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.

Start with this

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

Worked example

A jacket marked Rs 2,400 is sold at a 15% discount. Selling price?

1. Discount = 15% of 2400 = 360.
   Why: Discount is on the marked price.
2. SP = 2400 - 360 = 2040.

Answer: 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%.

Worked example

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

1. a + b - ab/100 = 20 + 15 - 300/100.
   Why: The second discount is on the reduced price.
2. = 32%.

Answer: 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).

Worked example

A shopkeeper marks goods 40% above cost and gives a 20% discount. Profit %?

1. CP = 100, MP = 140.
   Why: Take 100.
2. SP = 140 × 0.8 = 112.
   Why: Discount on MP.
3. Profit 12%.

Answer: 12%

Worked example

At what % above cost should an item be marked so that after a 10% discount the shop still makes 17% profit?

1. CP = 100, needed SP = 117.
   Why: Profit on CP.
2. MP × 0.9 = 117, so MP = 130.
   Why: SP after discount must be 117.
3. Mark up 30%.

Answer: 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).

Worked example

A shop offers 'buy 3 get 2 free'. What is the effective discount?

1. You take 5 and pay for 3.
2. Free 2 out of 5.
   Why: Discount is over what you receive.
3. 40%.

Answer: 40%

Shortcut: Markup needed for a target profit

Use it when: 'How much above cost should he mark?'

1. MP/CP = (100 + P)/(100 - D).

Markup needed for a target profit: try it

Wants 20% profit after a 25% discount. Mark up by?

1. 120/75 = 1.6.

Answer: 60%

Common mistakes

Your turn medium

Single discount equal to 20%, 10% and 5% successively? (1 d.p.)

1. 1 - 0.8 × 0.9 × 0.95 = 0.316.

Answer: 31.6%

Your turn medium

A trader marks goods 50% above CP and gives discounts of 20% and 10%. Profit %?

1. 1.5 × 0.8 × 0.9 = 1.08.

Answer: 8%

Your turn hard

After a 12% discount a shirt sells for Rs 1,452 at a 10% profit. CP?

1. 1452 / 1.1 = 1320.

Answer: Rs 1,320

Your turn hard

A shop gives 10% off and still makes 17% profit. If it gave no discount, profit % would be?

1. MP/CP = 117/90 = 1.3.

Answer: 30%

Recap

• 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

Now practise

10 questions with full solutions.

Open practice Back to the lesson