Question

Two dials O and P have pointers that start from the vertical position as shown. Pointer O rotates counterclockwise at a rate of 5 degrees per second and pointer P rotates clockwise at 9 degrees per second. How many complete revolutions will P have made when O completes 335 complete revolutions?

Answer 1

Hint: In this question the speed of both the pointers are given so first we will total time taken by pointer O to complete 335 revolutions and it is also given that during this time of rotation of the pointer O, the pointer P also rotates at a speed of 9 revolution per second so by using this speed and the total time we will find the total revolutions made by the pointer P.

Complete step-by-step answer:
Given O rotates in anticlockwise direction at speed of 5 degrees per second
Now since we know to complete one revolution the pointer needs to travel 360 degrees, so total time it will take to make one revolution with a speed of 5 degrees per second will be
\[ = \dfrac{{360}}{5} = 72{\text{second}}\]
So the total time taken by pointer O to complete 335 revolutions will be
\[ = 335 \times 72 = 24120\sec \]
Now, since pointer O takes 24120 seconds to complete 335 revolutions so the total number of revolutions made by pointer P which is rotating at 9 degrees per second during that 24120 seconds will be
  \[
\Rightarrow R = 24120 \times 9 \\
   = 217080{\text{ degrees}} \;
 \]
Degrees can be converted into revolutions as:
 \[
\Rightarrow R = \dfrac{{217080}}{{360}} \\
   = 603{\text{ }}revolutions \;
 \]
Hence, the number of revolutions will P have made when O completes 335 complete revolutions is 603 revolutions.
So, the correct answer is “603”.

Note: It is interesting to note here that revolution and degrees are inter related to each other. One complete revolution states that 360 degrees rotation of the object has been done. In other words, to complete one revolution a pointer or an object needs to travel a total of 360 degrees in a circular path since it must need to reach the same point from where it has started.