Question

If the cost of an item increased by a percentage and decreased by the same percentage, what would that percentage be if the new cost was 84% of the original?

Answer 1

The percentage, if the new cost was 84% of the original is 40%

Let the cost of the item be x.

When the price increased by y%, the new price is:

$New =x \times (1 + y\%)$

When the price decreased by the same percentage (i.e. y%), the new price is:

$New =x \times (1 + y\%) \times (1 - y\%)$

The cost is said to be 84% of the original price.

So, we have:

$x \times (1 + y\%) \times (1 - y\%) =84\% \times x$

Divide both sides by x

$(1 + y\%) \times (1 - y\%) =84\%$

Apply the difference of two squares

$1 - (y\%)^2 =84\%$

Subtract 1 from both sides of the equation

$- (y\%)^2 =-16\%$

Cancel out the common factors

$(y\%)^2 =16\%$

Take the square root of both sides

$y\% =0.4$

Multiply both sides by 100

$y =40$

Hence, the percentage is 40%

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