SSC CGL Maths · Percentage, Profit and Loss

Successive Discounts and Offers

Two or more discounts one after another, and offers such as 'buy 5, get 2 free', each turned into a single equal discount so they can be priced and compared.

All Percentage, Profit and Loss notes

Why this matters

54 questions in the bank and 47 of them EASY, so this is the quickest page in the chapter to master. The work is always the share of the price that is kept, multiplied through. The only real traps are adding discounts and reading a free-item offer over the wrong total.

Concept 1 of 3: Single discount equal to successive discounts

The second discount is taken on the price that is already reduced, so it saves less than it would on the marked price. Two discounts of a% and b% therefore add up to less than

(a + b)\%

Definition

Price paid $= MP\left(1 - \frac{a}{100}\right)\left(1 - \frac{b}{100}\right)$ .
Single equal discount $= a + b - \frac{ab}{100}$ per cent.
For three discounts, combine two with the formula and then combine that result with the third.
The order of the discounts does not change the final price.
Fast route: multiply what is kept. Discounts of 20% and 25% keep $0.8 \times 0.75 = 0.6$ of the price, so the single discount is 40%.

Equal single discount

D = a + b - \frac{ab}{100}

a, bthe two successive discounts, in per cent

Worked example

Find the single discount equal to successive discounts of 20% and 15%.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 23 Sep 2025, Shift 3 · Q66Easy

Example 1 · Percentage, Profit and Loss · Successive Discounts and Offers

A wholesaler offers a bulk order deal where a 10% discount is applied to orders above Rs. 15,000, and a 5% additional seasonal discount is available. What is the effective price paid for an order worth Rs. 20,000?

Adding successive discounts

Discounts of 30% and 20% one after the other are a single discount of 44%, not 50%.

Giving the share paid as the discount

If the buyer pays 0.528 of the marked price, the single discount is 47.2%, not 52.8%. Subtract the kept share from 1.

Drill 25 more on single discount equal to successive discounts

Concept 2 of 3: Finding a missing discount or the bill

If you know the marked price, the final price and one discount, the other discount is whatever share is still missing. If you know how far apart two discount schemes are in rupees, that gap is a known percentage of the bill.

Definition

Missing second discount: find the price after the first discount, then second discount $= \frac{\text{price after first} - \text{final}}{\text{price after first}} \times 100$ .
Missing first discount: divide the final price by the second factor to get the price after the first.
Gap between schemes: a single discount D and successive discounts with equal single discount $D_{eq}$ differ by $(D - D_{eq})\%$ of the bill, so bill $=$ rupee gap $\div \frac{D - D_{eq}}{100}$ .
Missing third discount: the product of the kept factors equals $1 - \frac{\text{single discount}}{100}$ .

Bill from the gap between two schemes

\text{bill} = \frac{\text{rupee gap}}{(D - D_{eq}) / 100}

Worked example

A bag marked ₹2,500 is sold for ₹1,800 after two successive discounts. The first discount is 20%. Find the second.

Practice this conceptself-check · 2 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 16 Sep 2025, Shift 1 · Q61Easy

Example 2 · Percentage, Profit and Loss · Successive Discounts and Offers

A television set has a marked price of ₹ 20,000. It is sold after two successive discounts. If the first discount is 15% and the final selling price is ₹ 15,300, what is the percentage of the second discount?

Taking the second discount on the marked price

The second discount is a share of the price after the first one. ₹1,200 down to ₹900 with a first 10% leaves a second discount of 180 out of 1,080, which is

16\frac{2}{3}\%

, not 180 out of 1,200.

Drill 13 more on finding a missing discount or the bill

Concept 3 of 3: Comparing schemes and free-item offers

To compare schemes that look different (two discounts, one discount, free items), turn every one into the same number: the share of the price the buyer actually pays. The smallest share is the biggest discount and the lowest price.

Definition

Buy x, get y free: the buyer pays for x and takes away $x + y$ , so the discount is $\frac{y}{x + y}$ .
'Buy 3 for the price of 2' gives one free in every three: a discount of $\frac{1}{3}$ .
For successive schemes, compare the products of the kept factors.
Read the question's direction: the lowest selling price has the largest discount, and the highest selling price has the smallest.
Free items given away by the seller still cost him money, so in a profit question count them in the cost but not in the sales.

Discount from free items

\text{buy } x \text{ get } y \text{ free: discount} = \frac{y}{x + y} \times 100\%

Worked example

Which is better for a buyer: 'buy 4, get 1 free' or a single discount of 22%?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 20 Jul 2023, Shift 2 · Q75Moderate

Example 3 · Percentage, Profit and Loss · Successive Discounts and Offers

A shopkeeper offers three schemes as given below to sell a particular type of product. Which of the following schemes offer(s) the maximum discount percentage? A.Buy 6, get 4 free B.Buy 5, get 5 free C. Two successive discounts of 18% and 24%

Dividing the free items by the items paid for

'Buy 5, get 2 free' is a discount of

\frac{2}{7}

, about 28.6%, because the buyer takes away 7 items. Dividing 2 by 5 gives 40%, which is wrong.

Answering the opposite of the question

A question that asks under which scheme the selling price is highest wants the scheme with the smallest discount, not the largest.

Drill 13 more on comparing schemes and free-item offers

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Single discount equal to successive discounts
Equal single discount
$D = a + b - \frac{ab}{100}$
Finding a missing discount or the bill
Bill from the gap between two schemes
$\text{bill} = \frac{\text{rupee gap}}{(D - D_{eq}) / 100}$
Comparing schemes and free-item offers
Discount from free items
$\text{buy } x \text{ get } y \text{ free: discount} = \frac{y}{x + y} \times 100\%$

Watch out for (5)

Adding successive discounts
→ Single discount equal to successive discounts
Giving the share paid as the discount
→ Single discount equal to successive discounts
Taking the second discount on the marked price
→ Finding a missing discount or the bill
Dividing the free items by the items paid for
→ Comparing schemes and free-item offers
Answering the opposite of the question
→ Comparing schemes and free-item offers

Test yourself on Percentage, Profit and Loss

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Percentage, Profit and Loss chapter test Drill all 54 questions