A shopkeeper allows a discount of 20% on the marked price of an item and thus gains 10%. What is the ratio of the cost price to the marked price of the item?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 8 : 11.
Let M be the marked price and C be the cost price
Since the shopkeeper gives a 20% discount on the marked price:
Selling Price (SP) = M - 20/100M
⇒ M - 0.2M = 0.8M
The shopkeeper gains a 10% profit on the cost price,
⇒ SP = C + 10/100C
⇒ C + 0.1C = 1.1C
Since both expressions equal the selling price, we can set them equal to each other
⇒ 0.8M = 1.1C
⇒ C/M = 0.8/1.1
⇒ C/M = 8/11
⇒ C : M = 8 : 11
Thus, the required ratio is 8 : 11