MathematicsSita takes 35 seconds to pack and label a box. For Ram, the same job takes 42 seconds and for Garima, it takes 28 seconds. If they all start using labeling machines at the same time, after how many seconds will they be using the labeled machines together?

Sita takes 35 seconds to pack and label a box. For Ram, the same job takes 42 seconds and for Garima, it takes 28 seconds. If they all start using labeling machines at the same time, after how many seconds will they be using the labeled machines together?


  1. A
    After 120 seconds
  2. B
    After 220 seconds
  3. C
    After 320 seconds
  4. D
    After 420 seconds 

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    Solution:

    Given that,
    Time taken by Sita to pack and label a box = 35 seconds.
    Time taken by Ram to pack and label a box = 42 seconds.
    Time taken by Garima to pack and label a box = 28 seconds.
    To find the time after which they will be using labeled machines together, find the L.C.M. of 35, 42 and 28.
    35=5×7  
    42=2×3×7 28=2×2×7   So
    L.C.M. 35,42,28 = 2 2 × 3 1 ×5×7   ⇒ L.C.M. 35,42,28 =420     Hence, after 420 seconds, they will be using the labeled machines together.
    Therefore, option (4) is correct.
     
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