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Question
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
Solution
Number divisible by both 2 and 5 are 110, 120, 130,......,990
Here a = 110, d = 120 – 110 = 0
an = 990
⇒ a + (n – 1)d = 990
⇒ 110 + (n – 1)(10) = 990
⇒ (n – 1)(10)
= 990 – 110
= 880
⇒ (n – 1) = `(880)/(10)` = 88
∴ n = 88 + 1
= 89
Hence, number between 101 and 999 which are divisible by both 2 and 5 are 89.
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