Percentage - REET Maths Notes
Percentage is one of the most practical topics in REET Maths, extending from area changes to mixed fraction-percentage calculations. This page presents every formula, the conversion table, and REET 2024's solved questions.
- 2 questions in REET 2024
- Class 7-8 level
- 6 min read
How REET asks this topic
REET 2024 had one question asking for the percentage increase in area when a square's side increases by 25% (the answer is 56.25%, not simply 50%), and another based on comparing mixed fraction-percentage values (like '20% of 1/2'). In other words, instead of simply asking 'what is Y% of X', the concept is tested by combining it with measurement and fractions.
Fraction-decimal-percentage conversion table
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
| 1/6 | 0.1666... | 16.67% |
| 2/3 | 0.666... | 66.67% |
| 3/4 | 0.75 | 75% |
| 2/5 | 0.4 | 40% |
| 3/8 | 0.375 | 37.5% |
| 1/9 | 0.111... | 11.11% |
Memorising this table makes mental maths calculations many times faster.
Formula for percentage change
If two successive percentage changes (x% and y%) are applied to a quantity, the formula for the total net change is: net% = x + y + (xy/100). x and y are taken as positive for an increase and negative for a decrease.
When the side of a square is increased by x%, since area = side^2, and both 'increases' are equal to x, the net increase in area = 2x + x^2/100. In REET 2024's question, x=25: 2x25 + 25^2/100 = 50 + 6.25 = 56.25% - this is the correct answer.
You can also verify this by direct calculation: let the side be a, so area = a^2. When the side increases by 25%, the new side is 1.25a, and the new area is (1.25a)^2 = 1.5625a^2 - a 56.25% increase in area, which matches the formula.
Worked example: percentage of a fraction
REET 2024's question asked for the value of '20% of 1/2 + 30% of 1/3'. 20% of 1/2 = 1/2 x 20/100 = 10/100 = 0.1. 30% of 1/3 = 1/3 x 30/100 = 10/100 = 0.1. Their sum = 0.2. Among the options, '50% of 2/5' = 2/5 x 50/100 = 1/5 = 0.2, which matches the sum - so this is the correct answer.
Reverse percentage
Sometimes you're given the value after a discount or increase and asked for the original (marked) value - this is called reverse percentage. The general approach: if final value = original value x (1 +/- percentage/100), then original value = final value / (1 +/- percentage/100).
Example: if a 20% discount brings an item's selling price to Rs 800, what was the marked (original) price? Here 800 = original price x (1-20/100) = original price x 0.8, so original price = 800 / 0.8 = Rs 1,000. This type of question is also connected to the profit-and-loss and discount topics.
Another example: if a 25% discount brings an item's selling price to Rs 1,500, what was the marked price? Here 1500 = original price x (1-25/100) = original price x 0.75, so original price = 1500 / 0.75 = Rs 2,000. Similarly, for increase-based questions, the sign would be positive (+).
Percentage error
- Formula
- Percentage error = (|measured value - actual value| / actual value) x 100
- Example
- A rod's actual length is 50 metres, but it measures 51 metres. Error% = (1/50)x100 = 2%.
Percentage points vs percentage change
If the pass percentage in an exam rises from 40% to 50%, this increase is called '10 percentage points', not '10% increase'. The actual relative percentage increase = (10/40)x100 = 25%. It's important to read this distinction carefully in exam questions, because the two numbers are entirely different.
How to teach this to children
Classroom activity
In Classes 7-8, colour in a 10x10 grid (100 squares) to show percentages - for example, colouring 25 squares shows 25%. Follow this up by solving real-life examples like a shop bill or a discount.
Teaching aids
Hang the three-column fraction-decimal-percentage table (like the one above) as a chart in class, so children can convert quickly between all three forms.
Common misconception
Children often think that increasing something by x% and then decreasing it by x% brings you back to the original amount - whereas in fact, the net change is always (-x^2/100)%, i.e. a loss, never zero (unless x=0).
Assessment idea
Have students practise converting their own actual exam marks into percentages - this connects directly to their day-to-day life.
Cross-curricular link
In social studies class, use real data like literacy rates or population growth rates to have students calculate percentages - this helps students see percentage as more than just a maths concept.
Trick to remember / exam tip
'x% of y' always equals 'y% of x' - swapping the order makes calculation easier. For example, if finding 8% of 50 feels hard, think of it instead as 50% of 8, i.e. half of 8 = 4. Both methods give the same answer of 4, but the second one is much faster mentally.
