Do They Cancel Each Other Out?

Relevant wiki: Percentage Change

Let $\$x$ be the price of an item. Increasing the price of an item by $50\%$ means that the new price of the item is:

$\$(1+\frac{50}{100})x = \$1.5x$

Decreasing this new price by $50\%$ will give the final price of this item as:

$\$1.5(1-\frac{50}{100})x = \$0.75x < \$x$

Thus, it is seen that increasing the price of an item by $50\%$ and then decreasing it by $50\%$ will reduce the initial price of that item.

Relevant wiki: Percentage Change

100% times ( 100 + 50 )% = 150%

150% times 50% = 75%

Therefore the price decreases.

Lets say that the price is 50$. You increase it by 50% which is with 25$. You get 75$. 50% of 75 is 37,5. 75 - 37,5 = 37,5. The original price was 50$ and after increased with 50% and then decreased with 50% you get 37,5$. The price decreased.

Logical solution

If you increase something by x% and then decrease by x% then you decreased more amount than you increased as x% of the new number will be greater.