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प्रश्न
How many two-digits numbers are divisible by 3?
संख्यात्मक
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उत्तर
The two-digit numbers divisible by 3 are 12, 15, 18, ..., 99.
Clearly, these number are in AP.
Here, a = 12 and d = 15 – 12 = 3
Let this AP contain n terms. Then,
an = 99
⇒ 12 + (n – 1) × 3 = 99 ...[an = a + (n – 1)d]
⇒ 3n + 9 = 99
⇒ 3n = 99 – 9 = 90
⇒ n = 30
Hence, there are 30 two-digit numbers divisible by 3.
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