Question

A school has 8 periods a day each of 45 minutes duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same ?

Answer 1

If the school has more periods per day, then the duration would be less.
Hence, the number of periods per day and the duration of each period are in inverse proportion.

Let the duration of each period if there are $9$ periods per day, be $aminutes$

Then, $8:9::$ inverse ratio of $45:a$

$=>8:9=a:45$

Applying the rule, product of extremes $=$ product of means

$8\times 45=9\times a$

$a=\frac{8\times 45}{9}$

$a=40$
Hence, if there are $9$ periods, the duration of each period is $40$ minutes.