiples of 11. Simplify the fraction by dividing both by 11: (3/8) • To convert this simplified fraction to a percentage, multiply by 100: (3/8) × 100 • This becomes: (300/8) • Divide 300 by 8: 300 \div 2 = 150 150 \div 2 = 75 75 \div 2 = 37.5 Exam Strategy & Shortcut: Memorizing standard fraction-to-percentage conversions is essential for speed. You should immediately recognize (33/88) as (3/8). You must know that (1/8) = 12.5%. Therefore, (3/8) is simply 3 × 12.5%, which instantly yields 37.5%. This completely bypasses the need to multiply by 100 or perform long division. Common Pitfall: The most frequent mistake in this type of phrasing is reversing the numerator and denominator, incorrectly calculating (88/33) instead of (33/88). Always identify the number immediately following the word "of" as the base (denominator). Final Answer: Therefore, the correct answer is 37.5%.

Question 7

What percent is 1 minute and 12 seconds of an hour?

Accepted Answer

Concept & Formula: Before determining a percentage ratio, all quantities must be expressed in the exact same unit of measurement. The core concept here is converting mixed time units into a single common unit (seconds) before applying the percentage formula. Percentage = ( \frac{Target Time in Seconds}{Base Time in Seconds} ) × 100 Step-by-Step Solution: Given: • Target Time = 1 minute and 12 seconds • Base Time = 1 hour Calculation / Deduction: • Convert the Target Time entirely into seconds. We know 1 minute = 60 seconds. 60 seconds + 12 seconds = 72 seconds • Convert the Base Time (1 hour) entirely into seconds. We know 1 hour = 60 minutes, and 1 minute = 60 seconds. 60 × 60 = 3600 seconds • Set up the percentage fraction: ( (72/3600) ) × 100 • Simplify the expression by cancelling the two trailing zeros in 3600 with the 100: (72/36) • Perform the final simple division: 72 \div 36 = 2 • The resulting value is 2%. Exam Strategy & Shortcut: You can also solve this efficiently using minutes as the base unit to keep the numbers smaller. Target Time: 12 seconds is (12/60) minutes, which is 0.2 minutes. So, Target = 1.2 minutes. Base Time: 1 hour = 60 minutes. Setup: (1.2/60) × 100. Multiply 1.2 × 100 to get 120. Then divide: (120/60) = 2%. This method uses smaller baseline numbers and is faster for mental math. Common Pitfall: The primary mistake is failing to standardize the units. A student might try to write the target time as 1.12 (treating seconds directly as decimals of a minute) and dividing by 1, leading to a wildly incorrect and confusing calculation. Always convert fully to the smallest shared unit. Final Answer: Therefore, the correct answer is 2%.

Question 8

The marks obtained by a student are given below. What is his total percentage in all the subjects?  | Subjects | Total Marks | Marks Obtained | | :--- | :---: | :---: | | Mathematics | 100 | 100 | | Science | 100 | 84 | | Social Studies | 100 | 67 |…

Accepted Answer

Concept & Formula: To find the aggregate or total percentage across multiple subjects, you must sum up all the maximum possible marks to find the overall denominator, and sum up all the obtained marks to find the overall numerator. Total Percentage = ( \frac{Sum of Marks Obtained}{Sum of Total Marks} ) × 100 Step-by-Step Solution: • Given: • Maximum marks per subject: 100, 100, 100, 50, 50 • Marks obtained per subject: 100, 84, 67, 25, 24 • Calculation: • Calculate the grand total of maximum marks: • 100 + 100 + 100 + 50 + 50 = 400 • Calculate the grand total of marks obtained: • 100 + 84 + 67 + 25 + 24 = 300 • Apply the percentage formula: • Percentage = ( (300/400) ) × 100 • Percentage = (3/4) × 100 = 75% Exam Strategy & Shortcut: Addition speed is the key here. Group numbers that complement each other: For obtained marks: (25 + 24) = 49. Then (84 + 67) = 151. Finally, 151 + 49 + 100 = 300. Recognizing that (300/400) reduces to the standard fraction (3/4) instantly gives you 75% without multiplying by 100. Common Pitfall: A common mistake is calculating the percentage for each subject individually and then averaging those percentages. Because the "Total Marks" (denominators) are not uniform (100 vs 50), taking a simple average of individual percentages will yield a mathematically incorrect result. Always aggregate the raw scores first. Final Answer: Therefore, the correct answer is 75%.

