MathematicsA fruit vendor has 990 apples and 945 oranges. He packs them into baskets. Each basket contains only one of the two fruits, but in equal number. Find the number of fruits to be put in each basket in order to have minimum number of baskets.

A fruit vendor has 990 apples and 945 oranges. He packs them into baskets. Each basket contains only one of the two fruits, but in equal number. Find the number of fruits to be put in each basket in order to have minimum number of baskets.


  1. A
        20
  2. B
        45
  3. C
        56
  4. D
        65 

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    Solution:

    Given,
    The apples are 990.
    The oranges are 945.
    Let a=990   and b=945  ,
    Now as we know,
    Euclid division lemma states that if we have two numbers a and b, then there exist unique integers p   and q which satisfies the condition a=bq+r,0≤r<b  .
    Using Euclid division lemma, we get,
    ⇒990=945×1+45  
    ⇒945=45×21+0  
    ⇒HCF 990,945 =45  
    Thus, the HCF is 45.
    Thus, the required number of fruits in each basket is 45.
    Therefore, option(2)     is correct answer.
     

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