20% loss on selling price is what percent loss on the cost price?

The correct answer is Option (2) → 16.66%

Here the loss is given as a percentage of the selling price, while the question asks for it as a percentage of the cost price. Write both prices in terms of the selling price, then divide the loss by the cost price.

Assuming the selling price to be 100:

• Loss \(=20\%\) of 100 \(=20\)

• Cost price \(=\) selling price \(+\) loss \(=100+20=120\)

• Loss % on cost price \(=\displaystyle\frac{20}{120}\times100=16\frac{2}{3}\%\), that is, 16.66%

Tip: A loss of \(x\%\) of the selling price is \(\displaystyle\frac{100x}{100+x}\%\) of the cost price; a profit of \(x\%\) of the selling price is \(\displaystyle\frac{100x}{100-x}\%\) of the cost price.