Puzzle First 1: Build any percent from blocks
No rules yet. Try each puzzle, even if you guess. The rule will come out of your own answers.
Before the puzzles: the basic words
These are not rules for the puzzles, just the meaning of the words. You will discover the rules yourself.
1. What is a percent? "Per cent" means per hundred. 35% means 35 out of every 100. Think of ₹100 as 100 coins of ₹1. If you spend 35 of the coins, you spent 35 out of 100, which is 35% of your money. On a 100-square grid each square is 1%, so 35% is 35 shaded squares:
███████████████████████████████████·································································
Text version: 35 of the 100 squares are shaded (35%); 65 are not (65%).
2. What does "of" mean? "Of" tells you which thing the percent is taken from. "35% of ₹200" means: cut ₹200 into 100 equal pieces (each piece is ₹200 ÷ 100 = ₹2) and take 35 pieces: 35 × ₹2 = ₹70.
3. Whole and part. The number after "of" is the whole: all of it, 100%. A part is a piece of the whole. The rest is what is left: whole − part, which is (100 − percent)%. In the example: whole ₹200, part ₹70 (35%), rest ₹130 (65%).
4. The one tool you will use in every question: find 1% first. 1% of anything = that thing ÷ 100. From 1% you can build any percent (multiply by the percent) or get back to the whole (multiply by 100). Try it now: 1% of ₹300 = 300 ÷ 100 = ₹3, so 35% of ₹300 = 35 × 3 = ₹105.
Words to know
- Percent (%)
- out of every 100 35% = 35 out of 100
- Whole
- the number after 'of' = 100% ₹200 in '35% of ₹200'
- Part
- a piece of the whole ₹70 = 35% of ₹200
- Rest
- whole − part ₹130 = 65% of ₹200
- 1%
- whole ÷ 100 1% of ₹200 = ₹2
Puzzle 1
Puzzle: 10% of a number is 14. What is 30% of the same number?
Show answer
Correct answer: B
You never needed the number itself: 30% of it = 3 × (10% of it) = 3 × 14 = 42.
Option A: Answered the whole: 140 is the whole number (100%).
Option C: Percent read as units: Adding 30 to 14 mixes a percent with units.
Option D: Decimal slip: 4.2 is only 3% of the number (a decimal slip).
Hint: How many 10%s make 30%?
What did you just do?
- You treated 10% of the number as a block worth 14.
- You counted blocks: 30% of the number is 3 blocks = 42.
- The whole number is 10 blocks = 140, but you never needed it.
Puzzle 2: run it backwards
Twist: 15% of a number is 21. What is the number?
Show answer
Correct answer: D
We know: 15% of the number = 21. Step 1: 1% = 21 ÷ 15 = 1.4 (or 5% = 21 ÷ 3 = 7). Step 2: 100% = 1.4 × 100 = 140 (or 20 × 7 = 140). Check: 15% of 140 = 21 ✓.
Option A: Took percent of the part: 3.15 is 15% of 21.
Option B: Multiplied by the percent: 21 × 15 multiplies by the percent.
Option C: Wrong fraction: 105 = 21 × 5 treats 15% as one fifth; one fifth is 20%.
Hint: What is 5%?
Puzzle 2, solved slowly
Whatever you answered, here is the same puzzle as a story, one small step at a time.
Question
15% of a number is 21. What is the number?
Solution
- What is the question asking?
- ₹21 is only a part. It is 15% of a bigger amount.
- We must find that bigger amount: the whole, which is 100%.
- Make it a story
- You save 15% of your monthly pocket money. This month you saved ₹21. How much pocket money do you get?
- We know / We need
- We know: 15% of your pocket money = ₹21
- We need: 100% of your pocket money = ?
- Step 1: find 1%
- 15% of your pocket money = ₹21
- 15% means 15 equal pieces of 1%. Share ₹21 equally among 15 pieces.
- 1% of your pocket money = 21 ÷ 15 = ₹1.4
- Step 2: find 100%
- 1% of your pocket money = ₹1.4
- 100% is 100 such pieces: 100% of your pocket money = 1.4 × 100 = ₹140
- See it on a bar
███░░░░░░░░░░░░░░░░░each block = 5% of your pocket money- █ 15% = ₹21 (saved)
- ░ 85% = ₹119 (spent)
- Whole bar = 100% = ₹21 + ₹119 = ₹140
- Shortcut (only after you understand)
- Whole = Part × 100 ÷ Percent = 21 × 100 ÷ 15 = 140
- Faster way (optional): Use blocks: 15% = 3 × 5%. So 5% = 21 ÷ 3 = ₹7, and 100% = 20 × 5% = 20 × 7 = ₹140.
- Quick check
- 15% of ₹140 = 140 × 15 ÷ 100 = ₹21 ✓
- Part + rest = 21 + 119 = 140 ✓
Answer: ₹140, so the number is 140
Watch out: Most important concept: ₹21 is only a PART of your pocket money. Work backward from the part to the whole (100%). Do not calculate 15% of 21: that gives 3.15, which is even smaller than the part.
Test your understanding: 24 is 30% of which number?
Show answer
Correct answer: A
We know: 30% of the number = 24. Step 1: 1% = 24 ÷ 30 = 0.8 (or 10% = 24 ÷ 3 = 8). Step 2: 100% = 0.8 × 100 = 80. Check: 30% of 80 = 24 ✓.
Option B: Took percent of the part: 7.2 is 30% of 24. But 24 is the part; the whole must be bigger than 24.
Option C: Added the percent: 54 = 24 + 30 adds a percent to a number of units.
Option D: Multiplied by the blocks: 72 = 3 × 24 multiplies by the number of 10% blocks instead of dividing by it.
Hint: 30% is three 10% blocks. Find one block first.
Puzzle 3: swap
Notice: 18% of 50 and 50% of 18. Which is bigger?
Show answer
Correct answer: A
x% of y = x × y ÷ 100 = y% of x. Swap whenever one side is easier.
Option B: Thought order matters: Both equal 9.
Option C: Thought order matters: Both equal 9.
Option D: Gave up early: Both can be computed: 9 and 9.
Hint: Compute 50% of 18.
What you discovered (the shortcuts)
- Blocks
- 10% = ÷10, 5% = half of that, 1% = ÷100 35% of 60 = 18 + 3 = 21
- Backwards
- find 1% (or one block), then scale to 100% 15% of x = 21 → 5% of x = 7 → x = 140
- Swap
- x% of y = y% of x 18% of 50 = 50% of 18 = 9
A percent is a count of hundredths of something. Find 1% (or one easy block) of that something, then count blocks. When a part is given, work backward to 100%.
Five questions are attached below. Try them before rereading anything: remembering is the practice.
Sign in to keep your progress. Sign in