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 EasyThe salary of a worker increased from Rs. 15,000 to Rs. 18,000. What is the percentage increase in their salary?ExplanationIncrease = Rs. 3,000. Percentage increase = (3,000/15,000) × 100 = 20%.
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Q2 EasyThe price of a book is increased from Rs. 200 to Rs. 220. What is the percentage increase in the price?ExplanationIncrease = Rs. 20. Percentage increase = (20/200) × 100 = 10%.
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Q3 EasyIf the price of a shirt increases from Rs. 400 to Rs. 500, what is the percentage increase in the price?ExplanationIncrease = Rs. 100. Percentage increase = (100/400) × 100 = 25%.
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Q4 EasyThe population of a village increased from 20,000 to 23,000 in a year. What is the percentage increase?ExplanationIncrease = 3,000. Percentage increase = (3,000/20,000) × 100 = 15%.
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Q5 EasyA 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.
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Q6 EasyThe 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.
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Q7 EasyA 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.
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Q8 EasyThe price of an item rises from Rs. 400 to Rs. 460. What is the percentage increase?ExplanationIncrease = 60. Percentage increase = (60/400) × 100 = 15%.
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Q9 MediumThe population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:ExplanationIncrease in 10 years = 2,62,500 − 1,75,000 = 87,500. Total increase = (87,500/1,75,000) × 100 = 50%. Average per year = 50/10 = 5%.
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Q10 MediumTwo tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?ExplanationLet Y be paid Rs. z. Then z + 120% of z = 550 → (11/5)z = 550 → z = Rs. 250.
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Q11 MediumAfter a 15% increase, the value becomes 690. What was the original value?ExplanationNew value = 115% of original. Original = 690 × (100/115) = 600.
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Q12 MediumA student's marks increase from 320 to 368. What is the percentage increase?ExplanationIncrease = 48. Percentage = (48/320) × 100 = 15%.
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Q13 MediumAn 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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Q14 HardAfter increasing a number by 30%, it becomes 520. Find the original number.Explanation130% of original = 520. Original = 520 × (100/130) = 400.
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DS1 Easy
In a population growth case study, 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 Easy
During a retail price audit, 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.
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DS3 Medium
A municipal report asks for the population before a recent rise. 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. -
DS4 Medium
A placement data-sufficiency set asks whether the percentage increase exceeds 10%. 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.