An office opens at $10 a . m .$ and closes at $6 : 30 p . m .$ with a lunch break of $30 m i n u t e s$ . What is the ratio of lunch break to the total period in the office?

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Solution

Finding the ratio
Given, office opens at $= 10 a . m .$
And the office closes at $= 6 : 30 p . m .$
Total hours of office $= 6 : 30 p . m . - 10 a . m .$
$= 8 h o u r 30 m i n u t e s$
Lunch break $= 30 m i n u t e s$
The ratio of lunch break to the total period $= \frac{30 m i n}{8 h 30 m i n}$
$= \frac{30 m i n}{(8 \times 60 + 30) m i n}$ [ $∵ 1 h o u r = 60 m i n$ ]
$= \frac{30 m i n}{510 m i n}$
$= \frac{1}{17}$ [On dividing numerator and denominator by $30$ ]
$= 1 : 17$
Hence, the ratio of lunch break to the total period in the office is $1 : 17$ .

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