Fractions, Decimals and Percentages: Practice Questions

A cake is shared among three friends. Alice takes \( \frac{1}{3} \) of the cake, and Bob takes \( \frac{2}{5} \) of the remaining part of the cake. What percentage of the original cake is left for the third friend?

A shop sells a jacket for \( \$480 \) after applying a discount of \( 20\% \) on its marked price. What was the original marked price of the jacket?<\/p>

In a school, \( 60\% \) of the students are girls. If \( 20\% \) of the girls and \( 10\% \) of the boys wear glasses, what percentage of the total students in the school wear glasses?

A student spent \( \frac{1}{4} \) of his monthly allowance on books and \( \frac{2}{5} \) of his allowance on food. What fraction of his monthly allowance is remaining? <\/p>

The price of a book is increased by \( 20\% \) and then decreased by \( 20\% \). What is the net percentage change in the price of the book?

A cake is shared among three friends. Alice takes \(\frac{1}{4}\) of the cake, and Bob takes \(\frac{2}{5}\) of the cake. What fraction of the cake is left for the third friend?

The price of a jacket was originally \(\$500\). During a sale, it is first discounted by \(10\%\). A further \(15\%\) discount is then applied to the already discounted price. What is the final selling price of the jacket?

A shopkeeper increases the price of an item by \( x\% \) and then later decreases the new price by \( x\% \). If the final price is \( 4\% \) less than the original price, find the value of \( x \).