Practice Questions
Concept Explanation
When a quantity grows by x%, the new value is (100 + x)% of the original, or original × (1 + x/100).
Formula
New value = Original × (1 + P/100). Increase amount = Original × (P/100).
Finding Original from Increased Value
If a P% increase gives new value N, then Original = N × 100/(100 + P).
Finding Percentage Increase
Increase % = ((New − Old)/Old) × 100.
Placement Shortcut
10% of a number is found by dividing by 10. For 12% increase on Rs. 25,000: 10% = 2,500 and 2% = 500, so increase = 3,000 and new salary = Rs. 28,000.
- Identify whether the question gives original or final value.
- Apply increase on the original base only — never on the increased value unless stated.
- Check units (marks, population, price) stay consistent.
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Q1 Easy
A number is increased by 10%. If the original number is 200, what is the new number?
Explanation10% of 200 = 20. New number = 200 + 20 = 220. -
Q2 Easy
The population of a town is 50,000. It increases by 20%. What is the new population?
Explanation20% of 50,000 = 10,000. New population = 50,000 + 10,000 = 60,000. -
Q3 Easy
A salary of Rs. 25,000 is increased by 12%. What is the new salary?
Explanation12% of 25,000 = 3,000. New salary = 25,000 + 3,000 = Rs. 28,000. -
Q4 Easy
The price of an item rises from Rs. 400 to Rs. 460. What is the percentage increase?
ExplanationIncrease = 60. Percentage increase = (60/400) × 100 = 15%. -
Q5 Medium
After a 15% increase, the value becomes 690. What was the original value?
ExplanationNew value = 115% of original. Original = 690 × (100/115) = 600. -
Q6 Medium
A student's marks increase from 320 to 368. What is the percentage increase?
ExplanationIncrease = 48. Percentage = (48/320) × 100 = 15%. -
Q7 Medium
An article costing Rs. 800 is marked up by 25%. What is the marked price?
Explanation25% of 800 = 200. Marked price = 800 + 200 = Rs. 1,000.
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Q8 Medium
Production increases from 1,250 units to 1,500 units. Find the percentage increase.
ExplanationIncrease = 250. Percentage = (250/1,250) × 100 = 20%. -
Q9 Medium
If the length of a rectangle is increased by 20%, by what percent does the area increase (width unchanged)?
ExplanationArea is proportional to length when width is fixed. A 20% increase in length gives a 20% increase in area. -
Q10 Hard
A number is increased by 30% and the result is 520. Find the original number.
Explanation130% of original = 520. Original = 520 × (100/130) = 400. -
Q11 Hard
The number of employees in a firm rises from 480 to 552. What is the percentage increase?
ExplanationIncrease = 72. Percentage = (72/480) × 100 = 15%. -
Q12 Hard
A shopkeeper increases the cost price by 40% to fix the selling price. If CP is Rs. 350, what is SP?
Explanation40% of 350 = 140. SP = 350 + 140 = Rs. 490. -
Q13 Medium
After increasing a number by 25%, it becomes 875. The original number is:
Explanation125% of original = 875. Original = 875 × (4/5) = 700. -
Q14 Hard
If the radius of a circle is increased by 10%, the area increases by:
ExplanationNew area = π(1.1r)² = 1.21πr². Increase = 21%.
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DS1 Easy
What is the new value after a percentage increase?
Statement IThe original value is 400.
Statement IIThe value increases by 15%.
ExplanationNew value = 400 × 1.15 = 460. Each statement alone is insufficient; together they determine the answer. -
DS2 Medium
What was the original population?
Statement IAfter a 20% increase, the population is 72,000.
Statement IIThe population increased by 12,000.
ExplanationStatement I: Original = 72,000/1.2 = 60,000. Statement II gives only the increase amount without the rate or final value.
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DS3 Easy
By what percent did the price increase?
Statement IThe price rose from Rs. 640 to Rs. 736.
Statement IIThe increase amount is Rs. 96.
ExplanationStatement I: increase % = (96/640) × 100 = 15%. Statement II alone gives only the increase amount without the base price. -
DS4 Medium
Is the percentage increase greater than 10%?
Statement IThe new value is 110% of the original.
Statement IIThe original value is 500.
ExplanationStatement I: increase is exactly 10%, so it is not greater than 10%. Statement II only gives the original value without the new value or rate.