Maths ·Class 9 Maths

How many 2-digit numbers are divisible by 3? What is the sum of all these 2-digit numbers? Class 9

RBSEGuide

· Jul 10, 2026 · Reviewed & updated Sep 17, 2026 · 1 min read

Question 1.

Solution:

The two digit numbers divisible by 3 are 12,15,18,..., 99

The list of numbers is an AP with

a = 12, d = 15 - 12 = 3

Let the numbers of terms in this AP be n.

Then t_n = 99

∴ a + (n - 1) d = 99

∴ 12 + (n - 1)3 = 99

∴ 3(n - 1) = 99 - 12

∴ 87 = 30(n - 1)

∴ n - 1 = 29

∴ n = 30

S_n = $\frac{n}{2}$(a + 1)

[result from Aryabhata's Aryabhatiya]

∴ S₃₀ = $\frac{30}{2}$(12 + 99)

∴ S₃₀ = 15 × 111

∴ S₃₀ = 1665

∴ There are 30 two digit numbers divisible by 3 and there sum is 1665.