Question 9

The following table gives the marks obtained by a student in the first and second semester examinations in four subjects in a given year.  | Subjects | 1st Semester | 2nd Semester | Maximum Marks | | :--- | :---: | :---: | :---: | | Physics | 35 | 3…

Accepted Answer

Concept & Strategy: To find the aggregate percentage for the entire year, we must calculate the total marks obtained across both semesters and divide it by the total maximum marks available for both semesters combined. Aggregate Percentage = ( \frac{Total Marks Obtained in Year}{Total Maximum Marks for Year} ) × 100 Step-by-Step Solution: • Deduction (Maximum Marks): • The "Maximum Marks" column denotes the total marks per subject per semester. • Maximum marks for one semester = 50 + 50 + 100 + 100 = 300. • Since there are two semesters in the year, the grand total maximum marks = 300 × 2 = 600. • Calculation (Marks Obtained): • Total marks obtained in 1st Semester = 35 + 30 + 65 + 80 = 210. • Total marks obtained in 2nd Semester = 30 + 25 + 45 + 85 = 185. • Total marks obtained in the year = 210 + 185 = 395. • Final Percentage Calculation: • Percentage = ( (395/600) ) × 100 • Percentage = (395/6) • 395 \div 6 = 65.833... • Rounding to the nearest whole number gives 66. Exam Strategy & Shortcut: Instead of adding columns vertically, you can add horizontally to find the total per subject first, which sometimes creates easier numbers: Physics: 35 + 30 = 65 out of 100 Chemistry: 30 + 25 = 55 out of 100 Maths: 65 + 45 = 110 out of 200 Social: 80 + 85 = 165 out of 200 Total Obtained = 65 + 55 + 110 + 165 = 120 + 275 = 395. Total Max = 100 + 100 + 200 + 200 = 600. (395/6) is just under (400/6). Since (400/6) = 66.66, (395/6) will be very close to 66. Common Pitfall: The most common trap is misinterpreting the "Maximum Marks" column. Many students assume the maximum marks listed (300 total) are for the whole year, rather than per semester. If you divide 395 by 300, you would get an impossible percentage over 100%, which should immediately alert you to double the denominator. Final Answer: Therefore, the correct answer is 66.

Question 10

What percent of $7.2$ kg is $18$ gms?

Accepted Answer

Concept & Formula: When finding what percentage one quantity is of another, both quantities must be in the exact same unit of measurement. Percentage = ( \frac{Part}{Whole} ) × 100 Step-by-Step Solution: • Given: • Part = 18 gms • Whole = 7.2 kg • Deduction: • Convert the whole amount from kilograms (kg) to grams (gms) so the units match. • Since 1 kg = 1000 gms, 7.2 kg = 7.2 × 1000 = 7200 gms. • Calculation: • Now apply the formula: • Percentage = ( (18/7200) ) × 100 • Simplify by cancelling the zeros: • Percentage = (18/72) • Divide numerator and denominator by 18: • Percentage = (1/4) • (1/4) = 0.25% Exam Strategy & Shortcut: Once you convert the base to 7200 gms, find 1%. 1% of 7200 = 72. The target is 18, which is exactly one-fourth ((1/4)) of 72. Therefore, the percentage is (1/4) of 1%, which is 0.25%. Common Pitfall: The most common mistake is ignoring the unit conversion and calculating ( (18/7.2) ) × 100, which incorrectly yields 250%. Always check that your units are identical before setting up the fraction. Final Answer: Therefore, the correct answer is .25%.

