Three percentage questions come up constantly — and people get them wrong surprisingly often
"What percentage is 340 of 1,700?" "A product marked ৳2,800 is now ৳2,100 — what's the discount?" "My rent went from ৳12,000 to ৳15,500 — is that a 25% increase or a 29% increase?" These feel like they should be quick, but the mental arithmetic trips people up because the three types of percentage questions use different formulas — and it's easy to apply the wrong one.
The Three Percentage Problems
Problem type 1: What is X% of Y? Formula: (X ÷ 100) × Y Example: What is 15% of ৳4,800? = (15 ÷ 100) × 4,800 = ৳720
Problem type 2: X is what percentage of Y? Formula: (X ÷ Y) × 100 Example: ৳720 is what percentage of ৳4,800? = (720 ÷ 4,800) × 100 = 15%
Problem type 3: What is the percentage change from X to Y? Formula: ((Y − X) ÷ X) × 100 Example: Rent increased from ৳12,000 to ৳15,500. What's the percentage increase? = ((15,500 − 12,000) ÷ 12,000) × 100 = (3,500 ÷ 12,000) × 100 = 29.17%
Note: it's 29.17%, not 25%. The error people make is calculating 3,500 ÷ 15,500 (using the new value as the base) instead of 3,500 ÷ 12,000 (using the original as the base). Percentage change is always calculated on the starting value.
How to Use the Percentage Calculator on sadiqbd.com
Select the problem type and enter your values — the result appears instantly. The calculator handles all three types, so you don't need to remember which formula applies.
Real-World Examples
Tax and VAT calculations
A restaurant bill is ৳3,200 before VAT. VAT is 15%. Total?
15% of 3,200 = 480. Total = ৳3,680.
But if the ৳3,200 is the VAT-inclusive price and you need the pre-VAT amount: the base is 115% of the original. Pre-VAT = 3,200 ÷ 1.15 = ৳2,782.61.
This is the reverse percentage calculation — extracting the base from a percentage-inclusive figure. Different from simply subtracting 15%.
Investment return tracking
You invested ৳75,000. It's now worth ৳1,08,500. What's your return?
((1,08,500 − 75,000) ÷ 75,000) × 100 = (33,500 ÷ 75,000) × 100 = 44.67%
Grade and score percentages
An exam out of 800 marks — you scored 612. What percentage?
(612 ÷ 800) × 100 = 76.5%
Needed for distinction: 75%. You're above it.
Comparing year-over-year business metrics
Revenue last year: ৳18,50,000. This year: ৳21,20,000.
Percentage growth: ((21,20,000 − 18,50,000) ÷ 18,50,000) × 100 = (2,70,000 ÷ 18,50,000) × 100 = 14.59%
The Asymmetry of Percentage Changes
One counterintuitive property: a 50% increase followed by a 50% decrease does not return you to the starting point.
Starting value: ৳10,000 After 50% increase: ৳15,000 After 50% decrease (on ৳15,000): ৳7,500
You lost ৳2,500 despite "equal" changes in opposite directions. The decrease's base (৳15,000) is larger than the increase's base (৳10,000), so the same percentage produces a larger absolute change.
This is why investment portfolios take longer to recover from a drop than people expect: a 40% drop requires a 66.7% gain just to break even, not a 40% gain.
Tips for Working With Percentages
Always identify the base. Percentage change requires clarity on what the "original" value is. When a salary changes from ৳50,000 to ৳60,000, the base is ৳50,000 (not ৳60,000). When a price drops from ৳1,000 to ৳800, the base is ৳1,000.
Percentage points ≠ percentages. If an interest rate moves from 5% to 8%, that's a 3 percentage point increase — but a 60% increase in the rate itself. Media and financial reports often conflate these; be aware of which is being stated.
Chain percentage calculations need care. Three consecutive 10% increases: not 30% total, but approximately 33.1% (1.1³ = 1.331). Each successive percentage is calculated on a larger base.
Frequently Asked Questions
Why does dividing by the wrong base give a wrong percentage? The percentage formula requires the base to be the "whole" you're expressing the part as a fraction of. Using the wrong base produces a number that doesn't have the meaning you intend.
How do I find the original price before a discount? Divide the discounted price by (1 − discount percentage). A ৳680 item after 15% discount: original = 680 ÷ 0.85 = ৳800. Don't add 15% to the discounted price — that gives you ৳782, not ৳800.
Is the percentage calculator free? Yes — completely free, no sign-up required.
Percentages are everywhere — and the three core problem types each have a slightly different formula. The calculator handles all three so you can focus on the decision, not the arithmetic.
Try the Percentage Calculator free at sadiqbd.com — solve any percentage problem instantly without formula lookup.
