Concept 3 of 7
Percentage of a Quantity
Today's big idea
Per cent of a quantity means the fraction over 100 multiplied by that quantity.
Up 10 then down 10 lands lower, since the fall comes off a bigger number.
How it works
👀 What's going on?
A shop takes 30 percent off a price and you need the number, not the label. The word that does the work in that sentence is a small one, and it means multiply.
💡 Here's the trick
Look at the bar above. Finding a percentage of a quantity is the fraction-of-a-quantity idea again, so per cent of X means the fraction over 100, multiplied by X.
🪄 How to do it
- 1.Shade the part you want on the bar above.
- 2.Turn the percentage into a fraction over 100 or a decimal.
- 3.Multiply it by the quantity.
✍️ Try it
Find 35 percent of 240 rupees. Then: 15 percent of a number is 45, so what is the number?
35 over 100 times 240 gives 84 rupees. For the second, 15 percent is 45, so 1 percent is 3, and the whole hundred percent is 300.
⚠️ Watch out
You might be thinking a rise of 10 percent followed by a fall of 10 percent brings you back to the start. It does not. The fall is taken from the bigger number, so you end up slightly lower.
🌟 Why this matters
Sale prices, service charges and tips are all this calculation, and doing it in your head stops you overpaying.
Exam tip: Ten percent is a tenth, so find that first and scale it to whatever you need.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find 30% of ₹250.”
- 1
Convert % to fraction
30% = 30/100 = 3/10.
- 2
Multiply by quantity
3/10 × 250
- 3
Compute
= 250 ÷ 10 × 3 = 75.
- 4
Answer ✓
₹75
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
To find a percentage of an amount: divide by 100 for 1%, then multiply by the percentage.
PERCENT · ROUND 1 OF 3
Find 20% of ₹350.
Quick check
✅ VERIFICATION
A price of 500 rupees rises by 20%, then falls by 20% of the new price. What is the final price?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Ratio & Proportion
Simplify by hcf. Cross-multiply to check proportions.