Build any percent from 10%, 5% and 1% blocks
In the exam you rarely need a pen for a percent. 10% moves the decimal point one place to the left, 5% is half of that, and 1% moves it two places. Every other percent is built from these blocks.
Guess first
Guess first: a ₹480 restaurant bill gets a 15% off coupon. Without a pen, how many rupees does the coupon save?
Show answer
Correct answer: B
10% of 480 = 48, and 5% is half of that: 48 ÷ 2 = 24. So 15% = 48 + 24 = ₹72.
Option A: ₹7.20 is ten times too small: the decimal point slipped one place.
Option C: ₹408 is what you pay after the coupon (480 − 72 = 408), not the saving.
Option D: 15% is not ₹15. It is ₹15 for every ₹100, and the bill is more than ₹100.
Hint: Find 10% first, then take half of it for 5%.
If you said ₹72 without writing, you already used two blocks: 10% and 5%. This lesson gives you the whole set.
An everyday picture
Building a percent is like paying with ₹10, ₹5 and ₹1 coins: a few kinds of coin make any amount.
₹10 coin 10%
move the decimal point one place to the left
₹5 coin 5%
half of the 10% block
₹1 coin 1%
move the decimal point two places to the left
Just as ₹35 is three ₹10 coins and one ₹5 coin, 35% is three 10% blocks and one 5% block.
See it: the blocks of ₹480
| Block | Working | Value |
|---|---|---|
| 10% | 480 ÷ 10 = 48 | 48 |
| 5% | 48 ÷ 2 = 24 | 24 |
| 1% | 480 ÷ 100 = 4.8 | 4.8 |
| 50% | 480 ÷ 2 = 240 | 240 |
| 25% | 240 ÷ 2 = 120 | 120 |
flowchart TD W["₹480 = 100%"] -->|"÷ 10"| T["10% = ₹48"] T -->|"half"| F["5% = ₹24"] T -->|"× 3"| H["30% = ₹144"] H --> S["35% = 144 + 24 = ₹168"] F --> S
The same picture in words: 10% of ₹480 is ₹48, half of it, ₹24, is 5%; three 10% blocks make 30%, ₹144; adding the 5% block gives 35%, ₹168.
Four percents of ₹480 from the blocks:
- 35% = 10% + 10% + 10% + 5%, so 48 + 48 + 48 + 24 = 168.
- 95% = 100% − 5%, so 480 − 24 = 456.
- 12.5% = 10% + 2.5%, and 2.5% is half of 5%, so 48 + 12 = 60.
- 2% = 1% + 1%, so 4.8 + 4.8 = 9.6.
Try it. Take your last mobile recharge amount. Find 15% of it with the 10% and 5% blocks, in your head. Then find 95% of it as "the whole minus 5%".
Find the rule
10% of the students in a school, 26 in all, come by bicycle. How many students make up 35% of the school?
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Correct answer: A
35% = 10% + 10% + 10% + 5%. 10% is 26 and 5% is 26 ÷ 2 = 13, so 35% = 26 + 26 + 26 + 13 = 91 students. Check: the school has 260 students, and 35% of 260 = 91.
Option B: 260 is the whole school (100%), not 35% of it.
Option C: 51 adds the gap between 35 and 10 as a plain number (26 + 25 = 51). That gap is 25% of the school, which is 65 students, not 25.
Option D: 910 multiplies 26 by 35. But 26 is already the 10% share: build up in blocks of 26 instead.
Hint: Build 35% from three 10% blocks and one 5% block.
What is 95% of 360?
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Correct answer: B
95% = 100% − 5%. 5% of 360 = 18, so 95% = 360 − 18 = 342.
Option A: 18 is the 5% block you take away, not what is left.
Option C: 34.2 is ten times too small: the decimal point slipped one place.
Option D: 95 is the percent, not the amount.
Hint: 95% is the whole minus one 5% block.
What is 28% of 25? Try swapping the two numbers.
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Correct answer: A
28% of 25 = 25% of 28, and 25% is a quarter: 28 ÷ 4 = 7.
Option B: 70 is ten times too big: the decimal point slipped one place.
Option C: 18 is 25 − 7, the part left over, not 28% of 25.
Option D: 28 is the percent, not the amount.
Hint: x% of y = y% of x. Which is easier: 28% of 25 or 25% of 28?
Name the rule
- 10%: move the decimal point one place left. 1%: two places.
- 5% is half of 10%; 50% is half; 25% is a quarter; 20% is a fifth.
- Build a percent by adding blocks (35% = 3 × 10% + 5%) or taking one away (95% = 100% − 5%).
- Swap: x% of y = y% of x.
- Scale: if a% of a number is v, then b% of it is v × b ÷ a.
