Question

Find the number of natural numbers between 103 and 997 which are divisible by 4 and 5 both.

Answer 1

P

The numbers divisible by both 4 and 5 should be divided by

4*5 = 20

so, natural numbers between 103 and 997 divisible by 20 are:

120 , 140 , 160............................... 980 .

here we can see that these numbers are forming an AP whose

first term = a = 120

common difference = d = 140-120 = 20

last term , l = 980

and ,

we have to find

total no. of terms in AP = 'n' = ?

l = a + ( n - 1 ) d

980 = 120 + ( n - 1 ) (20)

980 = 120 + 20 n - 20

980 = 100 + 20 n

980 - 100 = 20 n

180 = 20 n

n = 180 / 20

n = 9

HENCE THERE ARE 9 NATURAL NUMBERS BETWEEN 103 AND 997 WHICH ARE DIVISIBLE BY 4 AND 5 BOTH.