Question 11

What percent of a day is $3$ hours?

Accepted Answer

Concept & Formula: To find what percentage a specific number of hours represents out of an entire day, you must standardise the units by converting the day into hours. Percentage = ( \frac{Given Hours}{Total Hours in a Day} ) × 100 Step-by-Step Solution: • Given: • Part = 3 hours • Whole = 1 day • Deduction: • Convert 1 day into hours: 1 day = 24 hours. • Calculation: • Substitute the values into the formula: • Percentage = ( (3/24) ) × 100 • Simplify the fraction (3/24) to (1/8): • Percentage = (1/8) × 100 = (100/8) • Divide 100 by 8: • (100/8) = 12.5% • Convert 12.5% into a mixed fraction: 12(1/2)%. Exam Strategy & Shortcut: Memorize standard fraction-to-percentage conversions. Once you reduce (3/24) to (1/8), you should instantly know that (1/8) always equals 12.5% or 12(1/2)%. This eliminates the need for any actual calculation. Common Pitfall: A careless mistake is using 12 hours as the base for a "day" (thinking only of daytime) instead of the full 24-hour cycle. Using 12 would incorrectly result in (3/12) = 25%. Final Answer: Therefore, the correct answer is 12\(1/2)\%.

Question 12

$5$ kg of metal A and $20$ kg of metal B are mixed to form an alloy. The percentage of metal A in the alloy is

Accepted Answer

Concept & Formula: To find the percentage of a specific component in a mixture, divide the quantity of that component by the *total* quantity of the mixture, then multiply by 100. Percentage of A = ( \frac{Quantity of A}{Total Quantity of Mixture} ) × 100 Step-by-Step Solution: • Given: • Weight of metal A = 5 kg • Weight of metal B = 20 kg • Deduction: • Total weight of the alloy = Weight of A + Weight of B • Total weight = 5 + 20 = 25 kg • Calculation: • Apply the percentage formula for metal A: • Percentage = ( (5/25) ) × 100 • Simplify the fraction (5/25) to (1/5): • Percentage = (1/5) × 100 • 100 \div 5 = 20% Exam Strategy & Shortcut: Look at the ratio of the mixture. The ratio of A:B is 5:20, which simplifies to 1:4. This means metal A is 1 part out of a total of 5 parts (1 + 4). The fraction (1/5) is a standard percentage value that you should have memorized as 20%. No calculations are needed. Common Pitfall: A very common mistake is putting the quantity of metal A over the quantity of metal B, evaluating (5 / 20) × 100 = 25%. Remember that percentage composition is always relative to the *entire* mixture (the whole), not just the other part. Final Answer: Therefore, the correct answer is 20%.

Question 13

$30\%$ apples out of $450$ are rotten. How many apples are in good condition?

Accepted Answer

Concept & Strategy: When a total is divided into two distinct groups (e.g., rotten and good), the percentages of the two groups must add up to 100%. Calculating the percentage of the target group directly is more efficient than calculating the unwanted group and subtracting. Target Quantity = Total × (100% - Unwanted Percentage) Step-by-Step Solution: • Given: • Total apples = 450 • Rotten apples percentage = 30% • Deduction: • If 30% are rotten, the percentage of apples in good condition is 100% - 30% = 70%. • Calculation: • Calculate 70% of the total number of apples: • Good Apples = 70% of 450 • Good Apples = (70/100) × 450 • Cancel out the zeros: • Good Apples = 7 × 45 • 7 × 40 = 280 • 7 × 5 = 35 • 280 + 35 = 315 Exam Strategy & Shortcut: Use percentage building blocks. 10% of 450 is 45. Since we need 70%, we just multiply by 7. 45 × 7 = 315. Alternatively, if you find subtraction easier: 10% is 45, so 30% is 45 × 3 = 135. Then subtract: 450 - 135 = 315. The direct 70% method is usually slightly faster. Common Pitfall: A common error is calculating 30% of 450 (135) and hastily selecting it as the answer if it were an option. Always double-check what the question is asking for: the *rotten* quantity or the *good* condition quantity. Final Answer: Therefore, the correct answer is 315.

