Question

In an office, the working hours are \[9:30AM - 4:30PM\] and in between \[20\]minutes are spent on lunch. Find the ratio of office hours to the time spent on lunch.
A. \[21:1\]
B. \[1:14\]
C. \[7:30\]
D. \[30:7\]

Answer 1

Hint:We calculate the time period of office hours keeping in mind AM and PM and using the concept of ratio we calculate ratio of office hours to lunch time but we will convert time in the same unit throughout be it minutes be it hours.
* Convert hours into minutes using the conversion \[1\] hour \[ = 60\]minutes.

Complete step-by-step answer:
We are given that working hours in an office are \[9:30AM - 4:30PM\].
Calculating the time period of working hours we get \[7\]hours from \[9:30AM - 4:30PM\].
Therefore, converting time from hours into minutes using the conversion \[1\] hour \[ = 60\]minutes
Since, \[1\] hour \[ = 60\]minutes, multiply \[7\] on both sides of the equation.
\[1 \times 7\]hours \[ = 7 \times 60\] minutes \[ = 420\]minutes
Now we know the ratio of any two numbers is given by their fraction in simplest form which means there is no common factor between both the numbers.
We are given that lunch time in between is \[20\]minutes.
So, the ratio of office hours to lunch time is \[\dfrac{{420}}{{20}}\]
Now we convert the fraction into the simplest form. We can write numerator in the from \[420 = 21 \times 20\]
Therefore, the fraction becomes \[\dfrac{{420}}{{20}} = \dfrac{{20 \times 21}}{{20}}\]
Now we cancel out same terms from numerator and denominator,
\[\dfrac{{21}}{1}\]
Therefore the ratio of working hours to lunch time is \[21:1\].
So, option A is correct.

Note:Many times students make the mistake of leaving the fraction as it is and do not cancel the factors between denominator and numerator which is wrong, ratio should always be in simplest form. Also, when time is not taken in the same units, the answer will come out to be wrong. In this case if the student wrote the ratio of working hours to lunch time as \[7:20\] then it would have been wrong because conversion is not done.