Question

If a shopkeeper sells a TV at a discount of 42%, he loses 13%. At what discount should he sell the TV to earn a profit of 5%?​

Answer 1

Answer:

The discount if the item is sold at a gain of 5% will be 30%.

Step-by-step explanation:

Let the marked price of the item be x.

If the item is sold at a discount of 42% then the selling price will be :

100% - 42% = 58%

58/100 × x = 0.58x

If it is sold at this price the loss would be 13%.

This means the selling price is 87% of the cost price.

Hence :

87% = 0.58x

100% =?

100/87 × 0.58x = 58/87x

The cost price of the item = 58/87x

If we sell it at a profit of 5% the selling price will be 105% of the cost price.

This is = 105/100 × 58/87x = 7/10x

The marked price = x

The selling price = 7/10x

The discount = marked price - selling price

= x - 7/10x = 3/10x

3/10x × 1/x × 100% = 3/10 × 100% = 30%

The discount is therefore 30%.