Question 14

The following table gives the income distribution of 200 households of a village:  | Monthly Income (in ₹) | Number of Households | | :--- | :---: | | < 1000 | 25 | | < 2000 | 80 | | < 5000 | 170 | | < 10000 | 200 |  What is the percentage of househ…

Accepted Answer

Concept & Logic: This problem requires interpreting a Cumulative Frequency Distribution table. The table gives the cumulative number of households earning "less than" a certain amount. To find the number of households in a specific range, we subtract the lower boundary's cumulative frequency from the upper boundary's cumulative frequency. Required Percentage = ( \frac{Households in Range}{Total Households} ) × 100 Step-by-Step Solution: • Given: • Total households = 200 • Households earning < ₹ 5000 = 170 • Households earning < ₹ 2000 = 80 • Deduction: • The number of households earning between ₹ 2000 and ₹ 5000 is the difference between these two cumulative values. • Households in range = 170 - 80 = 90 • Calculation: • Percentage = ( (90/200) ) × 100 • Percentage = (90/2) = 45% Exam Strategy & Shortcut: Simply read the required range values directly from the table, subtract them mentally (170 - 80 = 90), and recognize that 90 out of 200 is exactly half of 90 out of 100. Thus, (90/2) = 45. This avoids writing down any intermediate steps. Common Pitfall: A major mistake is using just one row of the table (e.g., using 170 and calculating (170/200) = 85%). Always remember that "< 5000" includes the households already counted in "< 2000". You must subtract to find the specific class interval. Final Answer: Therefore, the correct answer is 45.

Question 15

In two successive years 100 and 75 students of a school appeared at the final examination. Respectively 75% and 60% of them passed. The average rate of pass is

Accepted Answer

Concept & Formula: This is a problem based on the Weighted Average of percentages. Instead of averaging the percentages directly (which would be incorrect since the base student numbers differ), we must find the total number of passed students and divide it by the total number of students. Overall Pass % = ( \frac{Total Passed Students}{Total Students} ) × 100 Step-by-Step Solution: • Given: • Year 1: 100 students, 75% passed. • Year 2: 75 students, 60% passed. • Calculation: • Passed in Year 1 = 75% of 100 = 75 • Passed in Year 2 = 60% of 75 = (3/5) × 75 = 45 • Total students = 100 + 75 = 175 • Total passed = 75 + 45 = 120 • Overall Average Rate = ( (120/175) ) × 100% • Simplifying: • Divide numerator and denominator by 5: ( (24/35) ) × 100 = (2400/35) • Divide by 5 again: (480/7) = 68 (4/7)% Exam Strategy & Shortcut: Use the Ratio Method for weights to keep numbers small. The ratio of students is 100 : 75 = 4 : 3. Total parts = 7. Weighted sum = (4 × 75%) + (3 × 60%) = 300% + 180% = 480%. Average pass rate = (480%/7) = 68 (4/7)%. This significantly cuts down calculation time. Common Pitfall: The most common trap is calculating the simple average of the two percentages: (75 + 60/2) = 67.5%. This is mathematically invalid because the sample sizes (100 and 75) are different. Always find absolute totals first. Final Answer: Therefore, the correct answer is 68 (4/7)%.

Question 16

Kamal has 160 toffees. He gave 5% toffees to Ravi, 15% toffees to Anita and one-fourth of the toffees to Gagan. How many toffees are left with Kamal after the distribution?

