Question

In an office the working hours are 10.30 AM to 5.30 PM and in between 30 minutes are spent on lunch. Find the ratio of office hours to the time spent for lunch.
A. $\dfrac{7}{{30}}$
B. $\dfrac{1}{{14}}$
C. $\dfrac{{14}}{1}$
D. $\dfrac{{30}}{7}$

Answer 1

Hint: The starting time of the office is 10.30 AM (Ante meridiem) is before noon and the ending time of the office is 5.30 PM (Prime meridiem) is after noon. So count the time from 10.30 AM to 5.30 PM in minutes and find the ratio of office hours to the time spent for lunch.

Complete step-by-step answer:
We are given that in an office the working hours are 10.30 AM to 5.30 PM and in between 30 minutes lunch break.
We have to find the ratio of office hours to the time spent for lunch.
Office starts at 10.30 AM and ends at 5.30 PM.
So from 10.30 AM to 12.00 PM, we have 1 hour and 30 minutes and from 12.00 PM to 5.30 PM we have 5 hours and 30 minutes. So the total time is $\;1hour\; 30\;min + 5\;hours \;30\;min = 7\;hours$
1 hour is equal to 60 minutes, so 7 hours is equal to $7 \times 60 = 420$ minutes.
So the office time is 420 minutes and the lunch break is 30 minutes.
Ratio of office hours to the time spent for lunch is $\dfrac{{420\;min}}{{30\;min}} = \dfrac{{14}}{1}$
So, the correct answer is “14:1”.

Note: As the lunch break is given in minutes, we have to find the office hours in minutes or we can find the office hours in hours and convert the lunch break also into hours. For a ratio of two entities, their units also must be the same.
Another approach
We have 7 hours from 10.30 AM to 5.30 PM.
And 60 minutes make 1 hour, 30 minutes make $\dfrac{1}{2}$ (half) hour.
 Ratio of office hours to the time spent for lunch is $\dfrac{7}{{\left( {\dfrac{1}{2}} \right)}} = \dfrac{{7 \times 2}}{1} = \dfrac{{14}}{1}$