# At a shop, when an item is sold at 10% discount on

At a shop, when an item is sold at 10% discount on the label price, the profit is equivalent to 5% of the label price. When it is sold at a 20% discount, then how much is the loss or gain percentage?

A) 10%
B) 15%
C) 7%
D) 5%
E) 8%

Solution: This is a Profit and Loss question, which uses simple percentage formula.
Suppose x is the label price, y is the cost price and z is the profit / loss when the item is sold at 20% discount.

Equation (1)………….Selling price – Cost Price = Profit

Where, selling price = Label price – 10%* Label price

=> 90% * Label price

=> 90%*x

Plugging in values in Equation (1), we get,

Equation (2) ………….90%*x – y = 5% * x

When the item is sold at a 80% discount, the equation becomes,

Equation (3) ………….80%*x – y = z%*x

Solving equations (2) and (3), we get,

X / 10 = (5 – z) *x / 100

Z = - 5 , i.e. 5% loss

A loss of 5% would be incurred, if the item is sold at a 20% discount.

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