Practice Questions
Concept Explanation
When a quantity reduces by x%, the new value is (100 − x)% of the original, or original × (1 − x/100).
Formula
New value = Original × (1 − P/100). Decrease amount = Original × (P/100).
Finding Original from Decreased Value
If a P% decrease gives new value N, then Original = N × 100/(100 − P).
Finding Percentage Decrease
Decrease % = ((Old − New)/Old) × 100. Always divide by the original value.
Common Trap
A 20% drop from 500 gives 400, but a 20% rise from 400 gives 480, not 500. Increase and decrease percentages are not reversible unless the base is the same.
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Q1 Easy
A number is decreased by 20%. If the original number is 500, what is the new number?
Explanation20% of 500 = 100. New number = 500 − 100 = 400. -
Q2 Easy
The population of a city is 80,000. It decreases by 15%. What is the new population?
Explanation15% of 80,000 = 12,000. New population = 80,000 − 12,000 = 68,000. -
Q3 Easy
The price of a shirt drops from Rs. 1,200 to Rs. 960. What is the percentage decrease?
ExplanationDecrease = 240. Percentage = (240/1,200) × 100 = 20%. -
Q4 Medium
After a 25% decrease, a value becomes 450. What was the original value?
Explanation75% of original = 450. Original = 450 × (100/75) = 600. -
Q5 Medium
A student's attendance falls from 200 days to 170 days. What is the percentage decrease?
ExplanationDecrease = 30. Percentage = (30/200) × 100 = 15%. -
Q6 Easy
An article marked at Rs. 2,000 is sold at a discount of 10%. What is the selling price?
Explanation10% of 2,000 = 200. SP = 2,000 − 200 = Rs. 1,800. -
Q7 Medium
Production drops from 2,400 units to 2,040 units. Find the percentage decrease.
ExplanationDecrease = 360. Percentage = (360/2,400) × 100 = 15%.
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Q8 Hard
If the side of a square is reduced by 10%, by what percent does the area decrease?
ExplanationNew area = (0.9s)² = 0.81s². Decrease = 19%. -
Q9 Hard
After decreasing a number by 30%, it becomes 420. Find the original number.
Explanation70% of original = 420. Original = 420 × (10/7) = 600. -
Q10 Medium
The weight of an alloy is reduced from 750 g to 675 g. What is the percentage decrease?
ExplanationDecrease = 75. Percentage = (75/750) × 100 = 10%. -
Q11 Medium
A number is 800. After an x% decrease it becomes 680. Find x.
ExplanationDecrease = 120. x = (120/800) × 100 = 15%. -
Q12 Hard
The value of a machine depreciates by 20% every year. If its present value is Rs. 64,000, what was its value one year ago?
ExplanationAfter 20% depreciation, value = 80% of previous. Previous = 64,000/0.8 = Rs. 80,000. -
Q13 Hard
In an exam, pass marks are 40%. A student scores 30% and fails by 30 marks. What is the maximum marks?
ExplanationDifference between pass and scored = 10% of max = 30. Max marks = 30 × 10 = 300. -
Q14 Hard
A shop reduces the price of an item by 12% and the new price is Rs. 880. What was the original price?
Explanation88% of original = 880. Original = 880 × (100/88) = Rs. 1,000.
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DS1 Easy
What is the new value after a percentage decrease?
Statement IThe original value is 750.
Statement IIThe value decreases by 20%.
ExplanationNew value = 750 × 0.8 = 600. Both statements are needed to compute the result. -
DS2 Medium
What was the original price?
Statement IAfter a 10% discount, the price is Rs. 1,620.
Statement IIThe discount amount is Rs. 180.
ExplanationStatement I: Original = 1,620/0.9 = Rs. 1,800. Statement II gives only the discount amount without the rate or final price.
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DS3 Easy
By what percent did the quantity decrease?
Statement IThe quantity fell from 960 to 816.
Statement IIThe decrease is 144 units.
ExplanationStatement I: decrease % = (144/960) × 100 = 15%. Statement II alone does not give the original quantity. -
DS4 Medium
Is the percentage decrease more than 25%?
Statement IThe new value is 70% of the original.
Statement IIThe original value is 1,200.
ExplanationStatement I: decrease = 30%, which is more than 25%. Statement II only gives the original without the new value.