Accepted Answer

Concept & Logic: This problem is solved efficiently by tracking percentages instead of calculating individual quantities. Converting fractions to percentages unifies the data. Remaining % = 100% - (Sum of distributed percentages) Step-by-Step Solution: • Given: • Total toffees = 160 • To Ravi = 5% • To Anita = 15% • To Gagan = (1/4) of total • Deduction: • Convert Gagan's share to a percentage: (1/4) = 25%. • Total percentage distributed = 5% + 15% + 25% = 45%. • Percentage of toffees left = 100% - 45% = 55%. • Calculation: • Number of toffees left = 55% of 160. • Calculation: ( (55/100) ) × 160 = 55 × 1.6 = 88. Exam Strategy & Shortcut: Always unify units (fractions to percentages). Total given away is 5 + 15 + 25 = 45%. Left over is 55%. Mentally split the remaining percentage for faster calculation: 50% of 160 is 80. 5% of 160 is 8. 80 + 8 = 88. Done mentally in 10 seconds. Common Pitfall: A common mistake is calculating the absolute number of toffees for each person sequentially (5% of 160, then 15% of 160, then (1/4) of 160) and then subtracting the sum from 160. This introduces multiple calculation steps and heavily increases the risk of arithmetic errors. Final Answer: Therefore, the correct answer is 88.

Question 17

A shopkeeper sells note-books at the rate of ₹ 45 each and earns a commission of 4%. He also sells pencil boxes at the rate of ₹ 80 each and earns a commission of 20%. How much amount of commission will he earn in two weeks if he sells 10 note-books…

Accepted Answer

Concept & Logic: The total commission earned is the sum of commissions from each product type over a specific period. Calculate the daily commission first, then multiply by the total number of days. Total Commission = (Daily Comm. Type A + Daily Comm. Type B) × Number of Days Step-by-Step Solution: • Given: • Note-books: Rate = ₹ 45, Commission = 4%, Daily Sales = 10 • Pencil boxes: Rate = ₹ 80, Commission = 20%, Daily Sales = 6 • Duration = 2 weeks = 14 days • Calculation: • Daily commission from note-books = 10 × 45 × ( (4/100) ) = 450 × 0.04 = ₹ 18 • Daily commission from pencil boxes = 6 × 80 × ( (20/100) ) = 480 × 0.20 = ₹ 96 • Total daily commission = 18 + 96 = ₹ 114 • Total commission for 14 days = 114 × 14 • 114 × 14 = 114 × (10 + 4) = 1140 + 456 = ₹ 1596 Exam Strategy & Shortcut: Group the calculations per day to minimize steps. Daily Notebook Comm: 4% of 450 = 18. Daily Pencil Box Comm: 20% of 480 = 96. Daily Total = 114. Multiply by 14 days. Look at the unit digit: 4 × 4 = 16, so the answer must end in 6. Only 1496, 1586, and 1596 are candidates. Quickly approximate: 100 × 14 = 1400, so it must be comfortably higher than 1400. 114 × 14 = 1596. Common Pitfall: Students often forget that "two weeks" strictly means 14 days, particularly in a high-stress exam environment, and might multiply the daily earnings by 2 instead of 14, leading to completely incorrect options. Final Answer: Therefore, the correct answer is ₹ 1596.

Question 18

It costs ₹ 1 to photocopy a sheet of paper. However, 2% discount is allowed on all photocopies done after first 1000 sheets. How much will it cost to copy 5000 sheets of paper?

Accepted Answer

Concept & Logic: This is a tiered pricing problem. The total cost is split into two distinct segments: a fixed cost for the initial threshold and a discounted cost for the remainder. Total Cost = (Initial Sheets × Base Price) + (Remaining Sheets × Discounted Price) Step-by-Step Solution: • Given: • Total sheets to copy = 5000 • Cost per sheet for first 1000 sheets = ₹ 1 • Discount on sheets after 1000 = 2% • Deduction: • Discounted price per sheet = 1 - (2% of 1) = 1 - 0.02 = ₹ 0.98 • Number of sheets at discounted price = 5000 - 1000 = 4000 sheets • Calculation: • Cost of first 1000 sheets = 1000 × 1 = ₹ 1000 • Cost of remaining 4000 sheets = 4000 × 0.98 • 4000 × 0.98 = 40 × 98 = 3920 • Total Cost = 1000 + 3920 = ₹ 4920 Exam Strategy & Shortcut: Instead of calculating the discounted unit price (0.98), calculate the total cost *without* any discount first, then simply subtract the total discount value. Total cost without discount = 5000 × 1 = 5000. The discount is 2% strictly on the extra 4000 sheets. Total discount amount = 2% of 4000 = 80. Final Cost = 5000 - 80 = 4920. This method completely bypasses decimal multiplication. Common Pitfall: A very frequent error is applying the 2% discount to the entire bulk order of 5000 sheets. This leads to calculating 5000 × 0.98 = 4900, which is placed as a trap option (option c). Always respect the "after first 1000" condition. Final Answer: Therefore, the correct answer is ₹ 4920.

