Question

How many degrees, minutes and seconds are respectively passed over with 111 minutes by the hour and minute hands of watch?

Answer 1

Hint:-Before solving this question, let us know about the conversion of Degree, Minute and Seconds. Given below is the method:-
1.For the degrees use the whole number part of the decimal.
2.For the conversion of degree to minutes, multiply the remaining decimal by 60. Use the whole number part of the answer as minutes.
3.For the conversion of degree to seconds, multiply the new remaining decimal by 60.
So, we will be using this method for converting degrees into minutes, and then degree into seconds.

Complete step-by-step answer:
Let us now solve the question.
Let us firstly calculate for the Minute hand:
Degrees-So, as we know that in 60 minutes, the minute hand of a watch covers 360 degree
Therefore, in 111 minutes, the minute hand shall cover = \[\dfrac{360}{60}\times \] 111 = 666 degree
So, in 111 minutes, the minute hand will cover 666 degrees, i.e. 666°.
Degrees to minutes -Let us now see how many minutes will the minute hand cover in 111 minutes.
For the conversion of degree to minutes, we shall multiply decimal by 60. So, let us now convert.
We shall multiply 666 degrees with 60.
666° \[\times \] 60 = 39960
So, in 111 minutes, the minute hand will cover 39960 minutes.
Degrees to second- Let us now see how many seconds will the minute hand cover in 111 minutes.
For the conversion of degree to seconds, we shall multiply the decimal by 3600. So, let us now convert.
We shall multiply 666 degrees with 3600.
\[666{}^\circ ~\times 3600\text{ }=\text{ }2397600\]
So, in 111 minutes, the minute hand will cover 2397600 seconds.

Let us firstly calculate for the Hour hand:
Degrees-So, as we know that the hour hand of a clock or watch covers 360 degrees in 720 minutes.
Therefore, in 111 minutes, the hour hand shall cover = \[\left( \dfrac{360}{720} \right)\times \left( 111 \right)\] = 55.5 degree
So, in 111 minutes, the hour hand will cover 55.5 degrees, i.e. 55.5°.

Degrees to minutes-Let us now see how many minutes will the hour hand cover in 111 minutes.
For the conversion of degree to minutes, we shall multiply decimal by 60. So, let us now convert.
We shall multiply 55.5 degrees by 60.
\[55.5{}^\circ ~\times 60\text{ }=\text{ }3330\]
So, in 111 minutes, the hour hand will cover 3330 minutes.
Degrees to seconds-Let us now see how many seconds will the hour hand cover in 111 minutes.
For the conversion of degree to seconds, we shall multiply the decimal by 3600. So, let us now convert.
We shall multiply 55.5 degrees with 3600.
\[55.5{}^\circ ~\times 3600\text{ }=\text{ }199800\]
So, in 111 minutes, the hour hand will cover 199800 seconds.

Note:-The student must know about the method that we use for the conversion of degrees to minutes and seconds.
If the students do not know about these conversion methods, then he/she will not be able to solve such questions.
Also, one must be very careful while doing the calculus part of such questions, as any mistake or error can make the answer wrong.