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The Mathematics lesson starts at $11:05$ . The lesson lasts for $75$ minutes. Work out the time that the lesson ends.

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Answer
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Hint: First convert the given minutes in hours and minutes by breaking it in $\left( {60 + x} \right)$ terms.
There are 60 minutes in 1 hour, therefore when the minutes are more than 60 then subtract 60 from the minute and increase 1 hour. After that add the time to the given time.

Complete step-by-step answer:
It is given that the Mathematics lesson starts at $11:05$ and the lesson lasts for 75 minutes.
First, make a conversion of $75$ minutes in hours by breaking it in hours and minutes. We know that $75$ minutes can be broken as $60$ minutes and $15$ minutes. That is,
$75{\text{ minutes}} = 60{\text{minutes}} + 15{\text{minutes}}$
We know that $60$ minutes is equal to one hour, then $75$ minutes can be given as:
 $75{\text{ minutes}} = 1{\text{ hour }}15{\text{ minutes}}$
So, 75 minutes can be expressed in terms of hours and minutes as:
 1 hour and 15 minutes
Now, first add hours in the time when the Mathematics class are started, so add $1{\text{ hour}}$in the given time$11:05$. So the addition is given as:
$11:05 + 1{\text{ hour}} = 12:05$.
Now, add the remaining minutes in the time to get the time when the Mathematics class ends.
$12:05 + 15{\text{ minutes}} = 12:20$
Therefore, when the mathematics class lasts for $75$ min, then the classes of Mathematics ends at $12:20$.

Note: When the hours are greater than 12, it means that the time is expressed in $24$hour format, and in case of 12 hours format, we need to express the time with AM for the first 12 hours and PM for the next 12 hours.