← Maths

Discount

Competitive Mathematics · Arithmetic

6 Part3 worked examples13 practice questions

A shop board says “Jacket ₹2,000 — 30% off”. ₹2,000 is the jacket’s marked price (MP), the price on the label. The customer actually pays less; the amount knocked off is the discount and the price paid is the selling price (SP). One rule runs through the whole chapter in three forms: a discount is always on the marked price, never on the cost price.

The three formulas
1

Marked price, discount and selling price

MP · discount · SP

Finding the third when two of these are given, and the rate of discount.

Three things, one formula

MP, SP, rate

Finding the SP, the MP and the rate of discount.

The multiplier method: an discount means the buyer pays **** of the marked price. For 15% off the multiplier is 0.85; for 40% off 0.60. SP = MP × multiplier; MP = SP ÷ multiplier. (This mirrors profit and loss — only the base is the MP, not the CP.)

Example 1 · Basic
A chair marked ₹2,400 is given at a 25% discount. What is the selling price?
Solution, step by step
  1. 1Discount of .
  2. 2SP
Answer ₹1,800
Example 2 · Standard
After a 15% discount a suit sold for ₹3,740. What was its marked price?
Solution, step by step
  1. 1SP of MP ⟹ MP .
  2. 2
Answer ₹4,400
Example 3 · Standard
An article marked ₹5,600 sold for ₹4,760. What was the rate of discount?
Solution, step by step
  1. 1Discount .
  2. 2Rate
Answer 15%
BasicTry it yourself first
An article is marked at ₹1,500 and a 20% discount is allowed. What is the selling price?
BasicTry it yourself first
An article is marked at ₹640 and a 35% discount is allowed. What is the selling price?
StandardTry it yourself first
An article is marked at ₹4,800 and a 12.5% discount is allowed. What is the selling price?
AdvancedTry it yourself first
An article is marked at ₹7,250 and a 18% discount is allowed. What is the selling price?
BasicTry it yourself first
After a 10% discount an article sold for ₹720. What was its marked price?
StandardTry it yourself first
After a 30% discount an article sold for ₹3,150. What was its marked price?
StandardTry it yourself first
After a 15% discount an article sold for ₹2,142. What was its marked price?
AdvancedTry it yourself first
After a 12.5% discount an article sold for ₹5,145. What was its marked price?
BasicTry it yourself first
An article marked ₹500 sold for ₹400. What was the rate of discount?
StandardTry it yourself first
An article marked ₹2,400 sold for ₹2,040. What was the rate of discount?
AdvancedTry it yourself first
An article marked ₹4,750 sold for ₹3,990. What was the rate of discount?
StandardTry it yourself first
Paying an electricity bill before the due date gives a 4% reduction. A man got a reduction of ₹260. What was the amount of the bill?
AdvancedTry it yourself first
Paying an electricity bill before the due date gives a 6% reduction. A man got a reduction of ₹525. What was the amount of the bill?
2

Successive discounts

A discount on a discount

When several discounts are given one after another, and their single equivalent.

Working out successive discounts

Each discount on what is left

Finding the SP and the single equivalent discount: .

🔒

Comparing offers and “free” schemes

Which one is cheaper

Single versus successive discounts, and turning “buy get free” into a discount.

🔒
3

Discount together with profit and loss

The CP–MP–SP relation

A shopkeeper first marks the price above cost and then gives a discount — the two per cents have different bases.

Mixed questions

The SP–MP–profit loop

When both prices are given for an article and one unknown must be found.

🔒
4

Traps and fast tricks

Slips · tricks

Where most marks are lost in discount questions.

The commonest mistakes

Six traps

The slips that cost marks.

🔒

Fast tricks

Multipliers and assuming 100

Tricks that shorten the work.

🔒
5

The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

🔒

Level 2 — Standard

Two ideas combined

Exam-level questions.

🔒

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

🔒
6

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.

🔒