# GMAT Quant: Word Problems on Discount

Discounts are the amount which a shopkeeper reduces from his quoted price and sells you the product. Generally, the discounts are calculated on the quoted price or the marked price. Therefore

$Discount \; \% = \frac{Marked \; Price – Selling \; Price}{Marked \; Price} \times 100$

Few other terminologies:

1. Marked price (MP): The initial quoted price
2. Selling price (SP): The Price which you pay after getting discounts.
3. Cost Price (CP): The price at which the shopkeeper purchased the good or the amount that the seller expend to manufacture the good.

1. A shopkeeper even after giving a discount of 20% on the marked price was still able to make a profit of 30%. By what percent is the marked price higher than the cost price?

Let the cost price be x

Selling price = 1.3x

Putting the selling price in the above formula, we get marked price as 1.3x/0.8 = 1.625x

Therefore, the percentage by which the marked price exceeds the cost price is

2. If a merchant sells a good at 80% of the marked price, he makes a loss of 12%. What will be the profit if he sold the good at 95% of the marked price?

Let the marked price be x

SP = 0.8x

CP = 0.8x/0.88 = 0.909x

New SP = 0.95x

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