"Of" is a multiplication, and a multiplication can be split into parts: 35% of 480 = (30% + 5%) of 480 = 30% of 480 + 5% of 480. Each block is the same whole times a smaller multiplier.
Worked, half-done, solo
Question
What is 37.5% of 640?
Solution
- Split 37.5% into blocks
37.5% = 10% + 10% + 10% + 5% + 2.5%.
- Find each block of 640
10% of 640 = 64, 5% of 640 = 32, 2.5% of 640 = 16.
- Add the blocks
64 + 64 + 64 + 32 + 16 = 240.
- Check with a fraction
37.5% = 3/8, and 640 × 3/8 = 240.
Answer: 240
Watch out: Every block must be a percent of the same number, 640. Halving the 5% block (32) gives the 2.5% block (16).
Now finish one that is half done.
What is 45% of 1,260? 50% of 1,260 = 630 and 5% of 1,260 = 63. So 45% = 50% − 5% = ...
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Correct answer: B
45% = 50% − 5%, so 630 − 63 = 567. Check: 567 + 693 = 1,260, and 693 is 55% of 1,260.
Option A: 693 adds the 5% block (630 + 63 = 693) instead of taking it away; 693 is the other 55% of 1,260.
Option C: 56.7 is ten times too small: the decimal point slipped one place.
Option D: 45 is the percent, not the amount.
Hint: Take the 5% block away from the 50% block.
And one on your own.
15% of a water tank holds 54 litres. How many litres does 40% of the tank hold?
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Correct answer: C
15% is three 5% blocks, so 5% = 54 ÷ 3 = 18 litres, and 40% = 8 × 18 = 144 litres. Check: the tank holds 360 litres, and 40% of 360 = 144.
Option A: 360 litres is the whole tank, 100%.
Option B: 79 litres adds the gap between 40 and 15 as a plain number (54 + 25 = 79). That gap is 25% of the tank.
Option D: 20.25 litres turns the scaling upside down (54 × 15 ÷ 40 = 20.25). 40% is more than 15%, so the answer must be more than 54.
Hint: Find the 5% block first: 15% is three of them.
The traps
- 5% made from 10% ÷ 5: that gives 2%. 5% is half of 10%.
- Decimal point moved the wrong number of places: one place for 10%, two places for 1%.
- A block added that should be taken away: 95% is the whole minus 5%, not 90% plus 5% of something else.
- Blocks of different wholes: every block must be a percent of the same number.
- The percent read as the amount: 15% of a bill is not ₹15.
Rohan worked out 15% of 340 as 34 + 6.8 = 40.8. What went wrong?
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Correct answer: B
10% of 340 = 34 is right. But 5% is half of 10%: 34 ÷ 2 = 17. So 15% = 34 + 17 = 51. Rohan divided 34 by 5, and 34 ÷ 5 = 6.8 is 2% of 340, not 5%.
Option A: 10% of 340 is 34: moving the decimal point one place is right.
Option C: 34 × 15 = 510 is far more than the whole 340, so it cannot be 15% of it.
Option D: 40.8 is 12% of 340 (10% + 2%), not 15%.
Hint: Is 5% half of 10%, or a fifth of it?
Mixed check
A ₹2,400 school bag is on a 12.5% discount. How many rupees off is that?
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Correct answer: C
12.5% = 10% + 2.5%. 10% of 2,400 = 240 and 2.5% of 2,400 = 60, so 240 + 60 = ₹300.
Option A: ₹30 is ten times too small: the decimal point slipped one place.
Option B: ₹240 is only the 10% block; the 2.5% block is missing.
Option D: ₹2,100 is the price you pay after the discount (2,400 − 300 = 2,100), not the discount.
Hint: 2.5% is a quarter of the 10% block.
From lesson 3:
A price rises by 25% and then falls by 25%. What is the overall change?
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Correct answer: B
1.25 × 0.75 = 0.9375, so the price ends at 93.75% of the start: a 6.25% decrease. Shortcut: 25 − 25 + 25 × (−25) ÷ 100 = −6.25.
Option A: The fall is 25% of a bigger price, so it takes away more than the rise added. They do not cancel.
Option C: A 6.25% increase has the right size but the wrong direction: 93.75% of the start is a fall.
Option D: A 25% decrease counts only the fall.
Hint: Multiply 1.25 by 0.75.
Quick reference
Percent blocks
- 10%
- move the decimal point one place left 10% of 480 = 48
- 5%
- half of the 10% block 5% of 480 = 24
- 1%
- move the decimal point two places left 1% of 480 = 4.8
- Build
- add blocks, or take one away 95% = 100% − 5%
- Swap
- x% of y = y% of x 28% of 25 = 25% of 28 = 7
- Scale
- if a% is v, then b% is v × b ÷ a 15% is 54, so 40% is 144
Why it works: "of" is a multiplication, and a multiplication can be split into blocks and added back together.
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