The number of boys in a school was 30 more than the number of girls. Subsequently, a few more girls joined the same school. Consequently, the ratio of boys and girls became 3:5. Find the minimum number of girls, who joined subsequently.

Assume that there was at least one girl at the start.

Let the number of girls in the school be G. 
=> Number of boys = G+30.
Some girls joined the class and the number of boys and girls became 3:5. 
Let the number of girls who joined the class be 'X'.
It has been given that (G+30)/(G+X) = 3/5
5G + 150 = 3G + 3X
2G + 150 = 3X
=> X = (2G/3) + 50.
2G has to be divisible by 3. 
Therefore, the least value that G can take is 3. 
When G = 3, X = 2 + 50
X = 52. 
The least number of girls who could have joined is 52. 
Therefore, option E is the right answer.