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Option 3 : 15th February

According to Sumitra,

Mother’s Birthday = After 13th February - Before 16th February = Either on 14th February or on 15th February

According to Sumitra’s Brother,

Mother’s Birthday = After 14th February - Before 17th February = Either on 15th February or on 16th February

So, the only common date in both statements = 15th February

Thus, Sumitra's mother's birthday will be celebrated on 15th February.
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