Discount
Discount is always on the marked price; profit is always on the cost price. Most questions are just connecting the two with CP = 100.
Why this topic matters
The price on the tag is the marked price. The discount comes off the marked price. Profit is still measured against what the shop paid.
Discount questions combine two percentages on two different bases: discount on the marked price, profit on the cost price. Keep the three prices apart and the rest is arithmetic.
MP, SP and discount
Marked price (MP) or list price: the tag. Discount = MP - SP. Discount % is always on the MP: discount % = discount / MP × 100.
SP = MP × (1 - d/100).
- Discount = 15% of 2400 = 360.Discount is on the marked price.
- SP = 2400 - 360 = 2040.
Successive discounts
'20% + 10% off' is not 30%. The 10% is taken on the price after the first discount.
Single equivalent discount for a% and b% = a + b - ab/100. 20% and 10% → 30 - 2 = 28%.
- a + b - ab/100 = 20 + 15 - 300/100.The second discount is on the reduced price.
- = 32%.
Marked price, discount and profit together
Take CP = 100. Mark up by m%: MP = 100 + m. Give d% discount: SP = MP × (1 - d/100). Profit % = SP - 100.
Or backwards: to make p% profit after a d% discount, mark up so that MP × (1 - d/100) = CP × (1 + p/100).
- CP = 100, MP = 140.Take 100.
- SP = 140 × 0.8 = 112.Discount on MP.
- Profit 12%.
- CP = 100, needed SP = 117.Profit on CP.
- MP × 0.9 = 117, so MP = 130.SP after discount must be 117.
- Mark up 30%.
'Buy × get y free'
Buy 4 get 1 free means you pay for 4 and take 5. Discount = 1/5 = 20% (the free item over the total you take).
- You take 5 and pay for 3.
- Free 2 out of 5.Discount is over what you receive.
- 40%.
Formula summary
Shortcuts and tricks
Markup needed for a target profit
Use it when: 'How much above cost should he mark?'
- MP/CP = (100 + P)/(100 - D).
- 120/75 = 1.6.
Common mistakes
Before you move on, you should be able to...
- take discount on MP and profit on CP
- combine two discounts with a + b - ab/100
- find the mark-up needed for a target profit
Practice questions (10)
Try each one before opening the solution. Or practise them one by one so your score is saved.
easy MP Rs 1,200, successive discounts 20% and 10%. SP?
- 1200 × 0.8 × 0.9.
Answer: Rs 864
easy MP is 40% above CP; a 20% discount is given. Profit %?
- 1.4 × 0.8 = 1.12.
Answer: 12%
easy Buy 4 get 1 free. Effective discount?
- 1/5.
Answer: 20%
medium Single discount equal to 20%, 10% and 5% successively? (1 d.p.)
- 1 - 0.8 × 0.9 × 0.95 = 0.316.
Answer: 31.6%
medium A trader marks goods 50% above CP and gives discounts of 20% and 10%. Profit %?
- 1.5 × 0.8 × 0.9 = 1.08.
Answer: 8%
hard After a 12% discount a shirt sells for Rs 1,452 at a 10% profit. CP?
- 1452 / 1.1 = 1320.
Answer: Rs 1,320
hard A shop gives 10% off and still makes 17% profit. If it gave no discount, profit % would be?
- MP/CP = 117/90 = 1.3.
Answer: 30%
hard What must the MP be above CP so that a 12.5% discount still gives 40% profit?
- 140/87.5 = 1.6.
Answer: 60%
hard Two successive discounts x% and 10% equal a single discount of 28%. x?
- (1 - x/100) × 0.9 = 0.72 → 0.8.
Answer: 20
hard Three successive 10% discounts equal what single discount?
- 1 - 0.93 = 0.271.
Answer: 27.1%
Class plan (2 hours, for trainers)
A tested order for teaching this topic in one 2-hour session. Present mode follows the same order.
| 10 min | Warm-up. |
| 20 min | Three prices: CP, MP, SP on the bar picture. |
| 20 min | Successive discounts. |
| 30 min | Mark-up with discount, both directions. |
| 10 min | Buy × get y free. |
| 25 min | Practice set. |
| 5 min | Recap. |