Can't give specific date for India but found this :
"Soon it appeared with a cut-out 5-pointed star in the middle of the top leaf , each of the inner and outer points of the star being said to represent one of the then 10 Guide laws, as an extra aid to remembering them."
"In 1932 it was altered again, this time to have a straight stem and stalk rather than a curving one."
"In 1968 it changed once again, now having a much narrower scroll"
So , cut out star , straight stem and wide scroll would date your badge somewhere between 1932 - 1950/51.
https://lesliesguidinghistory.webs.c...misebadges.htm