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Q.

The number of all positive integers with 3 digits which are divisible by 5 are ____.

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Detailed Solution

The number of all positive integers of 3 digits which are divisible by 5 are 180.
We need to find the number of all positive integers of 3 digits which are divisible by 5.
The series of positive integers of three digits divisible by 5 is 100, 102, 110,.....995 which is an A.P. because the common difference is same.
We know that the

n^{th}

term of A.P. is,

a n = a + n − 1 d

.
Now, according to the question,
The first term, a=100.
The common difference, d=5.
The number of terms are n.
Therefore, according to the question,

995 = 100 + n − 1 5 ⇒ 895 = n − 1 5 ⇒ n = 8955 + 1 ⇒ n = 895 + 5 5 ⇒ n = 9005 ⇒ n = 180

Thus, there are 180 three-digit numbers that are divisible by five.

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