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Question

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

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Solution

(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 Tn = 95
⇒ a + (n - 1)d = 95
⇒ 10 + (n - 1) ⨯ ​5 = 95
⇒ 5n = 90
⇒ n = 18

∴ S18 = n2a+l = 182×10+95 = 9×105 = 945

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