Question

Find the ratio of 30 days to 36 hours.

Answer 1

Hint- Here, we will proceed by converting the given number of days into the equivalent number of hours using the formula that 1 day = 24 hours. Then, we will divide this equivalent number of hours by 36 hours.

Complete step-by-step solution -
We have to find the ratio of 30 days to 36 hours. Here, both the quantities are mentioned in different units. In order to find the required ratio, we will make the units of both of these quantities same.
As we know that one day consists of 24 hours i.e., 1 day = 24 hours
For 30 days, we will multiply 30 with 24 hours i.e., 30 days = 30$ \times $24 = 720 hours
In the above equation, the given number of days are converted into the equivalent number of hours. Clearly, through the above obtained equation we can see that 30 days are equivalent to 720 hours.
Here, we have converted days into hours.
Required ratio is 30 days : 36 hours = $\dfrac{{30{\text{ days}}}}{{{\text{36 hours}}}}$ = $\dfrac{{{\text{720 hours}}}}{{{\text{36 hours}}}} = \dfrac{{720}}{{36}} = \dfrac{{20}}{1}$ = 20:1
So, the ratio of 30 days to 36 hours is reduced to 20:1

Note- In this particular problem, there is one more approach (i.e., converting hours into days) which we can use to obtain the required ratio. Here, we can also convert 36 hours into days. Since, 1 hour = $\dfrac{1}{{24}}$ days which means 36 hours = $36 \times \dfrac{1}{{24}} = \dfrac{{36}}{{24}} = \dfrac{3}{2}$ days. So, the required ratio is 30 days : 36 hours = $\dfrac{{30{\text{ days}}}}{{{\text{36 hours}}}}$ = $\dfrac{{{\text{30 days}}}}{{\dfrac{3}{2}{\text{ days}}}} = \dfrac{{30 \times 2}}{3} = \dfrac{{20}}{1}$ = 20:1 which is same as obtained before.