Questions asked in REET 2024 (with solutions)
Question 93
If the side of a square is increased by 25%, its area will increase by :
- A56.25%
- B66.25%
- C25%
- D125.25%
Explanation
माना भुजा a है, तो क्षेत्रफल a²। भुजा 25% बढ़ने पर नई भुजा 1.25a और नया क्षेत्रफल (1.25a)² = 1.5625a² होगा। अतः क्षेत्रफल में वृद्धि = 56.25%। सूत्र से भी: x + y + xy/100 = 25 + 25 + 625/100 = 56.25%।
Question 107
20% of 1/2 + 30% of 1/3 is equal to
- A5/6 का 50%
- B1/4 का 40%
- C1/5 का 50%
- D2/5 का 50%
Explanation
1/2 का 20% = 0.1 और 1/3 का 30% = 0.1, अतः योग = 0.2। विकल्पों में: 5/6 का 50% = 5/12 ≈ 0.417, 1/4 का 40% = 0.1, 1/5 का 50% = 0.1, जबकि 2/5 का 50% = 1/5 = 0.2। इसलिए उत्तर (D) है।
Practice Questions
Question 1
Convert 3/4 into a percentage.
- A70%
- B75%
- C80%
- D72%
Explanation
3/4 x 100 = 75%.
Question 2
Write 40% as a fraction in simplest form.
- A2/5
- B4/5
- C1/4
- D2/10
Explanation
40% = 40/100 = 2/5 (in simplest form).
Question 3
What is 20% of 250?
- A40
- B45
- C50
- D55
Explanation
250 x 20/100 = 50.
Question 4
15% of a number is 45. What is the number?
- A270
- B300
- C320
- D330
Explanation
Number = 45 / (15/100) = 45 x 100/15 = 300.
Question 5
If the price of an item is first increased by 20% and then decreased by 20%, the net change will be:
- Aकोई परिवर्तन नहीं
- B4% वृद्धि
- C4% कमी
- D40% कमी
Explanation
Net% = 20 + (-20) + (20x-20)/100 = 0 - 4 = -4%, i.e. a 4% decrease.
Question 6
If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, the change in area will be:
- Aकोई परिवर्तन नहीं
- B1% वृद्धि
- C1% कमी
- D20% कमी
Explanation
Net% = 10 + (-10) + (10x-10)/100 = 0 - 1 = -1%, i.e. a 1% decrease in area.
Question 7
15 is what percent of 60?
- A20%
- B25%
- C15%
- D30%
Explanation
(15/60)x100 = 25%.
Question 8
A class has 40 students, of which 60% are girls. How many boys are there in the class?
- A14
- B16
- C18
- D24
Explanation
Girls = 60% of 40 = 24; boys = 40-24 = 16.
Question 9
What is the value of 60% of 1/5 plus 40% of 1/4?
- A0.20
- B0.22
- C0.24
- D0.18
Explanation
60% of 1/5 = 0.2x0.6=0.12; 40% of 1/4 = 0.25x0.4=0.1; sum = 0.22.
Question 10
Which is the most suitable activity to teach the concept of percentage to Class 7-8 students by connecting it to daily life?
- A100 खानों वाली ग्रिड रंगकर प्रतिशत दिखाना और वास्तविक बाज़ार बिल/छूट के उदाहरण हल कराना
- Bकेवल परिभाषा याद कराना
- Cबिना उदाहरण के सूत्र बोर्ड पर लिखना
- Dप्रतिशत को पूर्णतः छोड़ देना
Explanation
A 100-square grid helps children see the visual meaning of percentage, and solving real bill/discount examples connects this knowledge to everyday life.
Frequently Asked Questions
How many questions come from Percentage in REET?+
REET 2024 had 1-2 questions from this topic in the Maths section, based on percentage change in area and mixed fraction-percentage calculations.
What's the net formula for two successive percentage changes?+
Net% = x + y + (xy/100), where positive signs are used for increases and negative signs for decreases.
When the side of a square increases by x%, how much does the area increase?+
The net increase in area is 2x + x^2/100 percent, because area is the square of the side.
How do you convert a percentage to a fraction?+
Divide the percentage by 100 and write it in its simplest form - for example, 40% = 40/100 = 2/5.
How is percentage error calculated?+
Percentage error = (|measured value - actual value| / actual value) x 100 - this shows the error in a measurement as a percentage.
What is reverse percentage?+
When the final value (like the selling price after a discount) is given and you're asked for the original value, it's found using original value = final value / (1 +/- percentage/100).
What's the difference between percentage points and percentage change?+
A percentage point is the direct difference between two percentage values (like 40% to 50%, i.e. 10 percentage points), while percentage change is that difference expressed relative to the original value (here, 25%).
What part of a number does 100% represent?+
100% represents the whole (entire) value of a number - that is, 100% of x equals x.
Can a percentage be more than 100?+
Yes, when a quantity is more than the original amount (like a profit or increase of more than 100%), the percentage can also exceed 100 - this is not impossible or wrong, just a normal mathematical situation.
If an amount is increased by 10% and then increased by another 10%, what is the total increase?+
Using the formula net% = x+y+(xy/100) with x=y=10: 10+10+(10x10/100) = 20+1 = 21%, i.e. a total increase of 21%, not 20%.
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- 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked