MathematicsIf there are 527 apples, 646 pears, and 748 oranges and these are to be arranged in heaps containing the same number of fruits, then the total numbers of apples, pears, and oranges possible in each heap are respectively

If there are 527 apples, 646 pears, and 748 oranges and these are to be arranged in heaps containing the same number of fruits, then the total numbers of apples, pears, and oranges possible in each heap are respectively


  1. A
    31, 38, 44
  2. B
    33, 38, 44
  3. C
    31, 36, 44
  4. D
    31, 32, 44 

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    Solution:

    We have given the total number of apples = 527.
    The total number of pears = 646.
    The total number of oranges = 748.
    Therefore, the total number of heaps to be formed is given by HCF of 527, 646, and 748.
    Finding the prime factorization of 527, 646, and 748:
    527=17×31 646=2×17×19 748=2×2×17×11
    Therefore, the HCF of 527, 646, and 748 = 17.
    Hence, the total number of heaps formed is 17.
    The number of apples in each heap is,
    = 527 17 =31
    The number of pears in each heap is,
    = 646 17 =38
    The number of oranges in each heap is,
    = 748 17 =44
    Therefore, the total numbers of apples, pears, and oranges possible in each heap are respectively 31, 38, and 44.
    Hence option (1) is correct.
     
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