Per hundred: find the part, the percent or the whole
A percent counts hundredths: 35% means 35 parts out of every 100. In this lesson you find 1% first and build everything from it, so one method answers all three basic questions: the part, the percent and the whole.
Guess first
Before any rule, try this with common sense.
Guess first: a school bag costs ₹800. Shop A takes ₹120 off. Shop B takes 12% off. How many rupees does Shop B take off?
Show answer
Correct answer: B
12% means ₹12 off for every ₹100 of the price. ₹800 = 8 × 100, so Shop B takes 8 × 12 = ₹96 off. Shop A's ₹120 off is the bigger saving, even though "12%" sounds large.
Option A: 12% is not ₹12. It is ₹12 for every ₹100 of the price, and this price has 8 hundreds.
Option C: ₹704 is what you still pay at Shop B (800 − 96 = 704), not the amount taken off.
Option D: ₹960 is ten times too big: the decimal point slipped one place to the right.
Hint: How many hundreds are there in ₹800? Each hundred gives ₹12 off.
If you chose ₹96, you already used the whole method: you split the price into hundreds and took 12 from each. This lesson writes that method down, so it still works when the numbers are not round.
An everyday picture
A percent is like paise in a rupee: the rupee is the whole, cut into 100 equal parts.
₹1 = 100 paise 100%
the whole: all 100 parts
25 paise 25%
25 parts out of 100, a quarter of the rupee
1 paisa 1%
one part out of 100: every question starts here
So "35% of a price" means: cut the price into 100 equal parts and take 35 of them. The word of tells you which thing is cut: the number after "of" is the whole, 100%.
See it: the 1% ladder
Take a monthly phone plan of ₹600. Climb down to 1%, then up to any percent you need.
| Share of ₹600 | How you get it | Amount |
|---|---|---|
| 100% | the whole | ₹600 |
| 1% | 600 ÷ 100 = 6 | ₹6 |
| 7% | 7 × 6 = 42 | ₹42 |
| 35% | 35 × 6 = 210 | ₹210 |
flowchart TD W["₹600 = 100%, the whole"] -->|"÷ 100"| O["₹6 = 1%"] O -->|"× 35"| P["₹210 = 35%, a part"] O -->|"× 7"| S["₹42 = 7%, a smaller part"]
The same ladder in words: the whole is ₹600; one hundredth of it, 1%, is ₹6; 35 of those hundredths make ₹210, and 7 of them make ₹42.
Three questions, one ladder:
- Find the part: 35% of ₹600. Go down to 1% (₹6), then up: 35 × 6 = 210, so the part is ₹210.
- Find the percent: ₹42 out of ₹600. 1% is ₹6, and 42 ÷ 6 = 7, so ₹42 is 7%.
- Find the whole: ₹42 is 7% of a price. 1% = 42 ÷ 7 = 6, so 100% = 6 × 100 = 600: the price is ₹600.
Try it on paper. Take your last test: the marks you scored and the total marks. Find 1% of the total (total ÷ 100), then count how many of those 1% pieces fit into your score. That count is your percentage.
Find the rule
Three quick checks on the same ₹600 plan. Each one hides a different number.
1% of ₹600 is ₹6. What is 9% of ₹600?
Show answer
Correct answer: A
9% is 9 pieces of 1%. So 9 × 6 = ₹54.
Option B: 9% is not ₹9. It is 9 pieces of the ₹6 piece.
Option C: ₹546 is what is left of ₹600 after taking 9% away (600 − 54 = 546).
Option D: ₹540 is ten times too big: the decimal point slipped one place to the right.
Hint: 9% means 9 pieces of the 1% piece.
1% of ₹600 is ₹6. ₹42 is what percent of ₹600?
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Correct answer: B
Count the 1% pieces in ₹42: 42 ÷ 6 = 7. So ₹42 is 7% of ₹600.
Option A: 93% is the share of ₹600 left after taking ₹42 away, not the share ₹42 makes.
Option C: 42 ÷ 600 = 0.07 is the answer as a decimal. As a percent it is 0.07 × 100 = 7%.
Option D: 70% would be 70 × 6 = ₹420, not ₹42. The decimal point slipped one place.
Hint: How many ₹6 pieces fit into ₹42?
₹42 is 7% of a price. What is the price?
Show answer
Correct answer: C
7% is 7 pieces of 1%, so 1% = 42 ÷ 7 = ₹6. The whole is 100 pieces: 100 × 6 = ₹600.
Option A: ₹6 is only 1% of the price. You stopped one step early: the price is 100 such pieces.
Option B: ₹2.94 is 7% of ₹42, but ₹42 is already the 7% piece. Taking a percent of the part makes the answer smaller than the part.
Option D: ₹294 multiplies 42 by 7. The 7% must be shared out to find 1%, so divide by 7.
Hint: Share ₹42 equally among 7 pieces of 1%.
