The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is

We know that,

Total number of three digit number will be $999-99=900$,

Now,

Number of $3-$ digit number which are divisible by $3$ will be $\left[\frac{900}{3}\right]=300$,

Number of $3-$ digit number which are divisible by $4$ will be $\left[\frac{900}{4}\right]=225$,

Number of $3-$ digit number which are divisible by $3 \& 4$ both will be $\left[\frac{900}{12}\right]=75$,

So , number of $3-$ digit number which are divisible by $3 \text{or} 4$ will be $300+225-75=450$,

Now, number of $3-$ digit number which are divisible by $48$ is $\left[\frac{900}{48}\right]=18$

So, number of $3-$ digit number which are divisible by $3 \text{or} 4 \text{but not} 48$ will be 

$=450-18=432$