A shopkeeper bought a pair of shorts for $24. He made a percentage profit of 45% despite selling it at a discount of 20% off the listed price. Calculate the listed price for this pair of shorts. Answer $...

1. Calculate the selling price after a 45% profit on the cost price.

Cost price $= \char36{}24$

Profit $=45\%$ of cost price, so
$\text{Selling price}=145\% \times 24=1.45\times 24=34.80.$

2. Use the discounted selling price to find the original listed price.

A discount of $20\%$ means the selling price is $80\%$ of the listed price.

Let the listed price be $L$.
$0.80L=34.80$
$L=\frac{34.80}{0.80}=43.50.$