Question

In a sale, a shopkeeper reduced the advertised selling price of a dress by 20%. This resulted in a profit of 4% over the cost price of the dress. What percentage profit would the shopkeeper have made if the dress had then been sold at the original selling price?
HELP my dad will kill me if I don't finish this and I'm stuck on this question

Answer 1

Answer:

30% profit

Step-by-step explanation:

The amount by which the shopkeeper reduced the advertised selling price = 20%

The resulting profit over the cost price = 4%

Let x represent the initial advertised selling price, and let y represent the new selling price, and let c represent the cost price, we have;

x - 20% of x = y

x - x × 20/100 = y

0.8·x = y

y = c + 4% of c = 1.04·c

∴ 0.8·x = 1.04·c

x = 1.04·c/0.8 = 1.3·c

x = 1.3·c = c + 0.3·c = c + 30% of c

x = c + 30% of c

From which we have that the initial advertised selling price, x = The cost price + 30% of the  cost price

Therefore, the initial advertised selling price = The cost price + 30%profit on   cost price.

The shopkeeper would have made 30% profit if the dress had then been sold at the original selling price.