Question

The sum of all 2-digit numbers divisible by 5 is
(a) 1035
(b) 1245
(c) 1230
(d) 945

Answer 1

(d) 945

The 2-digit numbers divisible by 5 are 10, 15, 20, 25, ..., 95.
This is an AP in which a = 10, d = (15 - 10) = 5.
Let the number of terms be n.
Then T_n = 95
⇒ a + (n - 1)d = 95
⇒ 10 + (n - 1) ⨯ ​5 = 95
⇒ 5n = 90
⇒ n = 18

∴ S₁₈ = $\frac{n}{2}\left(a+l\right)=\left(\frac{18}{2}\right)\times \left(10+95\right)=9\times 105=945$