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# 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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