💰 Quantity Quest 🚀
Master Class 8 Comparing Quantities with percentages, profit and loss, discounts, tax, simple interest, compound interest and real-life comparisons.
💰 Class 8 Comparing Quantities Worksheet
50 Questions🔐 Complete Answer Key
The complete answer key is locked until the test is completed. Individual answers become available only after checking that question.
Comparing Quantities in One Variable for Class 8 Online Practice Worksheet
Class 8 Comparing Quantities Worksheet Free Online: Build strong mathematical and financial reasoning skills with DigiSadhan's interactive Comparing Quantities in One Variable Online Practice Worksheet for Class 8 Mathematics. This free practice tool gives students fresh questions on percentages, percentage increase and decrease, profit and loss, discount, tax, simple interest, compound interest and comparison of quantities. Generate up to 1,000 questions for revision, homework, tuition, classroom practice and exam preparation. Select Foundation, Class 8 Core, Challenge or Mixed difficulty and choose a specific topic or a complete mixed worksheet. Every question includes an answer box and a Check Answer button. Correct answers turn the textbox green and trigger a positive animation and sound; incorrect answers turn the textbox red and trigger a retry animation and sound. Students cannot reveal an answer before attempting and checking the question. After checking, the Show Answer button becomes available for that question, while the complete answer key remains locked until the test is completed. A live progress bar, score counter and checked-question counter make practice measurable. Choose No Timer or a 5, 10, 15, 30 or 60-minute timed test. When the test is completed, the tool calculates the score and percentage and unlocks the complete answer key. A PDF download option creates a printable copy of the generated worksheet. The responsive mobile-first design works on smartphones, tablets and desktops, making it useful for students studying anywhere. Friendly percentage, money and discount graphics keep the practice approachable while dynamically generated numerical values make repeated tests different. This tool is useful for Class 8 Maths revision, CBSE-style preparation, school assignments, tutoring, remedial practice and independent learning.
Complete Class 8 Comparing Quantities Practice Guide
What Does Comparing Quantities Mean?
Comparing quantities means finding how one amount relates to another. In Class 8 Mathematics, comparisons are commonly expressed as ratios, fractions, decimals and percentages. Percentages are especially useful because they express a quantity out of 100. For example, 25% means 25 out of 100, which is also 0.25 or 1/4. Learning to move comfortably between these forms makes word problems much easier.
Converting Fractions, Decimals and Percentages
To convert a fraction into a percentage, multiply by 100. To convert a percentage into a decimal, divide by 100. To convert a decimal into a percentage, multiply by 100. These simple conversions are the foundation for many Class 8 Comparing Quantities questions.
Percentage Increase and Decrease
When a quantity becomes larger, the change is an increase. When it becomes smaller, the change is a decrease. First calculate the difference between the new and original values. Then compare that difference with the original value. A frequent mistake is using the new value as the denominator when the question asks for percentage change from the original value.
Profit and Loss
When an item is bought for a cost price (CP) and sold for a selling price (SP), the result depends on which is larger. If SP is greater than CP, there is a profit. If SP is less than CP, there is a loss. The percentage is calculated using the cost price as the base. This is important because profit or loss is measured in relation to what was originally invested.
Finding Selling Price
If a profit percentage is known, the selling price can be found by adding the profit to the cost price. If a loss percentage is known, subtract the loss from the cost price. Another efficient approach is to multiply the cost price by the appropriate percentage factor.
Discount
A discount is a reduction from the marked price of an item. The customer pays the marked price minus the discount. Discount percentage is calculated using the marked price as the base. For example, if an item marked at ₹800 receives a 15% discount, the discount is ₹120 and the selling price is ₹680.
Tax and GST-Style Questions
Tax is often represented as a percentage of the price before tax. To find the tax amount, multiply the taxable amount by the tax rate and divide by 100. Then add the tax to the original price to find the amount payable. Always read carefully whether a given price is before tax or after tax.
Simple Interest
Simple interest is calculated only on the original principal throughout the entire period. The three main quantities are principal (P), rate (R) and time (T). Keep the units consistent: if the rate is annual, time should be expressed in years unless the question provides a suitable conversion.
Compound Interest
In compound interest, interest is added to the amount after each compounding period, so later interest is calculated on an increased amount. For annual compounding, the standard amount formula is A = P(1 + R/100)^T. Compound interest is then A − P. Students should distinguish compound interest from simple interest rather than using the formulas interchangeably.
Comparing Two Quantities
When two quantities are compared, first identify the common basis. A difference alone may not be enough. For example, a ₹50 increase means something very different for an original price of ₹100 than for an original price of ₹1,000. Percentages make the comparison relative to the original quantity. Ratios can also show how many times one value is compared with another.
How to Solve Word Problems
- Read the question twice and identify the original quantity.
- Write down the known values and what must be found.
- Choose the correct formula.
- Keep units consistent.
- Substitute values carefully.
- Calculate and simplify the answer.
- Check whether the answer is reasonable.
- For money questions, check the currency and decimal placement.
Common Mistakes to Avoid
- Using the selling price instead of the cost price when finding profit or loss percentage.
- Using the discounted price instead of the marked price as the discount base.
- Forgetting to divide a percentage by 100 before using it as a decimal.
- Confusing simple interest with compound interest.
- Using months as years without converting the time.
- Forgetting to add tax or subtract discount after calculating the percentage amount.
- Using the new value instead of the original value for percentage change.
- Rounding too early and creating an avoidable error.
Quick Formula Sheet
Regular practice is the best way to become confident with Comparing Quantities. Begin with Foundation mode to build percentage fluency, use Core mode for Class 8-level applications, and move to Challenge mode for multi-step reasoning. Shuffle the worksheet to avoid memorising answers. When you make a mistake, identify whether the error came from selecting the wrong base quantity, choosing the wrong formula, calculating the percentage incorrectly or making an arithmetic mistake. Use the timer for exam-style sessions and the final answer key for structured revision. The most important habit is to label quantities clearly before calculating: CP, SP, MP, P, R, T, discount, tax and percentage change should never be mixed up.