Let the duration of each period, when there are 9 periods a day in the school, be x minutes. The following table is obtained.

Duration of each period (in minutes) | 45 | x |

Number of periods | 8 | 9 |

If there is more number of periods a day in the school, then the duration of each period will be lesser. Hence, this is a case of inverse proportion.

Therefore 45 × 8 = x × 9

x = (45 x 8)/9 = 40

Hence, in this case, the duration of each period will be 40 minutes.