# Percentage: change, profit and loss, discount and GST

> These study notes explain Percentage for the Group 4 / VAO (Combined Civil Services Examination-IV) exam in plain language: the same reviewed notes the TNPSC Guide app shows, published by our editors with their source. Read the key points first, then practise the unit's questions. For exam facts such as dates and vacancies, always check tnpsc.gov.in.

Last updated: 2026-11-02 · By TNPSC Guide editorial team
URL: https://www.tnpscguide.com/exams/group-4/notes/aptitude-percentage

## Why the exam asks this

The 2024 paper had two questions: saving ₹25 at a 20% discount, find the original price (question 139), a direct use of discount% = discount / marked price × 100; 45 of 5 dozen eggs are good, find the percentage of bad eggs (question 199), where the whole (60) is the base. The 2025 paper also had two: 25% of 80 students are absent, find how many are present (question 146); boys and girls 5 : 3 with 16% and 8% failing, find the pass percentage (question 147), the same numbers and answer as Std 8 Exercise 4.1 Q10. Finding the right base is the core of these questions.

## What a percentage is

Per cent means per hundred or out of a hundred; it is written %; x% is the fraction x/100. Percentages make comparison easy: 32 out of 40 = 80% and 42 out of 50 = 84%, so the second class did better. The gap is 4 percentage points; on 80 it is 5% more. The book calls it "4% more"; do not write that in an answer. Example: if two schools pass 80% and 84% of their students, "a gap of four percentage points" is the right phrase.

## Finding the whole from a percentage

If x% of 600 is 450, then x/100 × 600 = 450 and x = 75. If 80% of the marks in an exam is 576, the maximum is 576 × 100/80 = 720. A student scored 31% and failed by 12 marks; the pass mark is 35%, so 4% = 12 and the maximum is 300. 12% of 250 litres equals 20% of 150 litres. Example: if 80% in a revision test is 576 marks, you can work back to a total of 720.

## Increase and decrease

A quantity A decreased by x% is D = (1 − x/100)A; increased by x% it is I = (1 + x/100)A. If a number decreased by 25% gives 120, then 75x/100 = 120 and the number is 160. If the price of urad dal after a 20% rise is ₹96 a kilo, then 120x/100 = 96 and the old price was ₹80. A change is always on the old value: 200 to 600 is a 200% increase; but 600 to 200 is not a 200% decrease; it is a fall of 400 on the old value 600, that is 400/600. Example: to find the old price of urad dal at the grocery after the rise, divide by 120 and multiply by 100.

## Successive change

If a number first increases by x% and then increases or decreases by y%, the total change is (x + y + xy/100)%; put a minus sign for a decrease; a minus answer means a decrease. If an income first rises by 10% and then falls by 10%: ₹100 → ₹110 → ₹99; the net change is a 1% decrease and the old value does not come back. A number increased by 25% and then decreased by 20% does not change. If P earns 25% more than Q, Q earns 20% less than P, not 25% less.

**Example: A ratio and a percentage together**

In a class the ratio of boys to girls is 5 : 3. If 16% of the boys and 8% of the girls fail, what percentage pass?

1. Boys are 5 parts and girls 3 parts; 8 parts in all.
2. The failure percentage = (5 × 16 + 3 × 8)/8.
3. Pass = 100 minus that failure percentage.

Answer: 87% (2025 question 147 uses these numbers).

## Cost price, selling price, profit and loss

The cost price (CP) is the price at which an article is bought; the selling price (SP) is the price at which it is sold. If the SP is more, profit = SP − CP; if less, loss = CP − SP. Profit and loss are always on the cost price: profit% = (profit / CP) × 100, loss% = (loss / CP) × 100. SP = ((100 + profit%) / 100) × CP; CP = (100 / (100 + profit%)) × SP; for a loss use (100 − loss%). Overhead expenses such as repairs, transport and loading charges are added to the cost price. Example: a washing machine bought for ₹16150 with ₹1350 transport costs ₹17500 in all; sold for ₹19250, the profit is ₹1750, that is 10%.

**Example: From a loss back to the cost price**

A bicycle sold for ₹4275 gives a 5% loss. At what price should it be sold for a 5% profit?

1. CP = (100 / (100 − 5)) × 4275 = ₹4500.
2. For a 5% profit, SP = ((100 + 5)/100) × 4500.

Answer: ₹4725.

## Profit and loss by number of articles

If the selling price is 5/4 of the cost price, the profit is 25%. If the CP of x articles = the SP of y articles, profit% = ((x − y)/y) × 100; a negative answer is a loss. If the CP of 16 boxes equals the SP of 20 boxes, (16 − 20)/20 × 100 = −20, that is a 20% loss. At the same selling price, x% profit on one and the same x% loss on the other always give an overall loss of x^2/100 %. If the rates differ, find both cost prices separately: two sarees sold for ₹2200 each, one at 10% profit and one at 12% loss, give an overall loss of 2 2/9 %.

