Jaidev takes $ 2 \frac{1}{5} $ minutes to walk across the school ground. Rahul takes $ \frac{7}{4} $ minutes to do the same. Who takes less time and by what fraction?
Given:
Jaidev takes \( 2 \frac{1}{5} \) minutes to walk across the school ground. Rahul takes \( \frac{7}{4} \) minutes to do the same.
To do:
We have to the find who takes less time and by what fraction.
Solution:
Time taken by Jaidev to walk across the school ground $=2\frac{1}{5}$ minutes
$= \frac{2\times5+1}{5}$ minutes
$=\frac{11}{5}$ minutes
Time taken by Rahul to walk across the school ground $= \frac{7}{4}$ minutes
To find who takes less time we have to convert them to like fractions.
LCM of denominators 5 and 4 is 20.
Time taken by Jaidev to walk across the school ground$=\frac{11}{5}$ minutes
$=\frac{11}{5}\times\frac{4}{4}$
$=\frac{11\times4}{5\times4}$
$=\frac{44}{20}$ minutes
Time taken by Rahul to walk across the school ground$=\frac{7}{4}$ minutes
$=\frac{7}{4}\times\frac{5}{5}$
$=\frac{7\times5}{4\times5}$
$=\frac{35}{20}$ minutes
Here,
$\frac{44}{20} > \frac{35}{20}$
This implies,
$\frac{11}{5} > \frac{7}{4}$
Therefore, Rahul takes less time than Jaidev to walk across the school ground
Rahul takes less time than Jaidev to walk across the school ground by,
$\frac{44}{20} - \frac{35}{20}$
$=\frac{44-35}{20}$
$=\frac{9}{20}$ minutes
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