SSC CGL Maths · Percentage, Profit and Loss

Marked Price and Discount

A discount is taken off the marked price; a trader marks above cost and discounts below the mark, and the profit is what survives both steps.

All Percentage, Profit and Loss notes

Why this matters

81 questions in the bank, the largest page of the chapter, and 42 of them from 2025. 53 are EASY. Almost every one is the chain cost price, then marked price, then selling price, run forwards to find a profit or backwards to find a price, so one equation does most of the work.

Concept 1 of 4: Discount on the marked price

The marked price (MP), also called the list, printed or labelled price, is what the tag says. A discount is a reduction from it, and its percentage is always measured on the marked price unless the question says 'on the discounted price'.

Definition

Discount $= MP - SP$ , and discount % $= \frac{\text{discount}}{MP} \times 100$ .
$SP = MP\left(1 - \frac{d}{100}\right)$ , so $MP = \frac{SP}{1 - d/100}$ .
A flat discount in rupees is simply subtracted; as a percentage it is $\frac{\text{rupees}}{MP} \times 100$ .
Tax such as GST or VAT is charged on the price after discount: amount paid $= MP\left(1 - \frac{d}{100}\right)\left(1 + \frac{t}{100}\right)$ .
Two percentage steps give the same answer in either order, but a flat rupee discount and a percentage discount do not: the order changes the answer.

Selling price after a discount

SP = MP\left(1 - \frac{d}{100}\right) \qquad d\% = \frac{MP - SP}{MP} \times 100

Worked example

A jacket marked ₹2,400 is sold for ₹2,040. Find the discount percentage.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 24 Sep 2025, Shift 3 · Q64Easy

Example 1 · Percentage, Profit and Loss · Marked Price and Discount

A seller gives a

20\%

discount and charges

18\%

GST on the discounted price. On a Rs. 2000 item, how much is payable?

Adding the discount back on the selling price

After a 20% discount the selling price is 0.8 of the marked price, so the marked price is SP divided by 0.8. Multiplying the SP by 1.2 gives too small an answer.

Treating a rupee discount like a percentage

₹500 off and then 7% off a ₹10,000 bill leaves

9500 \times 0.93 = 8835

; 7% off first and then ₹500 off leaves 8,800. Apply them in the order the question gives.

Drill 18 more on discount on the marked price

Concept 2 of 4: Profit after a mark-up and a discount

Marking up multiplies the cost by one factor and the discount multiplies the marked price by another. The profit factor is the product of the two, which is the successive-change rule with the discount as a fall.

Definition

$SP = CP\left(1 + \frac{m}{100}\right)\left(1 - \frac{d}{100}\right)$ .
Profit % $= m - d - \frac{m\,d}{100}$ . A negative answer is a loss.
Fast route: call the cost price 100. Then MP $= 100 + m$ , SP $=$ MP $\times \left(1 - \frac{d}{100}\right)$ , and the profit is SP $- 100$ .
If the cost is given as a share of the marked price (CP is 75% of MP), call the MP 100 instead.
If a selling price is given as a letter (sold at ₹P for a 20% profit), write CP in terms of P first, then follow the new marked price.

Profit after mark-up and discount

\text{profit}\% = m - d - \frac{m\,d}{100}

mmark-up above cost, in per cent
ddiscount on the marked price, in per cent

Worked example

A dealer marks his goods 30% above cost and gives a discount of 10%. Find his profit percentage.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 12 Sep 2025, Shift 3 · Q66Easy

Example 2 · Percentage, Profit and Loss · Marked Price and Discount

A shopkeeper marked an item

25\%

above its cost price. During a sale, he offered a discount of

10\%

. What was his profit percentage?

Subtracting the discount from the mark-up

A 40% mark-up with a 15% discount is a profit of

40 - 15 - 6 = 19\%

, not 25%. The discount is taken on the larger marked price.

Drill 20 more on profit after a mark-up and a discount

Concept 3 of 4: Finding the cost or marked price from the profit

The selling price can be reached from two sides: up from the cost by the profit, or down from the marked price by the discount. Setting the two equal gives one equation that answers almost every 'find the price' question.

Definition

$CP\left(1 + \frac{p}{100}\right) = SP = MP\left(1 - \frac{d}{100}\right)$ .
So $CP : MP = (100 - d) : (100 + p)$ .
Mark-up needed for a profit p after a discount d: $\frac{MP}{CP} = \frac{100 + p}{100 - d}$ .
Discount that gives a profit p from a mark-up m: SP $= 100 + p$ on MP $= 100 + m$ , so $d = \frac{m - p}{100 + m} \times 100$ .
A profit given in rupees is p% of CP, so CP $=$ rupees $\times \frac{100}{p}$ .

