Question

William spends 3 out of 8 hours a day studying while Jack studies for 2 out of 5 hours a day. Choose the correct statement:

• A. $\text{Jack studies for}\frac{1}{4}\text{hours}\text{more than William}$
• B. $\text{William studies for}\frac{1}{4}\text{hours}\text{more than Jack}$
• C. $\text{William studies for}\frac{1}{40}\text{hours}\text{more than Jack}$
• D. $\text{Jack studies for}\frac{1}{40}\text{hours}\text{more than William}$

Answer 1

The correct option is D $\text{Jack studies for}\frac{1}{40}\text{hours}\text{more than William}$

William spends 3 out of 8 hours a day studying.

$\text{So, the fraction of hours William spent}\text{on studying is}\frac{3}{8}$

Now the fraction can also be represented as:
$\frac{3}{8}=\frac{3\times 5}{8\times 5}=\frac{15}{40}$

Jack spends 2 out of 5 hours a day studying.

$\text{So, the fraction of hours Jack spent}\text{on studying is}\frac{2}{5}$

Now the fraction can also be represented as:
$\frac{2}{5}=\frac{2\times 8}{5\times 8}=\frac{16}{40}$

$\text{Now, as}16>15,\text{so}\frac{16}{40}>\frac{15}{40}$

$\therefore \text{The difference between the time spent}\text{by each person studying will be:}=(\frac{16}{40}-\frac{15}{40})hours$

$=\frac{(16-15)}{40}hours$

$=\frac{1}{40}hours$

$\therefore \text{Jack studies for}\frac{1}{40}\text{hours more than}\text{William.}$