The ratio of weight of three friends , namely, Aashiqui, Aarohi and Aamrohi is 4 : 9: 7. Their total weight is 100 kilograms. □How much weight would Aamrohi would have put on if the ratio after her weight gain is 4 : 7 : 9 and their collective weight becomes 140 kilograms?

Let the initial weights of Aashiqui, Aarohi and Aamrohi be 4x,9x and 7x respectively.
We are given total initial weight is 100kg.
So,4x+9x+7x=100, which gives x=5.
Initial Weights of Aashiqui, Aarohi and Aamrohi are 20kg,45kg and 35kg respectively.
Let the weights of Aashiqui, Aarohi and Aamrohi be 4y,7y and 9y respectively after Aamrohi weight gain.
So, we are given 4y+7y+9y=140.
We get y=7kg
Aamrohi's weight after weight gain=9y=63kg. 
Aamrohi's weight gain = Final weight - Initial weight = 63kg-35kg = 28kg.
Option A is the answer.