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Mathematics

Ajay exercised for 36\dfrac{3}{6} of an hour, while Vijay exercised for 34\dfrac{3}{4} of an hour. Who exercised for a longer time and by what fraction of an hour?

Fractions

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Answer

Time for which Ajay exercised = 36\dfrac{3}{6} hour.

Time for which Vijay exercised = 34\dfrac{3}{4} hour.

Compare 36\dfrac{3}{6} and 34\dfrac{3}{4}.

These are unlike fractions with same numerator 3.

In fractions with same numerator, the fraction with smaller denominator is greater.

Since 4 < 6, therefore, 34>36\dfrac{3}{4} \gt \dfrac{3}{6}.

So, Vijay exercised for a longer time.

Difference = 34−36\dfrac{3}{4} - \dfrac{3}{6}

LCM of 4 and 6 = 12.

⇒3×34×3−3×26×2⇒912−612⇒9−612⇒312⇒14 hour\Rightarrow \dfrac{3 \times 3}{4 \times 3} - \dfrac{3 \times 2}{6 \times 2}\\[1em] \Rightarrow \dfrac{9}{12} - \dfrac{6}{12}\\[1em] \Rightarrow \dfrac{9 - 6}{12}\\[1em] \Rightarrow \dfrac{3}{12}\\[1em] \Rightarrow \dfrac{1}{4} \text{ hour}

Hence, Vijay exercised for a longer time by 14\dfrac{1}{4} hour.

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