During a sale, the original price of a garment is lowered by 20%. Beca

One of the ways of solving this question is to assume the original price of the garment as 100 and then apply the corresponding percentages to obtain the final price. Once the final price is calculated, the effective single discount percentage can be obtained.

There is, however, a more efficient method. Since there are two successive discounts given here, applying the successive percentage formula to obtain the single discount is much faster and easier.

If two successive percentage changes of a% and b% are made on a quantity, the effective percentage change due to these two changes is given by the expression (a + b + \(\frac{ab }{ 100}\))%.
Depending on what kind of changes are made (increase / decrease), a and be could be positive or negative.

In the case of this problem, since a discount represents a reduction in price, both the changes are negative. When this happens, one needs to remember that the 3rd term in the successive percentage change expression will be positive – taking it as negative is the most common mistake a lot of test takers make while using this expression to solve the questions

So, a = -20 and b = -10. Substituting these values in the successive percentage change expression, we have,

Effective percentage change = ( - 20 – 10 + \(\frac{200 }{ 100}\)) = ( - 30 + 2) = -28 %.

Note that that negative sign here represents that there has been a NEGATIVE change in the initial value of the commodity we started with – in our case, the original price of the garment.
Since a discount is a reduction in the price, the -28% reduction in the original price of the garment is the same as giving a discount of 28% on the original price.
Therefore, x = 28.

The correct answer option is D.