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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions1 Mark
MCQ
How many three$-$digit numbers are divisible by $9?$
  • A
    $86$
  • B
    $90$
  • C
    $96$
  • ✓
    $100$
✓

Answer

Correct option: D.
$100$
The two-digit numbers divisible by $9$ start from
$108, 117, 126, 135, ......., 999$
Here,
$a = 108$
$d = 9$
$a_n = a + (n - 1)$
$\Rightarrow 999 = 108 + (n - 1)(9)$
$\Rightarrow 999 = 108 + 9n - 9$
$\Rightarrow 900 = 9n$
$\Rightarrow n = 100$

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