percentage problem

alfat wrote:a pen was sold at 10% loss.if the selling price was $ 6 more,then the seller could have made a pofit of 5%.what was the purchase price of the pen!

Let p denote selling price
Let c denote purchase price (aka cost to seller)

profit = p - c
%profit = (p - c)/c = -0.1

We have two unknowns and need two formulas to solve for those unknowns. Fortunately we are given a hypothetical situation to work with:

%profit (hypothetical) = ((p+6) - c)/c = .05

Solving for p in the first formula, we get:

p = (-.1)*cost+cost = .9c

Plugging this into the second formula yields the following:

(.9c +6 - c)/c = .05

-.1c + 6 = .05c
c = 40

You can also think of this problem in terms these terms

15% of what number is 6? or .15x=6

This is because 5% - -10% = 15%

These types of methods really help with time.

You still get 40 as your answer.