Question 772766
Let the age of the eldest child be E yrs.
Let the age of the middle child be M yrs.
Let the age of the youngest child be Y yrs.
Therefore according to the problem 
    Condition 1      E - M = 2 or M = E - 2 -------------(1)
    Condition 2      E - Y = 4 or Y = E - 4 -------------(2)
    Condition 3      E + M + Y = 51 ---------------------(3)
    Substituting the values of M and Y from equations 1 and 2 in 3 we get 
                     E + (E - 2) + (E - 4) = 51
                  or E + E - 2 + E - 4 = 51
                  or 3E - 6 = 51
                  or 3E = 51 + 6 = 57
                  or E = 57/3 = 19
                  So M = E - 2 = 19 - 2 = 17
                  Also Y = E - 4 = 19 - 4 =15

Hence the ages of the three children are respectively 19yrs, 17yrs, 15yrs.