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Among the subsequent choices, the number of three-digit natural numbers that are divisible by 9 is:

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100

150

125

answer is A.

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Detailed Solution

We have to find the number of three--digit natural numbers that are divisible by 9.
We know that the three-digit numbers that are completely divisible by 3 are-
108, 117, 126,…,999.
The above numbers are in the form of an AP.
So,

a 1 = 108 d = 9 a n = 999

To find the value of n, substitute the known values in the formula,

a n = a + (n − 1) d

a n = 999

108 + (n − 1) × 9 = 999 9 n + 99 = 999 9 n = 999 − 99 9 n = 900

n = 100
There are 100 three-digit numbers that are divisible by 9.
Hence the correct option is 1.

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