Determining Radhika's Birthday

The problem involves finding a specific date in June based on two sets of conditions provided by Ajay and Sita regarding their mother Radhika's birthday.

Ajay's Birthday Clue

Ajay remembers that Radhika's birthday is:

• After the $5^{\text{th}}$ of June.
• Before the $10^{\text{th}}$ of June.

This means the possible dates according to Ajay are $6^{\text{th}}, 7^{\text{th}}, 8^{\text{th}},$ or $9^{\text{th}}$ of June.

Sita's Birthday Clue

Sita remembers that Radhika's birthday is:

• After the $8^{\text{th}}$ of June.
• Before the $11^{\text{th}}$ of June.

This means the possible dates according to Sita are $9^{\text{th}}$ or $10^{\text{th}}$ of June.

Finding the Exact Date

To find the correct date, we need a day that satisfies both Ajay's and Sita's memories. We look for the common date in both lists of possibilities:

• Ajay's possible dates: {$6, 7, 8, 9$}
• Sita's possible dates: {$9, 10$}

The only date that appears in both lists is the $9^{\text{th}}$ of June.