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      Question

      How many numbers between 200 and 1000 are divisible by both

      20 and 30?
      A 30 Correct Answer Incorrect Answer
      B 28 Correct Answer Incorrect Answer
      C 13 Correct Answer Incorrect Answer
      D 20 Correct Answer Incorrect Answer

      Solution

      ATQ,

      A number divisible by both 20 and 30 must be divisible by L.C.M. of 20 and 30 = 60

      We look for numbers divisible by 60 in the given range:

      First term (a) = 60 Γ— 4 = 240

      Common difference (d) = 60

      Last term (L) = 60 Γ— 16 = 960

      Let the number of terms be n.

      Use the A.P. formula:

      a + (n - 1)d = L

      Substitute values:

      240 + (n - 1) Γ— 60 = 960

      β‡’ 240 + 60n - 60 = 960

      β‡’ 60n = 780

      β‡’ n = 780 Γ· 60 = 13

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