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    Question

    Vikas and Vishal can do a job in 7 days and 14 days respectively. They began the work together but 4 days before the completion of job, Vikas leaves the work. In how many days will the work be completed?

    A 22/3 days Correct Answer Incorrect Answer
    B 23/3 days Correct Answer Incorrect Answer
    C 41/3 days Correct Answer Incorrect Answer
    D Cannot be determined Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let work be completed in x [if gte msEquation 12]>x [if !msEquation]-->days. Then, work done by Vikas in ( x - 4) days + work done by Vishal in x days = 1 ⇒ [if gte msEquation 12]> x -4 7 [if !msEquation]-->[endif]-->`(x - 4)/7 + x/14 = 1` ⇒ [if gte msEquation 12]> 3x-8 14 [if !msEquation]-->[endif]-->`(3x - 8)/14 = 1` ⇒ 3x – 8 = 14 ⇒ 3 [if gte msEquation 12]> x [if !msEquation]--> x = 22 ⇒ [if gte msEquation 12]>x [if !msEquation]--> x = `22/3` days ∴ Total days = 22/3 days Alternate Method: Vikas Vishal Time taken 7 14 Total work = LCM 14 units 2 : 1 ATQ, Vishal 's work in last 4 days = 1`xx` 4 = 4 units So remainning work = 14 - 4 = 10 units which is completed by Both in = 10/(1+2)=10/3days

    Hence total days = 10/3+4 = 22/3 days

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