Question 19

A housewife saved ₹ 2.50 in buying an item on sale. If she spent ₹ 25 for the item, approximately how much percent she saved in the transaction?

Accepted Answer

Concept & Formula: To find the percentage saved, we must compare the amount saved to the original price of the item, not the final amount spent. Percentage Saved = ( \frac{Amount Saved}{Original Price} ) × 100 Step-by-Step Solution: • Given: Amount spent (Final Price) = ₹ 25 Amount saved = ₹ 2.50 • Calculation: First, determine the original price of the item before the savings were applied. Original Price = Amount Spent + Amount Saved Original Price = 25 + 2.50 = ₹ 27.50 Now, calculate the percentage saved using the formula: Percentage Saved = ( (2.50/27.50) ) × 100 Percentage Saved = ( (25/275) ) × 100 Percentage Saved = ( (1/11) ) × 100 Percentage Saved = 9.09% • Approximation: The value 9.09% is approximately 9%. Exam Strategy & Shortcut: Familiarize yourself with standard fraction-to-percentage conversions. When you simplify (25/275) , it quickly reduces to (1/11) . If you have memorized that (1/11) = 9.09% , you can bypass the multiplication and division steps entirely, saving valuable seconds. Common Pitfall: The most frequent mistake is calculating the percentage against the amount *spent* rather than the original price. Calculating ((2.50/25)) × 100 yields 10%, which is an incorrect option purposely provided as a trap. Always use the original base value for profit, loss, or savings percentages. Final Answer: Therefore, the correct answer is 9%.

Question 20

Rajeev buys goods worth ₹ 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.

Accepted Answer

Concept & Logic: When both a discount (rebate) and a tax are applied, they must be calculated sequentially, not simultaneously. The rebate decreases the initial cost, and the sales tax is then applied to that newly reduced amount. Final Amount = Initial Price × (1 - \frac{Rebate}{100}) × (1 + \frac{Tax}{100}) Step-by-Step Solution: • Given: Initial value of goods = ₹ 6650 Rebate (Discount) = 6% Sales Tax = 10% • Calculation: Step 1: Calculate the amount after the 6% rebate. Price after rebate = 6650 × (1 - 0.06) = 6650 × 0.94 Price after rebate = ₹ 6251 Step 2: Calculate the final amount by adding the 10% sales tax to the rebated price. Final Amount = 6251 × (1 + 0.10) = 6251 × 1.10 Final Amount = ₹ 6876.10 Exam Strategy & Shortcut: Use successive percentage multipliers to solve it in a single line. Final Price = 6650 × 0.94 × 1.10 . Instead of multiplying 0.94 by 6650 first, multiply 0.94 × 1.10 = 1.034 . Now, calculate 6650 × 1.034 . To do this mentally: 6650 × 1 = 6650 . Plus 3% of 6650 ( 199.5 ) plus 0.4% ( 26.6 ). 6650 + 199.5 + 26.6 = 6876.10 . Common Pitfall: A major mistake is combining the percentages by simply taking the net difference (e.g., 10% tax - 6% rebate = +4% ). Applying a flat 4% increase to ₹ 6650 yields ₹ 6916, which is incorrect because the base amount changes after the rebate. Final Answer: Therefore, the correct answer is ₹ 6876.10.

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