Name the rule
Every basic percent question links three numbers: the whole (100%), the percent, and the part.
part = whole × percent ÷ 100
The question hides one of the three numbers. Find 1% of whatever you know, and build the rest.
| You know | You want | Do this |
|---|---|---|
| whole, percent | part | whole ÷ 100, then × percent |
| part, whole | percent | part ÷ whole, then × 100 |
| part, percent | whole | part ÷ percent, then × 100 |
"35% of ₹600" means 35 hundredths of ₹600: ₹600 ÷ 100 × 35. A percent is a multiplier: 35% multiplies by 35/100 = 0.35. You will use this one idea in every later lesson.
Worked, half-done, solo
Question
A class test has 60 marks. Ritu scores 51. What percent did she score?
Solution
- Name the three numbers
The whole (100%) is 60 marks. The part is her 51 marks. The percent is missing.
- Find 1% of the whole
60 ÷ 100 = 0.6 marks.
- Count the 1% pieces in the part
51 ÷ 0.6 = 85, so 51 marks is 85%.
- Check the other way
85% of 60 = 51 marks.
Answer: 85%
Watch out: Divide by the whole (60), not by the part. A part smaller than the whole is always below 100%.
Now finish one that is half done.
A fan seller says that ₹45 is 15% of the fan's price. So 1% of the price = 45 ÷ 15 = ₹3. What is the price?
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Correct answer: B
1% is ₹3, and the price is 100%: 100 × 3 = ₹300. Check: 15% of ₹300 = ₹45.
Option A: ₹6.75 is 15% of ₹45, but ₹45 is already the 15% piece.
Option C: ₹3 is only 1% of the price. Go up to 100%.
Option D: ₹675 multiplies 45 by 15. Divide by the percent to reach 1%, then multiply by 100.
Hint: The price is 100 pieces of the 1% piece.
And one on your own.
A train has 1,250 seats, and 8% of them are kept for senior citizens. How many seats is that?
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Correct answer: C
1% of 1,250 = 12.5 seats, so 8% = 8 × 12.5 = 100 seats.
Option A: 1,150 is the number of other seats (1,250 − 100 = 1,150), not the kept seats.
Option B: 10 is ten times too small: the decimal point slipped one place to the left.
Option D: 8 is the percent, not the number of seats.
Hint: Find 1% of 1,250 first.
The traps
- Wrong base: in "what percent of", divide by the whole (the number after "of"), not by the part.
- Percent of the part: when the given number is already the percent piece, taking that percent of it gives an answer smaller than the part.
- The rest, not the part: whole minus part answers a different question.
- Percent read as money: 12% of ₹800 is not ₹12.
- Stopped at 1%: finding 1% is the middle of the ladder, not the end.
Asked "24 is what percent of 96?", Kavya wrote 96 ÷ 24 × 100 = 400%. What went wrong?
Show answer
Correct answer: B
The whole is 96, the number after "of". The right working is 24 ÷ 96 × 100 = 25%. A part smaller than the whole cannot be 400%.
Option A: 96 − 24 = 72 is the rest, not a percent.
Option C: She did multiply by 100. The problem is what she divided.
Option D: 400% would mean 24 is four times 96. It is a quarter of 96.
Hint: Which number comes after "of"?
Mixed check
A farmer sold 35% of his wheat. That was 420 kg. How much wheat did he have?
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Correct answer: B
35% is 420 kg, so 1% = 420 ÷ 35 = 12 kg, and 100% = 12 × 100 = 1,200 kg. Check: 35% of 1,200 = 420.
Option A: 147 kg is 35% of 420, but 420 kg is already the 35% piece.
Option C: 567 kg adds 35% of 420 to 420. The 420 kg is a part of the whole, not something to grow by 35%.
Option D: 12 kg is only 1% of the wheat.
Hint: 420 kg is a part. Find 1% of the whole first.
Meena gets ₹1,500 pocket money a month and saves ₹225. What percent does she save?
Show answer
Correct answer: C
1% of 1,500 = 15, and 225 ÷ 15 = 15. So she saves 15%. Check: 15% of 1,500 = 225.
Option A: 85% is the share she spends, not the share she saves.
Option B: 150% is ten times too big: the decimal point slipped one place to the right.
Option D: 666⅔% divides 1,500 by 225. The whole is ₹1,500, so divide by 1,500.
Hint: Divide the saving by the whole pocket money.
Quick reference
Part, percent and whole
- Percent
- parts per hundred 35% = 35/100
- 1% of a whole
- whole ÷ 100 1% of ₹600 = ₹6
- Find the part
- whole ÷ 100 × percent 35% of ₹600 = ₹210
- Find the percent
- part ÷ whole × 100 ₹42 of ₹600 = 7%
- Find the whole
- part ÷ percent × 100 ₹42 is 7%, so ₹600
Why it works: a percent is a count of hundredths, so 1% is the unit. Go down to 1%, then up to what you need.
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