Question

Alex takes 2$\frac{1}{5}$ minutes to walk across the school ground. His brother takes $\frac{7}{4}$ minutes to do same. Who takes less time and by what fraction?

• A. Alex's brother takes less time by 2$\frac{9}{20}$ minutes.
• B. Alex's brother takes less time by $\frac{9}{20}$ minutes.
• C. Alex's brother takes less time by $\frac{9}{20}$ minutes.
• D. Alex takes less time by 2$\frac{9}{20}$ minutes.

Answer 1

The correct option is B Alex's brother takes less time by $\frac{9}{20}$ minutes.

As per the question

Time taken by Alex to walk across the school ground = 2$\frac{1}{5}$ minutes = $\frac{11}{5}$ minutes

Time taken by Alex's brother to walk across the school ground = $\frac{7}{4}$ minutes

The LCM of 5 and 4 is 20.

$\therefore \frac{11}{5}=\frac{11\times 4}{5\times 4}=\frac{44}{20}$ and $\frac{7}{4}=\frac{7\times 5}{4\times 5}=\frac{35}{20}$.

Now, $\frac{35}{20}<\frac{44}{20}$.

$\therefore \frac{7}{4}<\frac{11}{5}$

$\Rightarrow$Alex's brother takes less time.

The difference between the time taken by Alex and Alex's brother to walk across the school ground = $\frac{11}{5}-\frac{7}{4}=\frac{11\times 4-7\times 5}{5\times 4}$

= $\frac{44-35}{20}=\frac{9}{20}$ minutes

Thus, Alex's brother takes $\frac{9}{20}$ minutes less than Alex to walk across the school ground.