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    Question

    (y+15) men can do a piece of work in (z-30) days. (y-15) men can do the same piece of work in (z+45) days. If (y+25) men can do the same work in (z-45) days, then find out the values of ‘y’ and ‘z’.

    A 60, 240 Correct Answer Incorrect Answer
    B 80, 200 Correct Answer Incorrect Answer
    C 75, 180 Correct Answer Incorrect Answer
    D 105, 120 Correct Answer Incorrect Answer
    E Cannot be determined Correct Answer Incorrect Answer

    Solution

    (y+15) men can do a piece of work in (z-30) days.

    Total work = Men_1 x Days_1

    = (y+15)x(z-30)    Eq.(i)

    (y-15) men can do the same piece of work in (z+45) days.

    Total work = Men_2 x Days_2

    = (y-15)x(z+45)    Eq.(ii)

    If (y+25) men can do the same work in (z-45) days.

    Total work = Men_3 x Days_3

    = (y+25)x(z-45)    Eq.(iii)

    So Eq.(i) = Eq.(ii).

    (y+15)x(z-30) = (y-15)x(z+45)

    yz-30y+15z-450 = yz+45y-15z-675

    -30y+15z-450 = 45y-15z-675

    45y-15z-675+30y-15z+450 = 0

    75y-30z = 675-450

    75y-30z = 225

    5y-2z = 15    Eq.(iv)

    So Eq.(i) = Eq.(iii).

    (y+15)x(z-30) = (y+25)x(z-45)

    yz-30y+15z-450 = yz-45y+25z-1125

    -30y+15z-450 = -45y+25z-1125

    45y-25z+1125-30y+15z-450 = 0

    15y-10z+675 = 0

    3y-2z = -135    Eq.(v)

    So Eq.(iv)-Eq.(v).

    5y-2z-(3y-2z) = 15-(-135)

    5y-2z-3y+2z = 15+135

    2y = 150

    y = 75

    Put the value of ‘y’ in Eq.(v)

    3x75-2z = -135

    225-2z = -135

    225+135 = 2z

    2z = 360

    z = 180

    So the values of ‘y’ and ‘z’ are 75 and 180 respectively.

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