Chapter 13.2, Problem 39PPSE

Solution

To find: The number that the clock will pass next.

  $5$

Given:

The movement of minute hand is ${128}^{\circ }$ .

Formula used:

1. The total number of degrees in the analog clock is ${360}^{\circ }$ .

Explanation:

Drawing the figure according to the problem helps to visualize the problem statement. And it also gives an idea of how to start solving the problem,

It is understood that the minute hand of analog clock moves ${360}^{\circ }$ in $12$ hours. So, the movement of minute hand in one hour is equivalent to the ${30}^{\circ }$ .

The minute hand of analog clock moves $6$ degree per minute. And according to the problem, it moves ${128}^{\circ }$ . So, the time taken to move ${128}^{\circ }$ degree is,

  $\frac{{128}^{\circ }}{6^{\circ }}\approx 21\text{ min}$

If we consider the minute hand of analog clock lies on $12$ so after $21\text{ min}$ , it will cross the number $4$ . So, the next number must be $5$ .

Conclusion:

Hence, the next number must be $5$ .