how to solve question (b)?

Question

In a shop, all prices were reduced by 30%. After reduction, a suit was sold at $78.40.

(a) Calculate the selling price of the suit before reduction.

(b) If the selling price before reduction was 28% more than the cost price, calculate the percentage loss made by the shop.

Answer 1

a) 78.40= P - .3P = .7P

P = 78.4/.7 = $112 = original price

b) if selling price before the reduction is 28% more than cost

then at first glance the shop seemingly suffered a loss of 30-28 = 2%.

But that's not accurate.

112 is 28% more than cost

112 = 1.28C

C = 112/1.28 = $87.50 = cost

what cost $87.50 was sold for $78.40, at a loss of 87.5-78.4 = 9.1 = $9.10 loss

loss divided by cost

= 9.10/87.50 = 10.4% loss