Confused between marked price , selling price , cost price

Question

By selling an article at 20% discount off the marked price , a shop keeper still makes 10% profit on his cost . If cost price is $1200 , calculate the marked price of the article .

I learned that marked price is the "base price" on an item before any discount is given.

From my understanding of the definition, marked price and cost price must be the same then? But it's not the same , so what's the difference ?

Selling price is the price after discount have been given and this price is what people have to pay to buy the item ?

Pls help... Thanks ..

Answer 1

Let S, M and C stand for selling , market and cost prize.

0) C = 1200

1)S = 80% of M, I.e. S = (8/10)M.

2) Profit : 10% of Cost, I.e. P = (1/10) 1200 = 120.

S = C + Profit = 1320, and this gives using 1):

S = (8/10)M = 1320, solve for M:

M = (10/8) 1320 = 13 200/8 = 1650.

Answer 2

$\frac{1200}{80} \times 110=1650$ which is marked price here we add $10$ in $100$ because of $10\%$ profit and reduce $20$ from $100$ because of $20\%$ discount