Percentages in real life: marks, discounts, GST and common mistakes
A percentage is just a share of 100, yet it trips people up all the time, because it is always a percentage of something. Nearly every mistake below comes from using the wrong "something". Each example can be checked in our percentage calculator.
Overall marks: don't average the percentages
Say you scored 90 out of 100 in one paper and 20 out of 50 in another. The papers come to 90% and 40%, and averaging those gives 65%. That is wrong, because the papers aren't the same size. Your overall result is total marks ÷ total maximum marks: 110 ÷ 150 = 73.33%. Averaging only works when every paper has the same maximum.
Converting CGPA to a percentage is a separate matter. The formula is set by each board or university, so use the official one rather than a general rule.
Stacked discounts don't add up
"40% + 10% off" sounds like 50%. The second discount applies to the already reduced price, though. On a ₹1,000 item, 40% off leaves ₹600, and 10% off that leaves ₹540. You have saved ₹460, which is 46%. It doesn't matter which discount comes first; the result is the same.
Working backwards from a reduced price
If something costs ₹800 after 20% off, the original price isn't ₹800 plus 20% (₹960). The ₹800 is 80% of the original, so the original was ₹800 ÷ 0.8 = ₹1,000. This is handy for checking whether a "was" price on a sale tag is believable.
Tax-inclusive prices
The same backwards logic applies to tax. If a bill says ₹1,180 including 18% GST, the tax isn't 18% of ₹1,180 (₹212.40). The ₹1,180 is 118% of the pre-tax price, so the pre-tax price is ₹1,180 ÷ 1.18 = ₹1,000, and the GST is ₹180.
Up then down isn't back to the start
A price of ₹100 that rises 20% becomes ₹120. If it then falls 20%, it becomes ₹96, not ₹100, because the fall is 20% of a bigger number. This matters for anything that moves in both directions, including investments. A 50% fall needs a 100% rise to get back to where it began.
Percentage change: divide by the starting value
A salary going from ₹50,000 to ₹56,000 is a rise of ₹6,000 ÷ ₹50,000 = 12%. Dividing by the new figure instead gives 10.7%, which understates your raise. Comparing an offer with your current pay? The current pay is the starting value.
Percentage points aren't percent
If a loan rate goes from 8% to 9%, it rose by 1 percentage point. In relative terms, that is a 12.5% increase in the rate. Both statements are true, and news reports and advertisements pick whichever suits them. When you see a claim, ask "percent of what?"
Quick mental shortcuts
- 10%: move the decimal one place left. 10% of ₹2,450 is ₹245.
- 5%: half of 10%. So ₹122.50.
- 15%: 10% plus 5%. So ₹367.50.
- Swap the numbers: 8% of 50 is the same as 50% of 8, which is 4.