Question

How many numbers between $1$ and $200$ are multiples of $5$ and are divisible by $3$?

• A. $100$
• B. $50$
• C. $95$
• D. $93$

Answer 1

The correct option is D $93$

Number divisible by $5$ are $5,10,\mathrm{15.....200}$

Here, $a=5,d=5$ and $a_n=200$

$a_n=a+(n-1)d$

$\Rightarrow$ $200=5+(n-1)5$

$\Rightarrow$ $195=5n-5$

$\Rightarrow$ $200=5n$

$\therefore$ $n=40$

Now,

Number divisible by $3$ are $3,6,\mathrm{9...198}$

Here, $a=3,d=3$ and $a_n=198$

$a_n=a+(n-1)d$

$\Rightarrow$ $198=3+(n-1)3$

$\Rightarrow$ $195=3n-3$

$\Rightarrow$ $198=3n$

$\therefore$ $n=66$

Number divisible by $15$ are $15,\mathrm{30....195}$

Here, $a=15,d=15$ and $a_n=195$

$a_n=a+(n-1)d$

$\Rightarrow$ $195=15+(n-1)15$

$\Rightarrow$ $195=15n$

$\therefore$ $n=13$

$\Rightarrow$ Numbers between $1$ and $200$ which is multiple of $5$ and divisible by $3$ $=40+66-13$

$=93$