Find the ratio of the following in the simplest form:
$2 h o u r s 45 m i n u t e s$ to $1 h o u r 15 m i n u t e s$

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Solution

To get the ratio of given term in the simplest form,
Convert the given terms into same unit:
We know that.
$1 h o u r = 60 m i n u t e s$
$2 h o u r s 45 m i n u t e s = (2 \times 60) m i n u t e s + 45 m i n u t e s = 165 m i n u t e s$
Also,
$1 h o u r 15 m i n u t e s = 60 m i n u t e s + 15 m i n u t e s = 75 m i n u t e s$
Therefore, ratio of $2 h o u r s 45 m i n u t e s$ to $1 h o u r 15 m i n u t e s$ $=$ $165 m i n u t e s : 75 m i n u t e s = 165 : 75$
Simplest form of $165 : 75$ can be obtained by dividing both term by their HCF $15$
$165 : 75 = \frac{165}{75} = \frac{11}{5} = 11 : 5$
Hence, ratio of $2 h o u r s 45 m i n u t e s$ to $1 h o u r 15 m i n u t e s$ is $11 : 5$

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