Two numbers are such that their difference, sum and product are in the ratio 1 : 9 : 60. The larger of the two number will be - 

15

 a - b  :  a + b  :  a \(\times \) b

   1     :      9    :   60

Let a - b = r  ----(i)

    a + b = 9r  ----(ii)

    a \(\times \) b = 60r

From eq. (i), (ii)

a = 5r, b = 4r

a  \(\times \) b = 20r² = 60r

r = 3

Thus, larger of the number will be a i.e. 5r = 15