Maths-
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Easy

Question

A and B can do a piece of work in 40 days while B and C can do it in 60 days. If A is twice as good a workman as C, then C alone will do the work in

  1. 120 days    
  2. 100 days    
  3. 80 days    
  4. 24 days    

hintHint:

The given question is about work and efficiency. A and B can do a work together in 40 days. B and C can do a work together in 60 days. A is twice efficient than C. We have to find the work done by C alone.

The correct answer is: 100 days


    Let the work done by A, B and C per day be denoted as a, b and c respectively.
    A and B does the work in 40 days.
    So, work done by them in 1 day is given by
    a + b = 1 over 40
…(1)
    B and C does the work in 60 days.
    So, work done by them in 1 day is given by
    c + b = 1 over 60 …(2)
    Let the number of days required by A = x
    It is given that A is twice efficient than C
    The number of days required by C = 2x
    So, a = 1 over x
    c = fraction numerator 1 over denominator 2 x end fraction
    We will subtract equation (2) from (1)
    space space space space space space space space space space space a space plus space b space equals space 1 over 40
minus space space space space space space space c space plus space b space equals space 1 over 60
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
space space space space space space space space space space space a space minus space c space equals space 1 over 40 minus 1 over 60
space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 60 space minus space 40 over denominator 2400 end fraction
space space space space space space space space space space space space space space space space space space space space space space space equals 20 over 2400
space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 over 120
space space space space space space space space space space space
    Substituting the values of a and c we get,
    a space minus space c space equals 1 over 120
1 over x minus fraction numerator 1 over denominator 2 x end fraction equals 1 over 120
space space fraction numerator 2 space minus space 1 over denominator 2 x end fraction equals 1 over 120
space space space space space fraction numerator 1 over denominator 2 x end fraction space equals 1 over 120
    So, 2x = 120
    So, the days required by C are 120 days.

    For such questions, we should know the concept of work and efficiency.

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