Question

How many three digit no. Are divisible by both 3 and 4?

Answer 1

1st 3 digit number divisible by both 3 and 4 = 108

2nd 3 digit number divisible by both 3 and 4 = 120

3rd 3 digit number divisible by both 3 and 4 = 132

last 3 digit number divisible by both 3 and 4 = 996

108,120,132...........996

these numbers are in A.P

by using the formula to find the nth term in an A.P, we can find the answer

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

a=108 , d=120-108=12 ,a(n)=996

996 =108+(n-1)12

996-108=(n-1)12

888=(n-1)12

888÷12= n-1

74=n-1

74+1=n

so n = 75

therefore there are 75 three digit numbers which are divisible by both 3 and 4