The two routes to the selling price

CP\left(1 + \frac{p}{100}\right) = MP\left(1 - \frac{d}{100}\right) \qquad \frac{CP}{MP} = \frac{100 - d}{100 + p}

Worked example

A trader gives a 25% discount and still makes a 20% profit. His cost price is ₹1,000. Find the marked price.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 24 Sep 2025, Shift 1 · Q63Easy

Example 3 · Percentage, Profit and Loss · Marked Price and Discount

A trader gave a

20\%

discount on the market price but still earned a

10\%

profit. What percentage was the market price above the cost price?

Marking up by profit plus discount

To gain 20% after a 25% discount, the marked price must be

\frac{120}{75} = 1.6

times the cost, that is 60% above cost, not 45%.

Taking the discount as a share of the cost

A discount percentage is of the marked price. With CP 100 and MP 140, a discount of 28 rupees is 20%, not 28%.

Drill 31 more on finding the cost or marked price from the profit

Concept 4 of 4: Several stages and fixed rupee amounts

The longest questions chain several steps: a wholesaler's mark-up and trade discount, then a retailer's mark-up and festival discount, a handling fee, a cash discount in rupees. The percentage steps multiply; the rupee amounts do not, so they go into an equation.

Definition

Every percentage step is a factor: a mark-up $1 + \frac{m}{100}$ , a discount $1 - \frac{d}{100}$ , a fee or tax $1 + \frac{f}{100}$ .
Final price $=$ first cost $\times$ all the factors. Divide by their product to go back.
A fixed rupee amount (cash discount, repairs) cannot go into the product. Write an equation: $CP \times \text{factors} - 150 = CP\left(1 + \frac{p}{100}\right)$ .
Read who is paying whom at each step: one trader's selling price is the next trader's cost price.

Price after several stages

\text{final} = C\left(1 + \frac{m_1}{100}\right)\left(1 - \frac{d_1}{100}\right)\left(1 + \frac{m_2}{100}\right)\left(1 - \frac{d_2}{100}\right)

Worked example

A maker sells a lamp to a dealer at a 25% profit. The dealer marks it 40% above his own cost and gives a 10% discount. The customer pays ₹1,575. What did the lamp cost the maker?

Practice this conceptself-check · 2 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 21 Sep 2025, Shift 3 · Q63Moderate

Example 4 · Percentage, Profit and Loss · Marked Price and Discount

A wholesaler sells a packet of tea to a retailer at a profit of 20%. The retailer then marks up the price by 50% and offers a discount of 20% to the customer. If the customer pays Rs. 480, find the cost price of the packet for the wholesaler.

Putting a rupee discount into the product

A cash discount of ₹150 is not a percentage, so it cannot be multiplied in. Finish the percentage steps, then subtract the rupees.

Drill 8 more on several stages and fixed rupee amounts

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 (4)

Discount on the marked price
Selling price after a discount
$SP = MP\left(1 - \frac{d}{100}\right) \qquad d\% = \frac{MP - SP}{MP} \times 100$
Profit after a mark-up and a discount
Profit after mark-up and discount
$\text{profit}\% = m - d - \frac{m\,d}{100}$
Finding the cost or marked price from the profit
The two routes to the selling price
$CP\left(1 + \frac{p}{100}\right) = MP\left(1 - \frac{d}{100}\right) \qquad \frac{CP}{MP} = \frac{100 - d}{100 + p}$
Several stages and fixed rupee amounts
Price after several stages
$\text{final} = C\left(1 + \frac{m_1}{100}\right)\left(1 - \frac{d_1}{100}\right)\left(1 + \frac{m_2}{100}\right)\left(1 - \frac{d_2}{100}\right)$

Watch out for (6)

Adding the discount back on the selling price
→ Discount on the marked price
Treating a rupee discount like a percentage
→ Discount on the marked price
Subtracting the discount from the mark-up
→ Profit after a mark-up and a discount
Marking up by profit plus discount
→ Finding the cost or marked price from the profit
Taking the discount as a share of the cost
→ Finding the cost or marked price from the profit
Putting a rupee discount into the product
→ Several stages and fixed rupee amounts

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.

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