First we find number of men , women and children . So :
6x + 5x + 2x = 39
==> 13x = 39
==> x = 3
Hence number of men , women and children are 18 , 15 and 6 respectively.
According to the question , pay is done according to work done in one day . Now it is given ,
Work done by child in 1 day = 1/3 of woman
Work done by woman in 1 day = 1/2 of man
Hence ,
18 * 6x + 15 * 3x + 6 * 1x = 1113
==> 108 x + 45x + 6x = 1113
==> 159 x = 1113
==> x = 1113 / 159
==> x = 7
Hence required amount to be paid to each child for each day = Rs 7