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Percentage: change, profit and loss, discount and GST

By TNPSC Guide editorial team · Last updated:

Key numbers

Key answers

x% of 600 = 450x = 75 (page 129)
Decreased by 25% gives 120the number is 160 (page 129)
80% of the marks = 576maximum 720 (page 129)
₹96 after a 20% riseold 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% failing87% pass (page 132)
SP = 5/4 of CP25% profit (page 134)
CP of 16 = SP of 2020% loss (page 135)
₹4275 at a 5% lossCP ₹4500; ₹4725 for a 5% profit (page 135)
₹1060 → ₹90115% discount (page 136)
25% then 20% discountsingle discount 40% (page 136)
₹10502 with 18% taxmarked 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)

Easy to confuse

Profit or loss percentage / discount percentageon the cost price; on the marked price
A 10% rise then a 10% fall / no changea 1% decrease; the old value does not come back
25% + 20% discount / the single discountnot 45%; 40%
200 to 600 / 600 to 200a 200% increase; not a 200% decrease (400/600)
P earns 25% more than Q / how much less Q earns than P25%; 20%
Same SP with the same x% profit and loss / different ratesalways 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
The full note

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.

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)

PYQ (2012-2025 papers)

Provisional key: until TNPSC publishes the final key; the answer may change.

Free questions

  1. Question 1

    Consider the following statements on successive percentage changes. 1. Increasing a number by 25% and then decreasing it by 20% leaves it unchanged. 2. An income that rises by 10% and then falls by 10% is unchanged. 3. If P's income is 50% more than Q's, then Q's income is 33⅓% less than P's. Which of these are correct?

    1. A. 1 only
    2. B. 1 and 2 only
    3. C. 1 and 3 only
    4. D. 1, 2 and 3
    Answer and explanation

    Correct answer: C. 1 and 3 only

    25 − 20 − 25 × 20/100 = 0, so 1 is correct; 10 − 10 − 10 × 10/100 = −1, a 1% decrease, so 2 is wrong; with Q = 100, P = 150 and 50/150 × 100 = 33⅓%, so 3 is correct.

    Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (விடைகள் (பயிற்சி 4.1, 4.2, 4.5), p. 286 (PDF p. 292))

  2. Question 2

    Write 45% as a fraction in its lowest form.

    1. A. 9/20
    2. B. 45/10
    3. C. 4/5
    4. D. 9/2
    Answer and explanation

    Correct answer: A. 9/20

    Per cent means per hundred; x% = x/100: 45% = 45/100 = 9/20.

    Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம், p. 128 (PDF p. 134))

  3. Question 3

    In one class 32 of 40 pupils took part in a contest, and in another class 42 of 50. Consider the following statements. 1. The first class took part at 80% and the second at 84%. 2. The second class is ahead by 4 percentage points. 3. A rise from 80 to 84 is a 4% rise on 80. Which of these are correct?

    1. A. 1 only
    2. B. 1 and 3 only
    3. C. 1, 2 and 3
    4. D. 1 and 2 only
    Answer and explanation

    Correct answer: D. 1 and 2 only

    32/40 × 100 = 80% and 42/50 × 100 = 84%; the gap is 4 percentage points (the book, p. 127, calls it "4% more"); but a rise from 80 to 84 is 4/80 × 100 = 5%, not 4%; so 1 and 2 are correct and 3 is wrong.

    Source: கணக்கு, எட்டாம் வகுப்பு, தமிழ் வழி (Mathematics, Standard VIII, Tamil medium; Samacheer Kalvi) (இயல் 4 வாழ்வியல் கணிதம், p. 127 (PDF p. 133))

The unit's 20 free questions

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Frequently asked questions

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?

87% (2025 question 147 uses these numbers).

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

₹4725.

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

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

Full guide: TNPSC Group 4 Part C Aptitude: 25 questions, 2 units and how to practise them

Sources

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