Answer

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**Hint:**Here first we will find the total time period for which the office and then convert the number of hours into minutes and then finally find the ratio of the duration of lunch to the total duration for which the office remains open.

**Complete step by step answer:**

It is given that the office opens at 9 a.m. and closes at 5 p.m.

This implies that the office remains open for 8 hours.

Now we know that 1 hour is equal to 60 minutes.

Therefore in order to find the number of minutes in 8 hours, we need to multiply 60 by 8

Hence on multiplying we get:-

\[{\text{Number of minutes in 8hrs}} = 8 \times 60\]

Solving it we get:-

\[{\text{Number of minutes in 8hrs}} = 480{\text{minutes}}\]

Now it is given that the lunch interval is 30 minutes.

We need to find the ratio of lunch intervals to the total period in the office.

Hence, we need to divide the time period of the lunch interval by the total time period of the office.

Hence, on dividing we get:-

\[{\text{ratio}} = \dfrac{{30}}{{480}}\]

Simplifying it we get:-

\[{\text{ratio}} = \dfrac{1}{{16}}\]

This implies lunch interval: total period=1:16

**Therefore, the ratio of lunch interval to the total period in office is 1:16.**

**Note:**

Students should note that in order to find the ratio we need to first make the units of the quantities for which we have to find the ratio the same and then proceed for further steps.

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