Discount Problem

Question

A shopkeeper allows a discount of 10% on the marked price. How much above the cost price must he mark his goods to gain 8%?

I assume cost price to be P. So the shopkeeper must get 1.08P to make a profit of 8%. He allows a discount of 10%. I am told that 90% of marked price is 1.08P because the shopkeeper offers a discount of 10%. Can somebody please explain why 90% of marked price is 1.08P?

marked up price $ \times (1 - 0.01) = 1.08 , \times ,$ actual cost. — Math Lover, Dec 09 '20 at 11:20
LHS is the final price the customer pays. RHS is the the price the shopkeeper should finally get to make $8%$ profit (over cost). Both are equal as per the question. — Math Lover, Dec 09 '20 at 11:23

score 1 · Answer 1 · answered Dec 09 '20 at 21:29

To flesh out Math Lover's brief description:

Let $M$ be the marked price of the prpoduct and $P$ be the cost price. As you've noted, the shopkeeper wants to get at least $1.08\cdot P$ from the sale.

Because of the $10\%$ discount, the amount the shopkeeper will get from the sale is $0.9\cdot M$.

So for the shopkeeper to get the amount they want, these two need to be equal: $$0.9\cdot M = 1.08 \cdot P$$ Solving for $M$, $$M = \dfrac{1.08}{0.9}P$$

Discount Problem

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