A percentage is always a percentage of something. Write that base quantity before calculating. This habit prevents the common mistake of treating a 20% rise followed by a 20% fall as if the two changes necessarily cancel.
Original foundation practice · choose by prerequisite skill.
PREDICT · CHANGE · EXPLAIN
An item starts at ₹800. Final price is 800−8d, where d is the discount percentage. There are no taxes or additional charges in this model.
The curve shows this simplified model over the labelled range. Read the exact point below; the sketch is not a measuring instrument.
Final price: 640 ₹
Does increasing the discount by 10 percentage points always remove the same rupee amount here?
Now close the explanation and try the independent retest. Moving a slider alone does not check your understanding.
Start here if you calculate a discount on the wrong price or assume a percentage rise and fall cancel. Use this after simple fraction and decimal multiplication are comfortable; reverse percentages are an extension, not a prerequisite for every younger learner.
A price of ₹200 has a 10% discount. Name the base, the amount saved and the final price.
You will need: Decimal multiplication, division and fractions of 100.
Attempt each task before opening a hint. If you need help, reveal the first hint, then the setup, then compare your written steps with the solution. Finish with the retests without referring back.
To find p% of an amount, multiply it by p/100. A 15% discount leaves 85% of the original price.
To reverse a change, divide the final amount by its multiplier. After a 20% discount, the final price is 0.8 times the original.
Successive percentage changes act on successive bases. Multipliers combine by multiplication, not by simply adding the percentage numbers.
The discount is a fraction of the original ₹800.
15/100 × 800=120.
The saving is ₹120.
Subtract 120 from 800, or calculate 0.85 × 800.
Answer: Save ₹120; pay ₹680
Before moving on: can you explain why your method works, as well as give the answer?
Write a method as well as an answer. The tasks change the reasoning, not just the numbers.
₹600 represents 80% of the original.
0.8 × original=600.
The remaining fraction is 0.8.
600/0.8=750.
Answer: ₹750
Before moving on: can you explain why your method works, as well as give the answer?
The decrease acts on 120, not 100.
Use 100 × 1.2 × 0.8.
The new value is 120.
20% of 120 is 24, leaving 96.
Answer: 96; a net 4% decrease
Before moving on: can you explain why your method works, as well as give the answer?
The point change is subtraction; the relative change uses 40 as base.
10/40 × 100.
50−40=10 percentage points.
10/40=25%.
Answer: 10 percentage points; 25% relative increase
Before moving on: can you explain why your method works, as well as give the answer?
A tempting claim: “Undo a 20% discount by adding 20% to the sale price.”
The sale price and original price are different bases.
These changed questions test whether you can reconstruct the method. If you use a hint, record where you got stuck and retry later. Completing this small set does not establish full chapter mastery.
The final amount is 90%.
450/0.9.
0.9x=450.
x=500.
Answer: ₹500
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
Each rise uses the current value.
200 × 1.1 × 1.1.
220.
220+22=242.
Answer: 242
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
Try the two retests with examples closed. If the same error returns, correct that step and retry later; this short practice is not a diagnostic score or a grade assessment.
Ask ‘a percentage of which amount?’ before asking for the answer. For an advanced learner, check whether they can reverse the calculation without adding a percentage of the sale price.
If the retests are independent, return to the problem that brought you here. The linked Class 10 application is optional for learners already studying that topic; younger learners should use their current school exercise.
It distinguishes direct subtraction of two percentage rates from a relative percentage change. Moving from 40% to 50% is a 10-point rise and a 25% rise relative to 40%.
Yes. Use the two print buttons above. The question sheet leaves working space and hides solutions; the worked-solutions option includes the solution steps. Your browser can save either view as a PDF.
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