Let that number is x

So, x + 13 7/8 = 29 5/24

=> x + 111/8 = 701/24

=> x = 701/24 - 111/8

=> x = (701 - 111*3)/24     {LCM of 8 and 24 is 24}

=> x = (701 - 333)/24

=> x = 368/24

=> x = 46/3                      {368 and 24 is divided by 8} 

=> x = 15 1/3

So, the number added is 15 1/3