How to Solve Percentage Problems
Solve percentage aptitude problems — per-hundred method, percentage change, fraction shortcuts and successive changes — with examples and practice questions.
Expected Interview Answer
Percentage problems are solved by treating "percent" as "per hundred": x% of a number is (x/100) × number, and a percentage change is (change ÷ original) × 100.
Convert percentages to fractions or decimals to compute quickly (25% = 1/4, 10% = 0.1). For successive changes, apply multipliers rather than adding percentages — a 10% rise then a 10% fall is ×1.1×0.9 = 0.99, a net 1% loss, not zero. Always identify the base: "increase" and "decrease" are measured against the original value, which is the most common source of errors.
- One "per hundred" idea covers all variations
- Fraction equivalents make mental math fast
- Multiplier method handles successive changes correctly
AI Mentor Explanation
A batter’s strike rate is just a percentage: runs per 100 balls. Scoring 60 off 50 balls is (60/50)×100 = 120 strike rate. Percentages everywhere work this way — "per hundred". And beware successive changes: a 10% form dip then a 10% recovery doesn’t return you to the start, because each change is measured against a different base, just like multiplying 1.1 by 0.9 gives 0.99, not 1.
Step-by-Step Explanation
Step 1
Read percent as per-hundred
x% of N = (x/100) × N. Use fractions: 25% = 1/4, 20% = 1/5.
Step 2
Identify the base
Increase/decrease is measured against the original value.
Step 3
Percentage change
Change % = (new − old) ÷ old × 100.
Step 4
Successive changes multiply
Apply multipliers (1 ± x/100) in sequence — do not add percentages.
What Interviewer Expects
- The per-hundred definition and fraction equivalents
- Correct identification of the base
- Percentage-change formula
- Multiplier method for successive changes
Common Mistakes
- Adding successive percentage changes instead of multiplying
- Using the wrong base for increase/decrease
- Confusing "percent" with "percentage points"
- Assuming a rise then equal fall returns to the start
Best Answer (HR Friendly)
“Treat "percent" as "per hundred": x% of a number is x/100 times it. For changes, divide the change by the original and multiply by 100. And when changes stack, multiply the factors instead of adding the percentages — a 10% rise then a 10% fall is a small net loss, not zero.”
Code Example
def pct_change(old, new):
return (new - old) / old * 100
print(pct_change(200, 250)) # 25.0 (%)
# 10% rise then 10% fall on 100
print(100 * 1.10 * 0.90) # 99.0 → net 1% loss, not 0Follow-up Questions
- What is the difference between percent and percentage points?
- If a price rises 20% then falls 20%, what is the net change?
- How do you find the original value after a known percentage change?
- How are percentages used in profit and loss problems?
MCQ Practice
1. A number increases from 80 to 100. The percentage increase is?
Change ÷ original × 100 = (20 ÷ 80) × 100 = 25%.
2. A value rises 10% then falls 10%. Net change?
×1.1×0.9 = 0.99 → a 1% net decrease, because the changes multiply on different bases.
3. 25% of 240 is?
25% = 1/4, and 240 ÷ 4 = 60.
Flash Cards
x% of N? — (x/100) × N — "percent" means "per hundred".
Percentage change? — (new − old) ÷ old × 100.
Successive changes? — Multiply the factors (1 ± x/100); never add the percentages.
10% up then 10% down? — ×1.1×0.9 = 0.99 → a 1% net loss, not 0.