## Discount

A discount is a reduction on the marked price, given in the Aadi month and in festival seasons to raise sales and clear old stock. Selling price = marked price − discount; discount% = (discount / marked price) × 100; the discount is always on the marked price. A raincoat cut from ₹1060 to ₹901 has a discount of ₹159, a rate of 15%. A cap bought for ₹210 at a 16% discount has a marked price of ₹250. Example: in an Aadi sale, the price tag at a textile shop is the marked price, and the discount is worked on it.

## Successive discounts

Two successive discounts of 25% and 20% equal a single discount of 40%: ₹100 → ₹75 → ₹60. It is not 45%. In the order 20% then 25% the answer is the same 40%. With successive discounts of a% and b%, SP = (1 − a/100)(1 − b/100) × marked price. The single discount equal to three discounts = (1 − (1 − a/100)(1 − b/100)(1 − c/100)) × 100%.

## Goods and Services Tax

The Goods and Services Tax (GST) is one common tax on most goods and services for domestic consumption in India; it is shared equally by the Centre and the State. Its kinds are the Central GST (CGST), the State GST (SGST) and the Integrated GST (IGST); in union territories, UTGST. A 5% tax on a ₹350 meal splits into 2.5% for each government: CGST = SGST = ₹8.75. The slabs and the exempt list the book prints are as of its printing; the slabs have since been changed, so this lesson does not give them. Use the rates of the examples (18%, 5%) only as rates for the sums.

**Example: From a price with tax to the marked price**

A water heater sells for ₹10502 including 18% GST. What is its marked price?

1. If the marked price is x, then x + 18x/100 = 10502, that is 118x/100 = 10502.
2. x = 10502 × 100/118 = 8900.
3. Tax = 10502 − 8900 = 1602.

Answer: marked price ₹8900, tax ₹1602. Taking 18% off 10502 gives 8611.64, which is wrong.

**Key answers**

| | |
| --- | --- |
| x% of 600 = 450 | x = 75 (page 129) |
| Decreased by 25% gives 120 | the number is 160 (page 129) |
| 80% of the marks = 576 | maximum 720 (page 129) |
| ₹96 after a 20% rise | old price ₹80 (page 130) |
| +10% then −10% | 1% decrease (page 130-131) |
| +25% then −20% | no change (page 286) |
| 5 : 3 with 16% and 8% failing | 87% pass (page 132) |
| SP = 5/4 of CP | 25% profit (page 134) |
| CP of 16 = SP of 20 | 20% loss (page 135) |
| ₹4275 at a 5% loss | CP ₹4500; ₹4725 for a 5% profit (page 135) |
| ₹1060 → ₹901 | 15% discount (page 136) |
| 25% then 20% discount | single discount 40% (page 136) |
| ₹10502 with 18% tax | marked price ₹8900 (page 137) |
| SP ₹2200 each, +10% and −12% | 2 2/9 % loss (page 286) |
| 31%, failed by 12, pass mark 35% | maximum 300 (page 286) |

> **Exam tip:** Memory hooks
"Profit on cost, discount on marked": profit and loss percentages are on the cost price, discount percentages on the marked price. "Up then down is a loss": up 10% then down 10% is a 1% decrease. "Do not add discounts, multiply": 75% × 80% = 60%, so the single discount is 40%. "Divide a tax-inclusive price by 118". "25 more means 20 less".

**Easy to confuse**

| | |
| --- | --- |
| Profit or loss percentage / discount percentage | on the cost price; on the marked price |
| A 10% rise then a 10% fall / no change | a 1% decrease; the old value does not come back |
| 25% + 20% discount / the single discount | not 45%; 40% |
| 200 to 600 / 600 to 200 | a 200% increase; not a 200% decrease (400/600) |
| P earns 25% more than Q / how much less Q earns than P | 25%; 20% |
| Same SP with the same x% profit and loss / different rates | always an x^2/100 % loss; find both cost prices separately |
| Marked price from a tax-inclusive price / taking off 18% | divide by 118 and multiply by 100 (8900); 8611.64 is wrong |
| 80% to 84% / "4% more" | a rise of 4 percentage points, 5% more on 80; do not give "4% more" as the answer; the book calls it right |

> **Exam tip:** Quick check
1. If x% of 600 is 450, x = ? Answer: 75.
2. A number rises by 10% and then falls by 10%; the net change? Answer: a 1% decrease.
3. The single discount equal to successive discounts of 25% and 20%? Answer: 40%.
4. A price cut from ₹1060 to ₹901 is what rate of discount? Answer: 15%.
5. If P earns 25% more than Q, what percentage less than P does Q earn? Answer: 20%.

Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (8ஆம் வகுப்புக் கணக்கு, இயல் 4 வாழ்வியல் கணிதம் (4.1-4.3), பக்கம் 127-137, விடைகள் பக்கம் 286)

## Sources

- [Official syllabus page](https://www.tnpsc.gov.in/english/syllabus.html)
- [Notifications](https://www.tnpsc.gov.in/English/Notification.aspx)