Question

How many three digit number are divisible by both 2 and 5

Answer 1

A.P. 110,120,130,.....,990

a = 110 , d = 120-110 = 10

an = a+(n-1)d

990 = 110 +(n-1)10

880/10 = n-1

n = 88+1

n = 89

so answer there are 89 numbers which are divisible by both 2&5

Answer 2

The Total Number Of 3-digit Numbers Divisible By 2 And 5 Is 90.

GIVEN

Numbers 2 and 5.

TO FIND

Total number of 3-digit numbers divisible by the given numbers.

SOLUTION

We can simply solve the above problem as follows-

A number that will be divisible by both 2 and 5 will also be divisible by, 5×2 = 10.

Lowest 3-digit number = 100

The greatest three-digit number = is 999

Lowest 3- digit number exactly divisible by 10 = 100

Greatest 3-digit number is exactly divisible by 10 = 990.

This is an arithmetic progression, represented by the formula -

l = a + (n-1)d

Where,

l = last term in the sequence

a= first term in the sequence (100 in this case)

n = number of terms

d = common difference.

990 = 100+(n-1)10

990 = 100 + 10n - 10

990 = 90 + 10n

990-90 = 10n

900 = 10n

n = 900/10 = 90

Hence, the Total number of 3-digit numbers divisible by 2 and 5 is 90.

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