Discount and Marked Price questions become much easier when you keep the three main values separate: Cost Price (CP), Marked Price (MP) and Selling Price (SP). A seller may mark an item above its cost, offer a discount on the marked price and still make a profit. The key is to apply each percentage to the correct base.
This guide focuses on the MP-discount-SP chain used in SSC, Banking and Railway exams. You will learn direct and reverse discount calculations, successive discounts, target-profit questions and faster methods for mixed profit-discount problems.
1. Understand MP, SP and Discount
Marked Price (MP) is the displayed or listed price of an item. Selling Price (SP) is the actual amount paid by the customer after discount.
Discount = MP − SP
If MP = ₹1,200 and SP = ₹1,020, the discount amount is ₹180.
2. Discount Percentage Uses MP as the Base
Discount percentage is normally calculated on Marked Price, not Cost Price.
Discount% = Discount ÷ MP × 100
For MP = ₹1,200 and discount = ₹180:
Discount% = 180 ÷ 1,200 × 100 = 15%.
This base rule is important because profit% and loss% normally use CP instead.
3. Find SP from MP and Discount%
If discount is d%, the customer pays (100 − d)% of MP.
SP = MP × (100 − d) ÷ 100
Example: MP = ₹900 and discount = 12%.
SP = 900 × 88 ÷ 100 = ₹792.
Thinking directly in terms of the remaining percentage is usually faster than finding the discount amount separately.
4. Find MP from SP and Discount%
Reverse questions require you to recognise what percentage of MP the final SP represents.
MP = SP × 100 ÷ (100 − d)
Example: SP = ₹680 after a 15% discount. SP is 85% of MP.
MP = 680 × 100 ÷ 85 = ₹800.
Do not add 15% of ₹680 to reverse the discount; the original base was MP.
5. Find Discount% When MP and SP Are Given
First find the discount amount, then compare it with MP.
Example: MP = ₹1,500 and SP = ₹1,200.
Discount = 1,500 − 1,200 = ₹300.
Discount% = 300 ÷ 1,500 × 100 = 20%.
6. Successive Discounts
Two successive discounts should not normally be added directly because the second discount applies to the reduced price.
For discounts a% and b%:
Effective Discount% = a + b − ab/100
Example: 10% and 20% successive discounts:
10 + 20 − (10 × 20)/100 = 28%.
On MP ₹2,000, final SP = 2,000 × 0.90 × 0.80 = ₹1,440.
For more changing-base questions, see Successive Profit and Loss Changes.
7. Discount and Profit in the Same Question
When CP, MP and discount appear together, solve the chain in order:
MP → apply discount → SP → compare SP with CP
Example: CP = ₹1,000, MP = ₹1,500 and discount = 20%.
SP = 1,500 × 80/100 = ₹1,200. Profit = ₹200, so profit% = 200/1,000 × 100 = 20%.
The 20% discount and 20% profit can exist together because their percentage bases are different.
8. Required MP for a Target Profit
A common exam pattern gives CP, desired profit% and discount%, then asks for the required MP.
Example: CP = ₹800. The seller wants 20% profit after giving 20% discount.
Required SP = 800 × 120/100 = ₹960.
After 20% discount, SP is 80% of MP.
MP = 960 × 100/80 = ₹1,200.
The safest order is: target profit first, required SP second, reverse discount last.
9. Find Required Discount for a Target SP
If MP and desired SP are known:
Required Discount% = (MP − SP) ÷ MP × 100
Example: MP = ₹2,400 and the seller wants SP = ₹2,040.
Discount = ₹360, so discount% = 360/2,400 × 100 = 15%.
10. Ratio and Multiplier Shortcuts
Discount percentages can be converted into the percentage that remains:
- 10% discount → SP = 90% of MP → SP:MP = 9:10
- 20% discount → SP = 80% of MP → SP:MP = 4:5
- 25% discount → SP = 75% of MP → SP:MP = 3:4
Example: at 25% discount, SP = ₹900. Since SP:MP = 3:4, MP = 900 × 4/3 = ₹1,200.
