Question

A treasure is split between 5 explorers equally. Each explorer further divides his share of the treasure into 4 equal parts and pays one of those parts as tax. What fraction of the treasure do the 5 explorers together pay as tax ?

• A. $\frac{1}{20}\text{th of the treasure}$
• B. $\frac{1}{5}\text{th of the treasure}$
• C. $\frac{1}{16}\text{th of the treasure}$
• D. $\frac{1}{4}\text{th of the treasure}$

Answer 1

The correct option is D $\frac{1}{4}\text{th of the treasure}$

We convert each sentence of the question into a mathematical statement:

$\text{Sentence 1:}Atreasureissplitbetween5explorersequally$

$\text{Number of treasures}=1$
$\text{Number of explorers}=5$
$⟹\text{Fraction of the treasure that each}\text{explorer gets}=1÷5=\frac{1}{5}$

$\text{Sentence 2:}Eachexplorerfurtherdivideshisshareofthetreasureinto4equalpartsandpaysoneofthosepartsastax.$

$\text{Share of the treasure that each explorer}\text{gets}=\frac{1}{5}$

$\text{Dividing the share into 4 equal parts}=\frac{1}{5}÷4$

$\text{Calculating}\frac{1}{5}÷4\text{, we get:}$


$\therefore \text{The share of the treasure that}each\text{explorer pays as tax is}\frac{1}{20}$

$\text{Sentence 3:}Whatfractionofthetreasuredothe5explorerstogetherpayastax?$

$\text{Each explorer pays}\frac{1}{20}\text{th of the whole}\text{treasure as tax.}$

$⟹\text{Fraction of the treasure paid as tax}\text{by the 5 explorers together}=5\times \frac{1}{20}$

$\text{Calculating}5\times \frac{1}{20}\text{, we get:}$

$5times\frac{1}{20}=5\times \frac{1}{20}=\frac{5}{20}$

$\text{Now,}\frac{5}{20}=\frac{5÷5}{20÷5}=\frac{1}{4}$

$\therefore \text{The 5 explorers together pay}\frac{1}{4}\text{th of}\text{the treasure as tax.}$