Chapter 6.5, Problem 44HP

To determine

To find: By what percent does the store have to increase the price of an item in order to sell it for original amount.

Answer to Problem 44HP

  $33\%$

Explanation of Solution

Given information:

The discount on the original amount of an item = 25%

The new price of the item after the discount is given = Original amount

Explanation:

Consider, the Original amount to be $x$ .

From the given information, the discount is 25%

  $\Rightarrow$ Discount = $0.25\times$ Original amount

  $\Rightarrow$ Discount = $0.25x$

We know that,

Selling price $=$ Original amount $-$ Discount

  $\Rightarrow$ Selling price $=x-0.25x$

  $\Rightarrow$ Selling price $=0.75x$

Now, let the New amount be $y$ .

From the given information, the discount is 25%

  $\Rightarrow$ Discount = $0.25\times$ New amount

  $\Rightarrow$ Discount = $=0.25y$

We know that,

Selling price $=$ Original amount $-$ Discount

  $\Rightarrow$ New Selling price $=y-0.25y$

  $\Rightarrow$ New Selling price $=0.75y$

From the given information,

New Selling price $=$ Original amount

  $\Rightarrow$$0.75y=x$

  $\Rightarrow$$y=\frac{x}{0.75}$

  $\Rightarrow$$y=1.33x$

Therefore, the New amount of the item is $1.33x$

Since the original amount is $x$

Percentage increase of Original amount = $=\frac{New-Original}{Original}\times 100$

  $\Rightarrow$ Percentage increase $=\frac{1.33x-x}{x}\times 100$

  $\Rightarrow$ Percentage increase $=\frac{0.33x}{x}\times 100$

  $\Rightarrow$ Percentage increase $=0.33\times 100$

  $\Rightarrow$ Percentage increase $=33\%$

Therefore, the percentage increase in original amount of the item in order to make it to sell at the original amount is $33\%$