Question

A period of 4 hours 30 min is what percent of a day?
A) $18\dfrac{3}{4}\% $
B) $20\% $
C) $16\dfrac{2}{3}\% $
D) $19\% $

Answer 1

Hint: Here in this question we will use percent and minute to hour conversion which is mentioned below:-
Percentage ( $\% $ ) = $\dfrac{{a \times 100}}{b}$ where a= Value and b= Total value
1 hour= 60 minutes

Complete step-by-step answer:
Given value of time in question is 4 hours 30 min and the total hours in a day is 24 hours. So we have asked that what percentage is given time is of the total time in a day. Firstly we will convert minute quantity into hour we will get,
As 1 hour = 60 minutes then 30 minutes = $\dfrac{{30}}{{60}} = \dfrac{1}{2}$ hours.
 Therefore 4 hours 30 min = ( $4 + \dfrac{1}{2}$) = $4 + 0.5 = 4.5$ hours
Now required percentage= $(\dfrac{{4.5 \times 100}}{{24}})\% $
Now we will solve the decimal value by placing 10 in the denominator.
$ \Rightarrow (\dfrac{{45 \times 100}}{{10 \times 24}})\% = (\dfrac{{45 \times 10}}{{24}})\% $
 $ \Rightarrow \dfrac{{75}}{4}\% = 18\dfrac{3}{4}\% $
Hence period 4 hours 30 min is $18\dfrac{3}{4}\% $ of a day.

Therefore the correct option is (A).

Note: This question can also be done by converting the given value of period in minutes instead of hours then you will not take total period in day equal to 24 hours rather you will have to take total minutes in a day that will be $24 \times 60 = 1440$ and value of given period in minutes will be
( $4 \times 60 + 30 = 270$ ), so percentage will be given by $(\dfrac{{270}}{{1440}} \times 100)\% = \dfrac{{75}}{4}\% = 18\dfrac{3}{4}\% $
Therefore whichever method is suitable to students they can apply but be very cautious about multiplying 100 because many students make mistakes by dividing 100 instead of multiplying.