For more speed techniques, use Profit and Loss Tricks for Faster Solving.
11. Markup and Discount Together
Sometimes MP is first set above CP and then a discount is offered.
Example: CP = ₹1,000. MP is 25% above CP, so MP = ₹1,250. A 10% discount gives:
SP = 1,250 × 90/100 = ₹1,125.
Profit = ₹125, therefore profit% = 12.5%.
Do not subtract the 10% discount directly from the 25% markup because the two percentages use different bases.
12. Direct CP-MP-Discount-Profit Shortcut
When Marked Price is set above Cost Price and a discount is offered, the full relation can be handled directly.
If MP is m% above CP and discount is d%, then:
SP = CP × (100 + m) × (100 − d) ÷ 10,000
If a profit of p% is required after d% discount, then:
MP ÷ CP = (100 + p) ÷ (100 − d)
Example: CP = ₹1,000, markup = 25% and discount = 10%. SP = ₹1,125, so profit% = 12.5%.
13. No Profit No Loss and Maximum Discount
At no profit no loss, SP = CP. If MP is x% above CP, then:
Maximum Discount% = x ÷ (100 + x) × 100
Example: MP is 60% above CP. Take CP = 100, so MP = 160. To keep SP = 100, maximum discount = 60/160 × 100 = 37.5%.
14. Verified Previous-Year Exam Pattern
An SSC CHSL previous-year question from 26 March 2018, Shift 1 used this exact pattern: MP was 60% above CP and the maximum discount for no profit no loss had to be found. Using CP = 100 and MP = 160 gives 37.5%.
15. Common Discount and Marked Price Mistakes
- Using CP as the discount base: discount% normally uses MP.
- Treating discount as loss: discount compares MP with SP; loss compares CP with SP.
- Adding successive discounts: 10% + 20% gives 28% effective discount, not 30%.
- Reversing discount incorrectly: a 20% discount means SP is 80% of MP.
- Mixing markup and profit: markup relates MP to CP, while actual profit depends on SP and CP.
For a complete error checklist, read Common Profit and Loss Mistakes.
16. Solved Mixed Examples
Example 1: MP = ₹1,600, discount = 25%. SP = 1,600 × 75/100 = ₹1,200.
Example 2: SP = ₹1,080 after 10% discount. MP = 1,080 × 100/90 = ₹1,200.
Example 3: CP = ₹1,200, MP = ₹1,800, discount = 20%. SP = ₹1,440, profit = ₹240, so profit% = 20%.
Example 4: MP = ₹2,500 with successive discounts of 20% and 10%. SP = 2,500 × 0.80 × 0.90 = ₹1,800.
17. Quick Practice Check
- MP = ₹1,250 and discount = 16%. Find SP.
- SP = ₹765 after 15% discount. Find MP.
- MP = ₹2,000 and SP = ₹1,600. Find discount%.
- Find the effective discount for successive discounts of 20% and 15%.
- CP = ₹1,000 and MP = ₹1,500. After 20% discount, find profit%.
- CP = ₹900. Find the MP required for 20% profit after a 10% discount.
Answers: (1) ₹1,050; (2) ₹900; (3) 20%; (4) 32%; (5) 20%; (6) ₹1,200.
18. Exam-Speed Decision Path
- MP + discount% given → multiply by the remaining percentage.
- SP + discount% given → reverse the remaining percentage.
- MP + SP given → find discount amount, then discount%.
- Two discounts → successive multiplier or effective-discount formula.
- CP + MP + discount given → calculate SP first, then profit/loss.
- Target profit + discount given → calculate required SP, then reverse to MP.
If you are unsure which formula to use, revise Profit and Loss Formulas for Exams.
19. Next Step
Discount questions are only one layer of the chapter. Return to the Profit and Loss Master Guide for the complete topic map. If CP, SP and percentage bases are not yet automatic, revise Profit and Loss Basics.
After revision, test mixed concepts in Profit and Loss Practice Set 1.