MathematicsTwo tankers contain 620 liters and 840 liters of diesel respectively. Find the maximum capacity of a container which can measure the diesel of both the tankers in an exact number of times.

Two tankers contain 620 liters and 840 liters of diesel respectively. Find the maximum capacity of a container which can measure the diesel of both the tankers in an exact number of times.


  1. A
        30 liters
  2. B
        20 liters
  3. C
        56 liters
  4. D
        23 liters 

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    Solution:

    Given,
    The diesel of 620 liters and 840 liters are there in two tankers.
    So, the maximum capacity of a container is the H.C.F of 620 and 840 liters.
    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  .
    Let a=620 and b=840  ,
    Using Euclid division lemma, we get,
    ⇒840=620×1+220  
    ⇒620=220×2+180  
    ⇒220=180×1+40  
    ⇒180=40×4+20  
    ⇒40=20×2+0  
    ⇒H.C.F 840,620 =20  
    Thus, the maximum capacity of a container is 20 liters.
    Therefore, option(2)     is the correct answer.
     
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